Wave propagation in laminated orthotropic circular cylindrical shells
NASA Technical Reports Server (NTRS)
Srinivas, S.
1976-01-01
An exact three-dimensional analysis of wave propagation in laminated orthotropic circular cylindrical-shells is developed. Numerical results are presented for three-ply shells, and for various axial wave lengths, circumferential wave numbers, and thicknesses. Results from a thin shell theory and a refined approximate theory are compared with the exact results.
Buckling of angle-ply laminated circular cylindrical shells
NASA Technical Reports Server (NTRS)
Hirano, Y.
1979-01-01
This note presents closed-form solutions for axisymmetrical and axially unsymmetrical buckling of angle-ply laminated circular cylindrical shells under axial compression. The axisymmetrical and axially unsymmetrical buckling stress are found to be different from each other, and the best lamination angles which give the highest buckling stress are obtained.
Buckling of circular cylindrical shells under dynamically applied axial loads
NASA Technical Reports Server (NTRS)
Tulk, J. D.
1972-01-01
A theoretical and experimental study was made of the buckling characteristics of perfect and imperfect circular cylindrical shells subjected to dynamic axial loading. Experimental data included dynamic buckling loads (124 data points), high speed photographs of buckling mode shapes and observations of the dynamic stability of shells subjected to rapidly applied sub-critical loads. A mathematical model was developed to describe the dynamic behavior of perfect and imperfect shells. This model was based on the Donnell-Von Karman compatibility and equilibrium equations and had a wall deflection function incorporating five separate modes of deflection. Close agreement between theory and experiment was found for both dynamic buckling strength and buckling mode shapes.
Nonobvious features of dynamics of circular cylindrical shells
NASA Astrophysics Data System (ADS)
Leizerovich, G. S.; Taranukha, N. A.
2008-04-01
In the framework of the nonlinear theory of flexible shallow shells, we study free bending vibrations of a thin-walled circular cylindrical shell hinged at the end faces. The finite-dimensional shell model assumes that the excitation of large-amplitude bending vibrations inevitably results in the appearance of radial vibrations of the shell. The modal equations are obtained by the Bubnov-Galerkin method. The periodic solutions are found by the Krylov-Bogolyubov method. We show that if the tangential boundary conditions are satisfied "in the mean," then, for a shell of finite length, significant errors arise in determining its nonlinear dynamic characteristics. We prove that small initial irregularities split the bending frequency spectrum, the basic frequency being smaller than in the case of an ideal shell.
Acoustic radiation from single and double ribbed circular cylindrical shells
NASA Astrophysics Data System (ADS)
Burroughs, C. B.; Hayek, S. I.; Hallander, J. E.; Bostian, D. A.
1984-03-01
Measurements of the acoustic radiation from single and double ribbed circular cylindrical shells were made on the NUSC Transducer Calibration Platform (TCP) in Lake Seneca, NY. Six different types of mechanical drives were used at each of three locations inside the inner shell. Measurements of the shell vibration and acoustic radiation were made with and without outer shells installed around the inner shell structure. For two types of drives, measurements were made with a pressure release layer installed between the inner and outer shell surfaces. Acoustic radiation measurements were made as a function of frequency from 20 to 5,000 Hz and as a function of observation direction at several frequencies for each shell and drive measurement configuration. Measured acoustic radiation data as a function of frequency have been processed. Analysis of the processed data is presented and discussed. It is shown that the location of the drive had a significant effect on the acoustic radiation. The outer shell reduced the acoustic radiation at shell resonant frequencies, but had little effect on other frequencies. The pressure release layer in the double shell had little effect on the acoustic radiation.
Vibrations of cantilevered circular cylindrical shells Shallow versus deep shell theory
NASA Technical Reports Server (NTRS)
Lee, J. K.; Leissa, A. W.; Wang, A. J.
1983-01-01
Free vibrations of cantilevered circular cylindrical shells having rectangular planforms are studied in this paper by means of the Ritz method. The deep shell theory of Novozhilov and Goldenveizer is used and compared with the usual shallow shell theory for a wide range of shell parameters. A thorough convergence study is presented along with comparisons to previously published finite element solutions and experimental results. Accurately computed frequency parameters and mode shapes for various shell configurations are presented. The present paper appears to be the first comprehensive study presenting rigorous comparisons between the two shell theories in dealing with free vibrations of cantilevered cylindrical shells.
Internal resonance of axially moving laminated circular cylindrical shells
NASA Astrophysics Data System (ADS)
Wang, Yan Qing; Liang, Li; Guo, Xing Hui
2013-11-01
The nonlinear vibrations of a thin, elastic, laminated composite circular cylindrical shell, moving in axial direction and having an internal resonance, are investigated in this study. Nonlinearities due to large-amplitude shell motion are considered by using Donnell's nonlinear shallow-shell theory, with consideration of the effect of viscous structure damping. Differently from conventional Donnell's nonlinear shallow-shell equations, an improved nonlinear model without employing Airy stress function is developed to study the nonlinear dynamics of thin shells. The system is discretized by Galerkin's method while a model involving four degrees of freedom, allowing for the traveling wave response of the shell, is adopted. The method of harmonic balance is applied to study the nonlinear dynamic responses of the multi-degrees-of-freedom system. When the structure is excited close to a resonant frequency, very intricate frequency-response curves are obtained, which show strong modal interactions and one-to-one-to-one-to-one internal resonance phenomenon. The effects of different parameters on the complex dynamic response are investigated in this study. The stability of steady-state solutions is also analyzed in detail.
Simplified dispersion curves for circular cylindrical shells using shallow shell theory
NASA Astrophysics Data System (ADS)
Sarkar, Abhijit; Sonti, Venkata R.
2009-04-01
An alternative derivation of the dispersion relation for the transverse vibration of a circular cylindrical shell is presented. The use of the shallow shell theory model leads to a simpler derivation of the same result. Further, the applicability of the dispersion relation is extended to the axisymmetric mode and the high frequency beam mode.
Nonlinear vibrations of fluid-filled clamped circular cylindrical shells
NASA Astrophysics Data System (ADS)
Karagiozis, K. N.; Amabili, M.; Païdoussis, M. P.; Misra, A. K.
2005-12-01
In this study, the nonlinear vibrations are investigated of circular cylindrical shells, empty or fluid-filled, clamped at both ends and subjected to a radial harmonic force excitation. Two different theoretical models are developed. In the first model, the standard form of the Donnell's nonlinear shallow-shell equations is used; in the second, the equations of motion are derived by a variational approach which permits the inclusion of constraining springs at the shell extremities and taking in-plane inertial terms into account. In both cases, the solution includes both driven and companion modes, thus allowing for a travelling wave in the circumferential direction; they also include axisymmetric modes to capture the nonlinear inward shell contraction and the correct type (softening) nonlinear behaviour observed in experiments. In the first model, the clamped beam eigenfunctions are used to describe the axial variations of the shell deformation, automatically satisfying the boundary conditions, leading to a 7 degree-of-freedom (dof) expansion for the solution. In the second model, rotational springs are used at the ends of the shell, which when large enough reproduce a clamped end; the solution involves a sine series for axial variations of the shell deformation, leading to a 54 dof expansion for the solution. In both cases the modal expansions satisfy the boundary conditions and the circumferential continuity condition exactly. The Galerkin method is used to discretize the equations of motion, and AUTO to integrate the discretized equations numerically. When the shells are fluid-filled, the fluid is assumed to be incompressible and inviscid, and the fluid structure interaction is described by linear potential flow theory. The results from the two theoretical models are compared with existing experimental data, and in all cases good qualitative and quantitative agreement is observed.
Free vibration analysis of skewed open circular cylindrical shells
NASA Astrophysics Data System (ADS)
Kandasamy, Selvakumar; Singh, Anand V.
2006-03-01
In this paper, a numerical study is presented for the free vibration of skewed open circular cylindrical deep shells. The formulation considers first-order shear deformation theory of shells and includes rotary inertia and shear deformation so that thin-to-moderately thick shells can be analyzed. A set of grid points, the number of which depends upon the orders of the polynomials chosen for the displacement and rotation components, on the middle surface of the shell is defined first. For a particular displacement component, the field functions are derived corresponding to each node from the above-mentioned set of points and are used in the Rayleigh-Ritz method to calculate frequencies and mode shapes. Convergence study with reference to the order of the polynomials used for the displacement fields was performed first. Numerical results obtained from the present method are compared with those from the finite element method and very good agreement is observed. Additional results are presented and discussed in this paper for skewed panels clamped at the curved edges and free at the straight parallel edges.
NASA Astrophysics Data System (ADS)
Amabili, M.
2003-07-01
Large-amplitude (geometrically non-linear) vibrations of circular cylindrical shells subjected to radial harmonic excitation in the spectral neighbourhood of the lowest resonances are investigated. The Lagrange equations of motion are obtained by an energy approach, retaining damping through Rayleigh's dissipation function. Four different non-linear thin shell theories, namely Donnell's, Sanders-Koiter, Flügge-Lur'e-Byrne and Novozhilov's theories, which neglect rotary inertia and shear deformation, are used to calculate the elastic strain energy. The formulation is also valid for orthotropic and symmetric cross-ply laminated composite shells. The large-amplitude response of perfect and imperfect, simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of the lowest natural frequency is computed for all these shell theories. Numerical responses obtained by using these four non-linear shell theories are also compared to results obtained by using the Donnell's non-linear shallow-shell equation of motion. A validation of calculations by comparison with experimental results is also performed. Both empty and fluid-filled shells are investigated by using a potential fluid model. The effects of radial pressure and axial load are also studied. Boundary conditions for simply supported shells are exactly satisfied. Different expansions involving from 14 to 48 generalized co-ordinates, associated with natural modes of simply supported shells, are used. The non-linear equations of motion are studied by using a code based on an arclength continuation method allowing bifurcation analysis.
Bending Boundary Layers in Laminated-Composite Circular Cylindrical Shells
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.; Smeltzer, Stanley S., III
2000-01-01
An analytical, parametric study of the attenuation of bending boundary layers or edge effects in balanced and unbalanced, symmetrically and unsymmetrically laminated thin cylindrical shells is presented for nine contemporary material systems. The analysis is based on the linear Sanders-Koiter shell equations and specializations to the Love-Kirchhoff shell equations and Donnell's equations are included. Two nondimensional parameters are identified that characterize and quantify the effects of laminate orthotropy and laminate anisotropy on the bending boundary-layer decay length in a very general and encompassing manner. A substantial number of structural design technology results are presented for a wide range of laminated-composite cylinders. For all the laminate constructions considered, the results show that the differences between results that were obtained with the Sanders-Koiter shell equations, the Love-Kirchhoff shell equations, and Donnell's equations are negligible. The results also show that the effect of anisotropy in the form of coupling between pure bending and twisting has a negligible effect on the size of the bending boundary-layer decay length of the balanced, symmetrically laminated cylinders considered. Moreover, the results show that coupling between the various types of shell anisotropies has a negligible effect on the calculation of the bending boundary-layer decay length in most cases. The results also show that in some cases neglecting the shell anisotropy results in underestimating the bending boundary-layer decay length and in other cases it results in an overestimation.
Bending Boundary Layers in Laminated-Composite Circular Cylindrical Shells
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.; Smeltzer, Stanley S., III
2000-01-01
A study of the attenuation of bending boundary layers in balanced and unbalanced, symmetrically and unsymmetrically laminated cylindrical shells is presented for nine contemporary material systems. The analysis is based on the linear Sanders-Koiter shell equations and specializations to the Love-Kirchhoff shell equations and Donnell's equations are included. Two nondimensional parameters are identified that characterize the effects of laminate orthotropy and anisotropy on the bending boundary-layer decay length in a very general manner. A substantial number of structural design technology results are presented for a wide range of laminated-composite cylinders. For all laminates considered, the results show that the differences between results obtained with the Sanders-Koiter shell equations, the Love-Kirchhoff shell equations, and Donnell's equations are negligible. The results also show that the effect of anisotropy in the form of coupling between pure bending and twisting has a negligible effect on the size of the bending boundary-layer decay length of the balanced, symmetrically laminated cylinders considered. Moreover, the results show that coupling between the various types of shell anisotropies has a negligible effect on the calculation of the bending boundary-layer decay length in most cases. The results also show that, in some cases, neglecting the shell anisotropy results in underestimating the bending boundary-layer decay length and, in other cases, results in an overestimation.
Analysis of laminated, composite, circular cylindrical shells with general boundary conditions
NASA Technical Reports Server (NTRS)
Srinivas, S.
1974-01-01
This report develops: (1) a refined approximate theory for the static and dynamic analyses of finite, laminated, composite, circular cylindrical shells with general boundary conditions; (2) an exact three-dimensional analysis of simply supported, laminated, composite, circular cylindrical shells, and (3) a thin-shell theory for laminated, composite, circular cylindrical shells. In the refined approximate theory the displacements are assumed piecewise linear across the thickness and the effects of transverse shear deformations and transverse normal stress are included. A variational approach is followed to obtain the governing differential equations and boundary conditions. A general solution of the governing differential equations is also presented. The results obtained by using the refined approximate theory and the thin-shell theory are compared with the exact results for the case of free vibrations of simply supported, laminated, composite, circular cylindrical shells. The refined approximate theory is very accurate, even for thick shells with short nodal distances, whereas thin-shell theory is reasonably accurate only for thin shells at moderate nodal distances and wave number less than 2.
Buckling of circular cylindrical shells under axial compression.
NASA Technical Reports Server (NTRS)
Budiansky, B.; Hutchinson, J. W.
1972-01-01
The infinitely long cylindrical shell under axial compression with axisymmetric sinusoidal imperfections is considered. The bifurcation problem is formulated exactly, and a complete family of buckling modes is identified. Koiter's (1963) upper bound pertains to the critical stress associated with one restricted set of modes, and the critical stress for a set of long wavelength modes reproduces some numerical results obtained by Almroth (1966). The initial postbuckling analysis is also formulated exactly. An exact analytical solution is obtained for the limiting case of modes with infinitely long wavelengths, and numerical analysis is used to solve the equations for the other cases. An appendix gives the details of the analysis.
Effect of a circular hole on the buckling of cylindrical shells loaded by axial compression.
NASA Technical Reports Server (NTRS)
Starnes, J. H., Jr.
1972-01-01
An experimental and analytical investigation of the effect of a circular hole on the buckling of thin cylindrical shells under axial compression was carried out. The experimental results were obtained from tests performed on seamless electroformed copper shells and Mylar shells with a lap joint seam. These results indicated that the character of the shell buckling was dependent on a parameter which is proportional to the hole radius divided by the square root of the product of the shell radius and thickness. For small values of this parameter, there was no apparent effect of the hole on the buckling load. For slightly larger values of the parameter, the shells still buckled into a general collapse configuration, but the buckling loads were sharply reduced as the parameter increased. For still larger values of the parameter, the buckling loads were further reduced, and the shells buckled into a stable local buckling configuration.
The input mobility of an infinite circular cylindrical elastic shell filled with fluid
NASA Technical Reports Server (NTRS)
Fuller, C. R.
1983-01-01
The force input mobility of an infinite elastic circular cylindrical shell filled with fluid is derived by using the spectral equations of motion. Mobilities are evaluated and their physical interpretations are discussed for a steel shell of thickness h/a = 0.05 filled with water and vibrating in the n = 0, 1 and 2 circumferential modes. The results are subsequently used to analyze the related situations of wave transmission through a radial ring constraint and the far field vibrational energy distributions between the contained fluid and the shell wall for line and point driving forces.
Acoustic Radiation from Single and Double Ribbed Circular Cylindrical Shells.
1984-03-30
Repeatability of Acoustic Radiation Measurements - Single Shell with T- haker Vertical ( =00), Single Radial Drive in Middle of Shell and Phone No. 1...LAYER 0 ~10 U LUU ~-40 -50 0 2-34 FRQENY(kz Fiue3. FreLvlItDieShkrwt n ihu trfa LL.l 0’ Lave -- oube Shll ith hakers orA and inge RaialDr,-.-eon he Ji...FORCE IN SHAKER NO.I ’ HAKER LOCATION - ON THE JOINT B,%ND LONG. DRIVE - OUT OF PH AS E IS THIS THE CORRECT HEADER INFO? Y NORMALIZATION MENU
NASA Astrophysics Data System (ADS)
Yuan, Li-Yun; Xiang, Yu; Lu, Jing; Jiang, Hong-Hua
2015-12-01
Based on the transfer matrix method of exploring the circular cylindrical shell treated with active constrained layer damping (i.e., ACLD), combined with the analytical solution of the Helmholtz equation for a point source, a multi-point multipole virtual source simulation method is for the first time proposed for solving the acoustic radiation problem of a submerged ACLD shell. This approach, wherein some virtual point sources are assumed to be evenly distributed on the axial line of the cylindrical shell, and the sound pressure could be written in the form of the sum of the wave functions series with the undetermined coefficients, is demonstrated to be accurate to achieve the radiation acoustic pressure of the pulsating and oscillating spheres respectively. Meanwhile, this approach is proved to be accurate to obtain the radiation acoustic pressure for a stiffened cylindrical shell. Then, the chosen number of the virtual distributed point sources and truncated number of the wave functions series are discussed to achieve the approximate radiation acoustic pressure of an ACLD cylindrical shell. Applying this method, different radiation acoustic pressures of a submerged ACLD cylindrical shell with different boundary conditions, different thickness values of viscoelastic and piezoelectric layer, different feedback gains for the piezoelectric layer and coverage of ACLD are discussed in detail. Results show that a thicker thickness and larger velocity gain for the piezoelectric layer and larger coverage of the ACLD layer can obtain a better damping effect for the whole structure in general. Whereas, laying a thicker viscoelastic layer is not always a better treatment to achieve a better acoustic characteristic. Project supported by the National Natural Science Foundation of China (Grant Nos. 11162001, 11502056, and 51105083), the Natural Science Foundation of Guangxi Zhuang Autonomous Region, China (Grant No. 2012GXNSFAA053207), the Doctor Foundation of Guangxi
Hydrothermoelastic Stability of Functionally Graded Circular Cylindrical Shells Containing a Fluid
NASA Astrophysics Data System (ADS)
Bochkarev, S. A.; Lekomtsev, S. V.; Matveenko, V. P.
2016-09-01
The thermoelastic and hydroelastic stability of heated circular cylindrical shells made of functionally graded materials and interacting with an internal flow of an ideal compressible fluid was investigated. The effective properties of the material vary across the shell thickness according to a power law and depend on temperature. By way of a mathematical formulation the problem on dynamics the elastic structure, the classical theory of shells and the principle of virtual displacements are used. The radial temperature distribution is determined by solving the one-dimensional heat conduction equation. Behavior of the fluid is described using the potential theory. The corresponding wave equation, together with impermeability and boundary conditions, are transformed to a system of equations with the use of the Bubnov-Galerkin method. The solution of the problem, found by employing a semianalytical version of the finite-element method, is reduced to computing the complex eigenvalues of a coupled system of equations. A comparative analysis of the circular cylindrical shells is carried out at different boundary conditions and for different values of the consistency index of the functionally graded material. The effect of a thermal load on the critical speed of the loss of stability and of flow speed on the thermoelastic stability is estimated. It is shown that a flowing fluid has the greatest effect on the stability boundaries of heated cantilevered shells.
NASA Astrophysics Data System (ADS)
Amabili, M.; Garziera, R.; Carra, S.
2005-12-01
This paper completes a study of Amabili and Garziera [2000, Vibrations of circular cylindrical shells with nonuniform constraints, elastic bed and added mass; Part I: empty and fluid-filled shells. J. Fluids Struct. 14, 669 690; 2002a, Vibrations of circular cylindrical shells with nonuniform constraints, elastic bed and added mass; Part II: shells containing or immersed in axial flow. J. Fluids Struct. 16, 31 51; 2002b, Vibrations of circular cylindrical shells with nonuniform constraints, elastic bed and added mass; Part III: steady viscous effects on shells conveying fluid. J. Fluids Struct. 16, 795 809] by adding the effect of rotary inertia of added masses to the DIVA code, based on the Rayleigh Ritz method and developed to study free vibrations of circular cylindrical shells with nonuniform boundary conditions, added masses, partial elastic bed, initial pre-stress, conveying flow or immersed in axial flow. The effect of rotary inertia has also been evaluated by commercial FEM software and experiments in order to validate the DIVA code. Calculations and experiments show that the effect of rotary inertia of added masses is generally negligible, except for additional local modes; this is in contrast with what has been found for thin plates, due to the geometric stiffness of the circular cylindrical shell.
NASA Astrophysics Data System (ADS)
AMABILI, M.; PELLICANO, F.; PAÏDOUSSIS, M. P.
1999-08-01
The study presented is an investigation of the non-linear dynamics and stability of simply supported, circular cylindrical shells containing inviscid incompressible fluid flow. Non-linearities due to large-amplitude shell motion are considered by using the non-linear Donnell's shallow shell theory, with account taken of the effect of viscous structural damping. Linear potential flow theory is applied to describe the fluid-structure interaction. The system is discretiszd by Galerkin's method, and is investigated by using a model involving seven degrees of freedom, allowing for travelling wave response of the shell and shell axisymmetric contraction. Two different boundary conditions are applied to the fluid flow beyond the shell, corresponding to: (i) infinite baffles (rigid extensions of the shell), and (ii) connection with a flexible wall of infinite extent in the longitudinal direction, permitting solution by separation of variables; they give two different kinds of dynamical behaviour of the system, as a consequence of the fact that axisymmetric contraction, responsible for the softening non-linear dynamical behaviour of shells, is not allowed if the fluid flow beyond the shell is constrained by rigid baffles. Results show that the system loses stability by divergence.
NASA Astrophysics Data System (ADS)
Wang, Y. Q.; Guo, X. H.; Li, Y. G.; Li, J.
2010-03-01
This is a study of nonlinear traveling wave response of a cantilever circular cylindrical shell subjected to a concentrated harmonic force moving in a concentric circular path at a constant velocity. Donnell's shallow-shell theory is used, so that moderately large vibrations are analyzed. The problem is reduced to a system of ordinary differential equations by means of the Galerkin method. Frequency-responses for six different mode expansions are studied and compared with that for single mode to find the more contracted and accurate mode expansion investigating traveling wave vibration. The method of harmonic balance is applied to study the nonlinear dynamic response in forced oscillations of this system. Results obtained with analytical method are compared with numerical simulation, and the agreement between them bespeaks the validity of the method developed in this paper. The stability of the period solutions is also examined in detail.
NASA Technical Reports Server (NTRS)
Ramsey, J. W., Jr.
1975-01-01
The effect on stresses in a cylindrical shell with a circular penetration subject to internal pressure was investigated in thin, shallow linearly, elastic cylindrical shells. Results provide numerical predictions of peak stress concentration factors around nonreinforced and reinforced penetrations in pressurized cylindrical shells. Analytical results were correlated with published formulas, as well as theoretical and experimental results. An accuracy study was made of the finite element program for each of the configurations considered important in pressure vessel technology. A formula is developed to predict the peak stress concentration factor for analysis and/or design in conjunction with the ASME Boiler and Pressure Vessel Code.
On the mechanism of buckling of a circular cylindrical shell under axial compression
NASA Technical Reports Server (NTRS)
Yoshimura, Yoshimaru
1955-01-01
The present paper deals with the buckling of a circular cylindrical shell under axial compression from the viewpoint of energy and the characteristics of deformation. It is shown first, both theoretically and experimentally, that the reason why the buckling of a cylindrical shell is quite different from that of a flat plate is attributable to the existence of a nearly developable surface far apart from the original cylindrical surface. Based upon this result, the experimental fact that the buckling is really not general but local, that is, that the buckled region is limited axially to a range of 1.5 times the wave length of the lobe, is explained by the theoretical result that the minimum buckling load is smaller in the local buckling than in the general buckling case. The occurrence of local buckling is affirmed also from the viewpoint of the energy barrier to be jumped over during buckling, and from a comparison of the theoretical post-buckling state with the experimental results. Finally, the local buckling with the load applied by a spring is analyzed, and it is proved that the minimum buckling load increased with an increase of rigidity of the spring.
NASA Astrophysics Data System (ADS)
Lee, HyunWook; Kwak, Moon K.
2015-09-01
This study uses the Rayleigh-Ritz method to derive a dynamic model for the free vibration analysis of a circular cylindrical shell. In particular, explicit expressions for the mass and stiffness matrices are obtained to easily implement a computer simulation under different shell theories and boundary conditions. The dynamic model is constructed according to the Donnell-Mushtari theory, which is fully discussed herein, and then, dynamic models are constructed by using Sanders theory, Love-Timoshenko theory, Reissner theory, Flügge theory, and Vlasov theory. This paper also discusses the use of eigenfunctions of a uniform beam as admissible functions that produce compact expressions for the mass and stiffness matrices. The numerical results indicate that the Donnell-Mushtari theory is not sufficiently accurate to calculate the natural frequencies and that there is no discernible difference between the other shell theories considered in this study.
Nonlinear response of infinitely long circular cylindrical shells to subharmonic radial loads
NASA Technical Reports Server (NTRS)
Nayfeh, Ali H.; Nayfeh, Jamal F.; Raouf, Raouf A.
1991-01-01
The nonlinear response of infinitely long circular cylindrical shells (thin circular rings) in the presence of a two-to-one internal (autoparametric) resonance to a subharmonic excitation of order one-half of the higher mode is analyzed with the multiple-scale method. Four autonomous first-order ordinary differential equations are derived for the modulation of the amplitudes and phases of the interacting models. These modulation equations are used to determine the fixed points and their stability. The fixed points correspond to periodic oscillations of the shell, whereas the limit-cycle solutions of the modulation equations correspond to amplitude and phase-modulated oscillations of the shell. The force response curves exhibit saturation, jumps, and Hopf bifurcation. As excitation frequency changes, all limit cycles deform and lose stability through either pitchfork or cyclic-fold (saddle-node) bifurcations. Some of these saddle-node bifurcations cause a transition to chaos. The pitchfork bifurcations break the symmetry of the limit cycles.
NASA Astrophysics Data System (ADS)
Sabri, Farhad
circular cylindrical shell or truncated conical shell subjected to internal/external pressure and axial compression loading. This is a typical example of external liquid propellant tanks of space shuttles and re-entry vehicles where they may experience this kind of loading during the flight. In the current work, different end boundary conditions of a circular cylindrical shell with different filling ratios were analyzed. To the best author' knowledge this is the first study where this kind of complex loading and boundary conditions are treated together during such an analysis. Only static instability, divergence, was observed where it showed that the fluid filling ratio does not have any effect on the critical buckling pressure and axial compression. It only reduces the vibration frequencies. It also revealed that the pressurized shell loses its stability at a higher critical axial load. (ii) Aeroelastic analysis of empty or partially liquid filled circular cylindrical and conical shells. Different boundary conditions with different geometries of shells subjected to supersonic air flow are studied here. In all of cases shell loses its stability though the coupled mode flutter. The results showed that internal pressure has a stabilizing effect and increases the critical flutter speed. It is seen that the value of critical dynamic pressure changes rapidly and widely as the filling ratio increases from a low value. In addition, by increasing the length ratio the decrement of flutter speed is decreased and vanishes. This rapid change in critical dynamic pressure at low filling ratios and its almost steady behaviour at large filling ratios indicate that the fluid near the bottom of the shell is largely influenced by elastic deformation when a shell is subjected to external subsonic flow. Based on comparison with the existing numerical, analytical and experimental data and the power of capabilities of this hybrid finite element method to model different boundary conditions and
Nonlinear dynamics and stability of cantilevered circular cylindrical shells conveying fluid
NASA Astrophysics Data System (ADS)
Paak, M.; Païdoussis, M. P.; Misra, A. K.
2013-07-01
In this paper, the nonlinear dynamics of thin circular cylindrical shells with clamped-free boundary conditions subjected to axial internal flow is theoretically analyzed for the first time. The nonlinearity is geometric and is related to the large deformation of the structure. The nonlinear model of the shell is based on the Flügge shell theory; in this model, in-plane inertia terms and all the nonlinear terms due to the mid-surface stretching are retained. The fluid is considered to be inviscid and incompressible, and its modelling is based on linearized potential flow theory. The fluid behaviour beyond the free end of the shell is described by an outflow model, which characterizes the fluid boundary condition at the free end of the shell. At the clamped end, however, it is assumed that the fluid remains unperturbed. The Fourier transform method is used to solve the governing equations for the fluid and to obtain the hydrodynamic forces. The extended Hamilton principle is utilized to formulate the coupled fluid-structure system, and a direct approach is employed to discretize the space domain of the problem. The resulting coupled nonlinear ODEs are integrated numerically, and bifurcation analyses are performed using the AUTO software. Results indicate that the shell loses stability through a supercritical Hopf bifurcation giving rise to a stable periodic motion (limit cycle). The amplitude of this oscillation grows with flow velocity until it loses stability to nonperiodic oscillatory motion, namely, quasiperiodic and chaotic oscillation. The values of the critical flow velocities for various length-to-radius ratios obtained by nonlinear theory agree well with available experimental data.
NASA Astrophysics Data System (ADS)
Bich, Dao Huy; Xuan Nguyen, Nguyen
2012-12-01
In the present work, the study of the nonlinear vibration of a functionally graded cylindrical shell subjected to axial and transverse mechanical loads is presented. Material properties are graded in the thickness direction of the shell according to a simple power law distribution in terms of volume fractions of the material constituents. Governing equations are derived using improved Donnell shell theory ignoring the shallowness of cylindrical shells and kinematic nonlinearity is taken into consideration. One-term approximate solution is assumed to satisfy simply supported boundary conditions. The Galerkin method, the Volmir's assumption and fourth-order Runge-Kutta method are used for dynamical analysis of shells to give explicit expressions of natural frequencies, nonlinear frequency-amplitude relation and nonlinear dynamic responses. Numerical results show the effects of characteristics of functionally graded materials, pre-loaded axial compression and dimensional ratios on the dynamical behavior of shells. The proposed results are validated by comparing with those in the literature.
NASA Astrophysics Data System (ADS)
Liu, Y. Z.; Hao, Y. X.; Zhang, W.; Chen, J.; Li, S. B.
2015-07-01
The nonlinear vibration of a simply supported FGM cylindrical shell with small initial geometric imperfection under complex loads is studied. The effects of radial harmonic excitation, compressive in-plane force combined with supersonic aerodynamic and thermal loads are considered. The small initial geometric imperfection of the cylindrical shell is characterized in the form of the sine-type trigonometric functions. The effective material properties of this FGM cylindrical shell are graded in the radial direction according to a simple power law in terms of the volume fractions. Based on Reddy's third-order shear deformation theory, von Karman-type nonlinear kinematics and Hamilton's principle, the nonlinear partial differential equation that controls the shell dynamics is derived. Both axial symmetric and driven modes of the cylindrical shell deflection pattern are included. Furthermore, the equations of motion can be reduced into a set of coupled nonlinear ordinary differential equations by applying Galerkin's method. In the study of the nonlinear dynamics responses of small initial geometric imperfect FGM cylindrical shell under complex loads, the 4th order Runge-Kutta method is used to obtain time history, phase portraits, bifurcation diagrams and Poincare maps with different parameters. The effects of external loads, geometric imperfections and volume fractions on the nonlinear dynamics of the system are discussed.
NASA Astrophysics Data System (ADS)
GARDONIO, P.; FERGUSON, N. S.; FAHY, F. J.
2001-07-01
This paper covers the development and application of a modal interaction analysis (MIA) to investigate the plane wave transmission characteristics of a circular cylindrical sandwich shell of the type used in the aerospace industry for satellite launch vehicles. The model is capable of handling many high order structural and acoustic modes, and can be used to investigate the sensitivity to different structural stiffness configurations, angles of incidence, damping and cavity absorption. The model has been developed to predict the structural response and transmitted noise when a number of discrete masses are applied to the shell. The study presented considers a set of cases where blocking masses, having a total weight equal to 8% of the cylinder weight, are attached to the cylinder. The simulations carried out show a substantial reduction of the sound transmission in many of the first 15 one-third octave frequency bands (frequency range 22·4-707 Hz). The blocking masses act on the shape of the cylinder normal modes and their orientations with respect to the plane of the incident wavenumber vector. In particular, the circumferential re-orientation reduces the coupling between the incident acoustic field and the structural modes of the cylinder. The modification of the structural mode shapes, both in axial and circumferential directions, also reduces the coupling between the cylinder modes and the acoustic modes of the interior.Simulations show the effect of the number of structural and acoustic modes included on the calculated frequency response, and indicate the number necessary for an accurate prediction of the resonant and non-resonant sound transmission through the structure. In particular, the effect of neglecting off-resonance acoustic and structural modes is investigated. It is shown that restricting the acoustic and structural modes to those having natural frequencies within an interval of ±40 and ±60 Hz, respectively, of the excitation frequency produces
NASA Astrophysics Data System (ADS)
Pellicano, F.; Amabili, M.
2006-05-01
In the present paper the dynamic stability of circular cylindrical shells subjected to static and dynamic axial loads is investigated. Both Donnell's nonlinear shallow shell and Sanders-Koiter shell theories have been applied to model finite-amplitude static and dynamic deformations. Results are compared in order to evaluate the accuracy of these theories in predicting instability onset and post-critical nonlinear response. The effect of a contained fluid on the stability and the post-critical behaviour is analyzed in detail. Geometric imperfections are considered and their influence on the dynamic instability and post-critical behaviour is investigated. Chaotic dynamics of pre-compressed shells is investigated by means of nonlinear time-series techniques, extracting correlation dimension and Lyapunov exponents.
Surface wave conversion analysis on a lengthwise soldered circular cylindrical shell.
Baillard, André; Chiumia, Jeremiah; Décultot, Dominique; Maze, Gérard; Klauson, Aleksander; Metsaveer, Jaan
2008-10-01
This paper deals with wave conversion phenomena through a study of the acoustic scattering from a stiffened cylindrical shell at normal incidence. The analysis presented follows the experimental study which explored the acoustic wave propagation and scattering processes in the case of air-filled submerged cylindrical shells having internal axial solder [J. Chiumia, N. Touraine, D. Decultot, G. Maze, A. Klauson, and J. Metsaveer, J. Acoust. Soc. Am. 105, 183-193 (1999)]. The significant observed phenomena were generation, reflection, and conversion of circumnavigating waves at the solder. The present work confirms the presence of the three phenomena through a theoretical approach based on the elasticity theory. In particular, resonances with new feature whose frequencies are very close to those of the S(0) wave are highlighted here. The origin of this new resonance feature is identified and can be associated to wave type conversions between A(0) and S(0) Lamb waves, occurring when these propagating waves encounter the solder. The air-filled stainless steel studied tube submerged in water has an internal lengthwise solder, which is, in theoretical computations, considered as an internal axial mass layer. The reduced frequency range (k(1)a) of the study is between 25 and 90, (k(1): wave number in water; a: external radius of the shell).
NASA Astrophysics Data System (ADS)
Amabili, M.
2003-05-01
The large-amplitude response of perfect and imperfect, simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of some of the lowest natural frequencies is investigated. Donnell's non-linear shallow-shell theory is used and the solution is obtained by the Galerkin method. Several expansions involving 16 or more natural modes of the shell are used. The boundary conditions on the radial displacement and the continuity of circumferential displacement are exactly satisfied. The effect of internal quiescent, incompressible and inviscid fluid is investigated. The non-linear equations of motion are studied by using a code based on the arclength continuation method. A series of accurate experiments on forced vibrations of an empty and water-filled stainless-steel shell have been performed. Several modes have been intensively investigated for different vibration amplitudes. A closed loop control of the force excitation has been used. The actual geometry of the test shell has been measured and the geometric imperfections have been introduced in the theoretical model. Several interesting non-linear phenomena have been experimentally observed and numerically reproduced, such as softening-type non-linearity, different types of travelling wave response in the proximity of resonances, interaction among modes with different numbers of circumferential waves and amplitude-modulated response. For all the modes investigated, the theoretical and experimental results are in strong agreement.
NASA Technical Reports Server (NTRS)
Mushtari, K. M.; Sachenkov, A. V.
1958-01-01
We consider in this report the determination of the upper limit of critical loads in the case of simultaneous action of a compressive force, uniformly distributed over plane cross sections, and of isotropic external normal pressure on cylindrical or conical shells of circular cross section. As a starting point we use the differential equations for neutral equilibrium of conical shells which have been used for the solution of the problem of stability of conical shells under torsion and under axial compression; upon solution of the problem it is possible to satisfy all boundary conditions, in contrast to the report where no attention is paid to the fulfillment of the boundary conditions, and to the report where only part of the boundary conditions are satisfied by solution of the problem according to Galerkin's method. Approximate formulas are used for the determination of the critical external normal pressure with simultaneous action of longituninal compression. Let us note that the formulas suggested in reference 5 are not well founded and may lead, in a number of cases, to a substantial mistake in the magnitude of the critical load.
NASA Astrophysics Data System (ADS)
Amabili, Marco; Balasubramanian, Prabakaran; Ferrari, Giovanni
2016-10-01
The nonlinear vibrations of a water-filled circular cylindrical shell subjected to radial harmonic excitation in the spectral neighbourhood of the lowest resonances are investigated experimentally and numerically by using a seamless aluminium sample. The experimental boundary conditions are close to simply supported edges. The presence of exact one-to-one internal resonance, giving rise to a travelling wave response around the shell circumference and non-stationary vibrations, is experimentally observed and the nonlinear response is numerically reproduced. The travelling wave is measured by means of state-of-the-art laser Doppler vibrometers applied to multiple points on the structure simultaneously. Chaos is detected in the frequency region where the travelling wave response is present. The reduced-order model is based on the Novozhilov nonlinear shell theory retaining in-plane inertia and the nonlinear equations of motion are numerically studied (i) by using a code based on arclength continuation method that allows bifurcation analysis in case of stationary vibrations, (ii) by a continuation code based on direct integration and Poincaré maps that evaluates also the maximum Lyapunov exponent in case of non-stationary vibrations. The comparison of experimental and numerical results is particularly satisfactory.
NASA Astrophysics Data System (ADS)
Leonov, V. I.
A cylindrical shell is considered which is loaded via a round rigid bracket by a force normal to its middle surface and also by a bending moment relative to the generatrix. The shell is reinforced by an annular patch around the bracket. The stressed state of the shell is analyzed as a function of the geometrical parameters of the reinforcement.
Static cylindrical matter shells
NASA Astrophysics Data System (ADS)
Arık, Metin; Delice, Özgür
2005-08-01
Static cylindrical shells composed of massive particles arising from matching of two different Levi-Civita space-times are studied for the shell satisfying either an isotropic or an anisotropic equation of state. We find that these solutions satisfy the energy conditions for certain ranges of the parameters.
Free vibrations of circular cylindrical shells with a small added concentrated mass
NASA Astrophysics Data System (ADS)
Leizerovich, G. S.; Seregin, S. V.
2016-09-01
The effect of a small added mass on the frequency and shape of free vibrations of a thin shell is studied using shallow shell theory. The proposed mathematical model assumes that mass asymmetry even in a linear formulation leads to coupled radial flexural vibrations. The interaction of shape-generating waves is studied using modal equations obtained by the Bubnov-Galerkin method. Splitting of the flexural frequency spectrum is found, which is caused not only by the added mass but also by the wave-formation parameters of the shell. The ranges of the relative lengths and shell thicknesses are determined in which the interaction of flexural and radial vibrations can be neglected.
NASA Astrophysics Data System (ADS)
AMABILI, M.; PELLICANO, F.; PAÏDOUSSIS, M. P.
2000-11-01
The response of simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of one of the lowest natural frequencies is investigated by using improved mode expansions with respect to those assumed in Parts I and II of the present study. Two cases are studied: (1) shells in vacuo; and (2) shells filled with stagnant water. The improved expansions allow checking the accuracy of the solutions previously obtained and giving definitive results within the limits of Donnell's non-linear shallow-shell theory. The improved mode expansions include: (1) harmonics of the circumferential mode number n under consideration, and (2) only the principal n, but with harmonics of the longitudinal mode included. The effect of additional longitudinal modes is absolutely insignificant in both the driven and companion mode responses. The effect of modes with 2 n circumferential waves is very limited on the trend of non-linearity, but is significant in the response with companion mode participation in the case of lightly damped shells (empty shells). In particular, the travelling wave response appears for much lower vibration amplitudes and presents a frequency range without stable responses, corresponding to a beating phenomenon. A liquid (water) contained in the shell generates a much stronger softening behaviour of the system. Experiments with a water-filled circular cylindrical shell made of steel are in very good agreement with the present theory.
NASA Astrophysics Data System (ADS)
Amabili, M.; Sarkar, A.; Païdoussis, M. P.
2006-03-01
The geometric nonlinear response of a water-filled, simply supported circular cylindrical shell to harmonic excitation in the spectral neighbourhood of the fundamental natural frequency is investigated. The response is investigated for a fixed excitation frequency by using the excitation amplitude as bifurcation parameter for a wide range of variation. Bifurcation diagrams of Poincaré maps obtained from direct time integration and calculation of the Lyapunov exponents and Lyapunov dimension have been used to study the system. By increasing the excitation amplitude, the response undergoes (i) a period-doubling bifurcation, (ii) subharmonic response, (iii) quasi-periodic response and (iv) chaotic behaviour with up to 16 positive Lyapunov exponents (hyperchaos). The model is based on Donnell's nonlinear shallow-shell theory, and the reference solution is obtained by the Galerkin method. The proper orthogonal decomposition (POD) method is used to extract proper orthogonal modes that describe the system behaviour from time-series response data. These time-series have been obtained via the conventional Galerkin approach (using normal modes as a projection basis) with an accurate model involving 16 degrees of freedom (dofs), validated in previous studies. The POD method, in conjunction with the Galerkin approach, permits to build a lower-dimensional model as compared to those obtainable via the conventional Galerkin approach. Periodic and quasi-periodic response around the fundamental resonance for fixed excitation amplitude, can be very successfully simulated with a 3-dof reduced-order model. However, in the case of large variation of the excitation, even a 5-dof reduced-order model is not fully accurate. Results show that the POD methodology is not as "robust" as the Galerkin method.
Estève, Simon J; Johnson, Marty E
2002-12-01
A modal expansion method is used to model a cylindrical enclosure excited by an external plane wave. A set of distributed vibration absorbers (DVAs) and Helmholtz resonators (HRs) are applied to the structure to control the interior acoustic levels. Using an impedance matching method, the structure, the acoustic cavity, and the noise reduction devices are fully coupled to yield an analytical formulation of the structural kinetic energy and acoustic potential energy of a treated cylindrical cavity. Lightweight DVAs and small HRs tuned to the natural frequencies of the targeted structural and acoustic modes, respectively, result in significant acoustic and structural attenuation when the devices are optimally damped. Simulations show that significant interior noise reduction can only be achieved by adding damping to both structural and acoustic modes, which are resonant in the frequency bandwidth of interest. In order to be independent of the azimuth angle of the excitation and to avoid unwanted modal interactions, the devices are distributed evenly around the cylinder in rings. This treatment can only achieve good performance if the structure and the acoustic cavity are lightly damped.
NASA Astrophysics Data System (ADS)
Estève, Simon J.; Johnson, Marty E.
2002-12-01
A modal expansion method is used to model a cylindrical enclosure excited by an external plane wave. A set of distributed vibration absorbers (DVAs) and Helmholtz resonators (HRs) are applied to the structure to control the interior acoustic levels. Using an impedance matching method, the structure, the acoustic cavity, and the noise reduction devices are fully coupled to yield an analytical formulation of the structural kinetic energy and acoustic potential energy of a treated cylindrical cavity. Lightweight DVAs and small HRs tuned to the natural frequencies of the targeted structural and acoustic modes, respectively, result in significant acoustic and structural attenuation when the devices are optimally damped. Simulations show that significant interior noise reduction can only be achieved by adding damping to both structural and acoustic modes, which are resonant in the frequency bandwidth of interest. In order to be independent of the azimuth angle of the excitation and to avoid unwanted modal interactions, the devices are distributed evenly around the cylinder in rings. This treatment can only achieve good performance if the structure and the acoustic cavity are lightly damped.
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.; Schultz, Marc R.
2012-01-01
A detailed exact solution is presented for laminated-composite circular cylinders with general wall construction and that undergo axisymmetric deformations. The overall solution is formulated in a general, systematic way and is based on the solution of a single fourth-order, nonhomogeneous ordinary differential equation with constant coefficients in which the radial displacement is the dependent variable. Moreover, the effects of general anisotropy are included and positive-definiteness of the strain energy is used to define uniquely the form of the basis functions spanning the solution space of the ordinary differential equation. Loading conditions are considered that include axisymmetric edge loads, surface tractions, and temperature fields. Likewise, all possible axisymmetric boundary conditions are considered. Results are presented for five examples that demonstrate a wide range of behavior for specially orthotropic and fully anisotropic cylinders.
NASA Astrophysics Data System (ADS)
AMABILI, M.; PELLICANO, F.; PAÏDOUSSIS, M. P.
1999-12-01
The non-linear response of empty and fluid-filled circular cylindrical shells to harmonic excitations is investigated. Both modal and point excitations have been considered. The model is suitable to study simply supported shells with and without axial constraints. Donnell's non-linear shallow-shell theory is used. The boundary conditions on radial displacement and the continuity of circumferential displacement are exactly satisfied. The radial deflection of the shell is expanded by using a basis of seven linear modes. The effect of internal quiescent, incompressible and inviscid fluid is investigated. The equations of motion, obtained in Part I of this study, are studied by using a code based on the collocation method. The validation of the present model is obtained by comparison with other authoritative results. The effect of the number of axisymmetric modes used in the expansion on the response of the shell is investigated, clarifying questions open for a long time. The results show the occurrence of travelling wave response in the proximity of the resonance frequency, the fundamental role of the first and third axisymmetric modes in the expansion of the radial deflection with one longitudinal half-wave, and limit cycle responses. Modes with two longitudinal half-waves are also investigated.
NASA Astrophysics Data System (ADS)
AMABILI, M.; PELLICANO, F.; PAÏDOUSSIS, M. P.
2000-11-01
The response of a shell conveying fluid to harmonic excitation, in the spectral neighbourhood of one of the lowest natural frequencies, is investigated for different flow velocities. The theoretical model has already been presented in Part I of the present study. Non-linearities due to moderately large-amplitude shell motion are considered by using Donnell's non-linear shallow-shell theory. Linear potential flow theory is applied to describe the fluid-structure interaction by using the model proposed by Paı̈doussis and Denise. For different amplitudes and frequencies of the excitation and for different flow velocities, the following are investigated numerically: (1) periodic response of the system; (2) unsteady and stochastic motion; (3) loss of stability by jumps to bifurcated branches. The effect of the flow velocity on the non-linear periodic response of the system has also been investigated. Poincaré maps and bifurcation diagrams are used to study the unsteady and stochastic dynamics of the system. Amplitude modulated motions, multi-periodic solutions, chaotic responses, cascades of bifurcations as the route to chaos and the so-called “blue sky catastrophe” phenomenon have all been observed for different values of the system parameters; the latter two have been predicted here probably for the first time for the dynamics of circular cylindrical shells.
Plastic buckling of cylindrical shells
Bandyopadhyay, K.; Xu, J.; Shteyngart, S.; Eckert, H.
1994-05-01
Cylindrical shells exhibit buckling under axial loads at stresses much less than the respective theoretical critical stresses. This is due primarily to the presence of geometrical imperfections even through such imperfections could be very small (e.g., comparable to thickness). Under internal pressure, the shell regains some of its buckling strength. For a relatively large radius-to-tickness ratio and low internal pressure, the effect can be reasonably estimated by an elastic analysis. However, for low radius-to-thickness ratios and greater pressures, the elastic-plastic collapse controls the failure load. In order to quantify the elastic-plastic buckling capacity of cylindrical shells, an analysis program was carried out by use of the computer code BOSOR5 developed by Bushnell of Lockheed Missiles and Space company. The analysis was performed for various radius-to- thickness ratios and imperfection amplitudes. The analysis results are presented in this paper.
1980-12-01
in two steps. A reference grid is prepared on the midsurface based upon various parameters specified by the user. Once the grid is ready the three...coordinate system b-Y is introduced. The ’S’ coordinate is the circumferential distance on the midsurface of the cylinder from the generator having the...C F 4 0.7 4# " " " Ř CF 1.0 Ratio of length to width for this shell elements for CYLSHELL r Midsurface radius of the nozzle t Thickness of the
Crack problems in cylindrical and spherical shells
NASA Technical Reports Server (NTRS)
Erdogan, F.
1976-01-01
Standard plate or shell theories were used as a starting point to study the fracture problems in thin-walled cylindrical and spherical shells, assuming that the plane of the crack is perpendicular to the surface of the sheet. Since recent studies have shown that local shell curvatures may have a rather considerable effect on the stress intensity factor, the crack problem was considered in conjunction with a shell rather than a plate theory. The material was assumed to be isotropic and homogeneous, so that approximate solutions may be obtained by approximating the local shell crack geometry with an ideal shell which has a solution, namely a spherical shell with a meridional crack, a cylindrical shell with a circumferential crack, or a cylindrical shell with an axial crack. A method of solution for the specially orthotropic shells containing a crack was described; symmetric and skew-symmetric problems are considered in cylindrical shells with an axial crack.
Exact solutions for laminated composite cylindrical shells in cylindrical bending
NASA Technical Reports Server (NTRS)
Yuan, F. G.
1992-01-01
Analytic elasticity solutions for laminated composite cylindrical shells under cylindrical bending are presented. The material of the shell is assumed to be general cylindrically anisotropic. Based on the theory of cylindrical anisotropic elasticity, coupled governing partial differential equations are developed. The general expressions for the stresses and displacements in the laminated composite cylinders are discussed. The closed form solutions based on Classical Shell Theory (CST) and Donnell's (1933) theory are also derived for comparison purposes. Three examples illustrate the effect of radius-to-thickness ratio, coupling and stacking sequence. The results show that, in general, CST yields poor stress and displacement distributions for thick-section composite shells, but converges to the exact elasticity solution as the radius-to-thickness ratio increases. It is also shown that Donnell's theory significantly underestimates the stress and displacement response.
Vibration of cylindrical shells of bimodulus composite materials
NASA Astrophysics Data System (ADS)
Bert, C. W.; Kumar, M.
1982-03-01
A theory is formulated for the small amplitude free vibration of thick, circular cylindrical shells laminated of bimodulus composite materials, which have different elastic properties depending upon whether the fiber-direction strain is tensile or compressive. The theory used is the dynamic, shear deformable (moderately thick shell) analog of the Sanders best first approximation thin shell theory. By means of tracers, the analysis can be reduced to that of various simpler shell theories, namely Love's first approximation, and Donnell's shallow shell theory. As an example of the application of the theory, a closed form solution is presented for a freely supported panel or complete shell. To validate the analysis, numerical results are compared with existing results for various special cases. Also, the effects of the various shell theories, thickness shear flexibility, and bimodulus action are investigated.
Omnidirectional, circularly polarized, cylindrical microstrip antenna
NASA Technical Reports Server (NTRS)
Stanton, Philip H. (Inventor)
1985-01-01
A microstrip cylindrical antenna comprised of two concentric subelements on a ground cylinder, a vertically polarized (E-field parallel to the axis of the antenna cylinder) subelement on the inside and a horizontally polarized (E-field perpendicular to the axis) subelement on the outside. The vertical subelement is a wraparound microstrip radiator. A Y-shaped microstrip patch configuration is used for the horizontally polarized radiator that is wrapped 1.5 times to provide radiating edges on opposite sides of the cylindrical antenna for improved azimuthal pattern uniformity. When these subelements are so fed that their far fields are equal in amplitude and phased 90.degree. from each other, a circularly polarized EM wave results. By stacking a plurality of like antenna elements on the ground cylinder, a linear phased array antenna is provided that can be beam steered to the desired elevation angle.
Distributed neural signals on parabolic cylindrical shells
NASA Astrophysics Data System (ADS)
Hu, S. D.; Li, H.; Tzou, H. S.
2013-06-01
Parabolic cylindrical shells are commonly used as key components in communication antennas, space telescopes, solar collectors, etc. This study focuses on distributed modal neural sensing signals on a flexible simply-supported parabolic cylindrical shell panel. The parabolic cylindrical shell is fully laminated with a piezoelectric layer on its outer surface and the piezoelectric layer is segmented into infinitesimal elements (neurons) to investigate the microscopic distributed neural sensing signals. Since the dominant vibration component of the shell is usually the transverse oscillation, a new transverse mode shape function is defined. Two shell cases, i.e., the ratio of the meridian height to the half span distance of a parabola at 1:4 (shallow) and 1:1 (deep), are studied to reveal the curvature effect to the neural sensing signals. Studies suggest that the membrane signal component dominates for lower natural modes and the bending signal component dominates for higher natural modes. The meridional membrane and bending signal components are mostly concentrated on the high-curvature areas, while the longitudinal bending component is mostly concentrated on the relatively flat areas. The concentration behavior becomes more prominent as the parabolic cylindrical shell deepens, primarily resulting from the enhanced membrane effect due to the increased curvature.
SPSM and its application in cylindrical shells
NASA Astrophysics Data System (ADS)
Nie, Wu; Zhou, Su-Lian; Peng, Hui
2008-03-01
In naval architectures, the structure of prismatic shell is used widely. But there is no suitable method to analyze this kind of structure. Stiffened prismatic shell method (SPSM) presented in this paper, is one of the harmonic semi-analytic methods. Theoretically, strong stiffened structure can be analyzed economically and accurately. SPSM is based on the analytical solution of the governing differential equations for orthotropic cylindrical shells. In these differential equations, the torsional stiffness, bending stiffness and the exact position of each stiffener are taken into account with the Heaviside singular function. An algorithm is introduced, in which the actions of stiffeners on shells are replaced by external loads at each stiffener position. Stiffened shells can be computed as non-stiffened shells. Eventually, the displacement solution of the equations is acquired by the introduction of Green function. The stresses in a corrugated transverse bulkhead without pier base of an oil tanker are computed by using SPSM.
Closed form solution to the semi-infinite cylindrical shell problem.
NASA Technical Reports Server (NTRS)
Sanders, J. L., Jr.
1972-01-01
Reconsideration of the problem of a complete semiinfinite circular cylindrical shell with a square cage investigated earlier by Reissner and Simmonds (1966). It is shown that the solution can be found in closed form rather than in the form of Fourier series, provided that the boundary data on the end of the shell are 'slowly varying.'
Vibrations of cantilevered shallow cylindrical shells of rectangular planform
NASA Technical Reports Server (NTRS)
Leissa, A. W.; Lee, J. K.; Wang, A. J.
1981-01-01
A cantilevered, shallow shell of circular cylindrical curvature and rectangular planform exhibits free vibration behavior which differs considerably from that of a cantilevered beam or of a flat plate. Some numerical results can be found for the problem in the previously published literature, mainly obtained by using various finite element methods. The present paper is the first definitive study of the problem, presenting accurate non-dimensional frequency parameters for wide ranges of aspect ratio, shallowness ratio and thickness ratio. The analysis is based upon shallow shell theory. Numerical results are obtained by using the Ritz method, with algebraic polynomial trial functions for the displacements. Convergence is investigated, with attention being given both to the number of terms taken for each co-ordinate direction and for each of the three components of displacement. Accuracy of the results is also established by comparison with finite element results for shallow shells and with other accurate flat plate solutions.
Vibrations of cantilevered shallow cylindrical shells of rectangular planform
NASA Astrophysics Data System (ADS)
Leissa, A. W.; Lee, J. K.; Wang, A. J.
1981-10-01
A cantilevered, shallow shell of circular cylindrical curvature and rectangular planform exhibits free vibration behavior which differs considerably from that of a cantilevered beam or of a flat plate. Some numerical results can be found for the problem in the previously published literature, mainly obtained by using various finite element methods. The present paper is the first definitive study of the problem, presenting accurate non-dimensional frequency parameters for wide ranges of aspect ratio, shallowness ratio and thickness ratio. The analysis is based upon shallow shell theory. Numerical results are obtained by using the Ritz method, with algebraic polynomial trial functions for the displacements. Convergence is investigated, with attention being given both to the number of terms taken for each co-ordinate direction and for each of the three components of displacement. Accuracy of the results is also established by comparison with finite element results for shallow shells and with other accurate flat plate solutions.
Dynamic Buckling of Composite Cylindrical Shells
NASA Astrophysics Data System (ADS)
Cheng, Sai-Wei; Wang, Xiao-Jun
2016-05-01
Considering the effect of stress wave, the dynamic buckling governing equations and boundary conditions of composite cylindrical shells under axial step load are derived based on the Hamilton principle. The expression of radial displacement function along the circumferential direction is assumed since the cylindrical shell is closed. The solutions of the governing equations are obtained by the state-space technique. The determinant of the coefficient matrix must be equal to zero if the linear equations have a non-trivial solution. The relationship between the critical load and length and the influences of boundary conditions, modes, etc. on critical load are obtained by programming with MATLAB software before and after the reflection of stress wave.
Diagonal piezoelectric sensors on cylindrical shells
NASA Astrophysics Data System (ADS)
Li, Hua; Zhang, Xufang; Tzou, Hornsen
2017-07-01
Piezoelectric sensors are effective for distributed health monitoring and sensing of structures. The signals of piezoelectric sensors are related to the orientation of the sensors. In this study, a diagonal piezoelectric sensor is proposed for cylindrical shells. The sensor is made of a rectangular piezoelectric patch and diagonally attached on the shell surface; and piezoelectric actuators are used for excitation. An analytical model of the sensor is derived based on thin shell assumption with simply-supported boundary conditions. The orientation angle of the piezoelectric sensor is introduced as an independent variable. The proposed model consists of an integral term over the electrode area, which is divided into three regions for calculation. The sensing signal is decomposed into six components to evaluate the contributions of the strain components. Case studies on signals with respect to the orientation and aspect ratios are accomplished. The cylindrical shell with piezoelectric actuators and diagonal sensors is fabricated and tested under laboratory condition. Comparison of theoretical results with experimental data is conducted, and the model of the diagonal sensors is validated. The errors between the predictions and experimental results are less than 10% for all evaluated modes.
Stresses in rotating composite cylindrical shells
NASA Astrophysics Data System (ADS)
Wang, James T.-S.; Lin, Chien-Chang
Stresses in composite cylindrical shells rotating with a constant speed about their longitudinal axis are analyzed. Each ply or ply group is treated as a separate thin layer of homogeneous and orthotropic material under the interfacial stresses as surface loading. There is no limitation on the total thickness of the shell. The circumferential stress, motivated by the conventional thin shell theory, is assumed to vary linearly through the thickness of the layer. The radial stress is determined in terms of the circumferential stress through the equilibrium condition, and an average compatibility condition through the thickness of the thin layer is used. Numerical results using the present analysis show nearly perfect agreement with the exact solution for homogeneous and isotropic cylinders. Some results for cylinders having orthotropic layers are presented for illustrative purposes.
Scaling Instability in Buckling of Axially Compressed Cylindrical Shells
NASA Astrophysics Data System (ADS)
Grabovsky, Yury; Harutyunyan, Davit
2016-02-01
In this paper, we continue the development of mathematically rigorous theory of "near-flip" buckling of slender bodies of arbitrary geometry, based on hyperelasticity. In order to showcase the capabilities of this theory, we apply it to buckling of axially compressed circular cylindrical shells. The theory confirms the classical formula for the buckling load, whereby the perfect structure buckles at the stress that scales as the first power of shell's thickness. However, in the case of imperfections of load, the theory predicts scaling instability of the buckling stress. Depending on the type of load imperfections, buckling may occur at stresses that scale as thickness to the power 1.5 or 1.25, corresponding to the lower and upper ends, respectively, of the historically accumulated experimental data.
The sound field in a finite cylindrical shell
NASA Technical Reports Server (NTRS)
Junger, M. C.
1985-01-01
The sound field excited by vibrating boundaries in a finite cylindrical space, e.g., in a cylindrical shell, differs from the pressure distribution in an infinite cylindrical shell of comparable structural wavelength by the pressure diffracted by the end caps. The latter pressure component is comparable in magnitude to the pressure generated by the vibrating cylindrical boundary, but does not introduce additional resonances or antiresonances. Finally, a third pressure component associated with end cap vibrations is formulated.
Vibration of in-vacuo elliptic cylindrical shells
NASA Astrophysics Data System (ADS)
Boisvert, Jeffrey E.; Hayek, Sabih I.
2003-10-01
The equations of motion for the vibration of elliptic cylindrical shells of constant thickness were derived using a Galerkin approach. The elastic strain energy density used in this derivation has seven independent kinematic variables: three displacements, two thickness-shear, and two thickness-stretch. The resulting seven coupled algebraic equations are symmetric and positive definite. The shell has a constant thickness, h, finite length, L, and is simply supported at its ends, (z=0,L), where z is the axial coordinate. The elliptic cross-section is defined by the shape parameter, a, and the half-length of the major axis, l. The modal solutions are expanded in a doubly infinite series of comparison functions in terms of circular functions in the angular and axial coordinates. The natural frequencies and the mode shapes were obtained by the Galerkin method. Numerical results were obtained for several h/l and L/l ratios, and various shape parameters, including the limiting case of a simply supported cylindrical shell (a=100). [Work supported by ONR and the Navy/ASEE Summer Faculty Program.
NASA Astrophysics Data System (ADS)
Mercan, Kadir; Demir, Çiǧdem; Civalek, Ömer
2016-01-01
In the present manuscript, free vibration response of circular cylindrical shells with functionally graded material (FGM) is investigated. The method of discrete singular convolution (DSC) is used for numerical solution of the related governing equation of motion of FGM cylindrical shell. The constitutive relations are based on the Love's first approximation shell theory. The material properties are graded in the thickness direction according to a volume fraction power law indexes. Frequency values are calculated for different types of boundary conditions, material and geometric parameters. In general, close agreement between the obtained results and those of other researchers has been found.
1997-10-01
plane wave by a circular cylindrical shell. Results of computations. Acustica - Acta Acustica , 82, 1996: 689-697. [5] de Billy M., Determination of the...circumferential waves on cylindrical elastic shells. Acustica - Acta Acustica , 82, 1996: 707-716. [14] Bhattacharyya G.K., and Johnson R.A., Statistical...22] Batard H, Talmant M., and Quentin G.J., The Acoustical Characteristics Estimation Method (MECA) applied to cylinders and shells. Acta Acustica
NASA Technical Reports Server (NTRS)
Leissa, A. W.
1973-01-01
The vibrational characteristics and mechanical properties of shell structures are discussed. The subjects presented are: (1) fundamental equations of thin shell theory, (2) characteristics of thin circular cylindrical shells, (3) complicating effects in circular cylindrical shells, (4) noncircular cylindrical shell properties, (5) characteristics of spherical shells, and (6) solution of three-dimensional equations of motion for cylinders.
A circumferential crack in a cylindrical shell under tension.
NASA Technical Reports Server (NTRS)
Duncan-Fama, M. E.; Sanders, J. L., Jr.
1972-01-01
A closed cylindrical shell under uniform internal pressure has a slit around a portion of its circumference. Linear shallow shell theory predicts inverse square-root-type singularities in certain of the stresses at the crack tips. This paper reports the computed strength of these singularities for different values of a dimensionless parameter based on crack length, shell radius and shell thickness.
Parity violating cylindrical shell in the framework of QED
NASA Astrophysics Data System (ADS)
Fialkovsky, I. V.; Markov, V. N.; Pis'mak, Yu M.
2008-02-01
We present calculations of Casimir energy (CE) in a system of quantized electromagnetic (EM) field interacting with an infinite circular cylindrical shell (which we call 'the defect'). Interaction is described in the only QFT-consistent way by Chern-Simon action concentrated on the defect, with a single coupling constant a. For the regularization of UV divergencies of the theory, we use the Pauli-Villars regularization of the free-EM action. The divergencies are extracted as a polynomial in the regularization mass M, and they renormalize the classical part of the surface action. We reveal the dependence of CE on the coupling constant a. Corresponding Casimir force is attractive for all values of a. For a → ∞, we reproduce the known results for CE for perfectly conducting cylindrical shell first obtained by DeRaad and Milton. As a future task for solving existing arguments on observational status of (rigid) self-pressure of a single object, we propose for investigation a system which we call 'Casimir drum'.
Cylindrical thin-shell wormholes supported by phantom energy
NASA Astrophysics Data System (ADS)
Eid, A.
2016-09-01
In the framework of Darmois-Israel formalism, the general equations describing the motion of cylindrical thin-shell wormholes supported by equation of state of phantom energy are derived. The linear perturbation approach is used to investigate the stability of a cylindrical thin-shell wormhole of a static solution.
Cylindrical shell buckling through strain hardening
Bandyopadhyay, K.; Xu, J.; Shteyngart, S.; Gupta, D.
1995-04-01
Recently, the authors published results of plastic buckling analysis of cylindrical shells. Ideal elastic-plastic material behavior was used for the analysis. Subsequently, the buckling analysis program was continued with the realistic stress-strain relationship of a stainless steel alloy which does not exhibit a clear yield point. The plastic buckling analysis was carried out through the initial stages of strain hardening for various internal pressure values. The computer program BOSOR5 was used for this purpose. Results were compared with those obtained from the idealized elastic-plastic relationship using the offset stress level at 0.2% strain as the yield stress. For moderate hoop stress values, the realistic stress-grain case shows a slight reduction of the buckling strength. But, a substantial gain in the buckling strength is observed as the hoop stress approaches the yield strength. Most importantly, the shell retains a residual strength to carry a small amount of axial compressive load even when the hoop stress has exceeded the offset yield strength.
1983-10-01
following basic equations can be deduced for orthotropic circular cylindrical shells. Let a be the radius of the midsurface of the shell, x, y, z the...axial, circumferential and radial coordinates and a, a the dimensionless midsurface coordinates along lines of curvatures (a - , a - . The threea a...8217The components of strain at an arbitrary point of the shell are related to the midsurface displacements by [8,15,16] e ( 1 v , 3 2w e a a a ,2)- 0 a
NASA Technical Reports Server (NTRS)
Gerhard, Craig Steven; Gurdal, Zafer; Kapania, Rakesh K.
1996-01-01
Layerwise finite element analyses of geodesically stiffened cylindrical shells are presented. The layerwise laminate theory of Reddy (LWTR) is developed and adapted to circular cylindrical shells. The Ritz variational method is used to develop an analytical approach for studying the buckling of simply supported geodesically stiffened shells with discrete stiffeners. This method utilizes a Lagrange multiplier technique to attach the stiffeners to the shell. The development of the layerwise shells couples a one-dimensional finite element through the thickness with a Navier solution that satisfies the boundary conditions. The buckling results from the Ritz discrete analytical method are compared with smeared buckling results and with NASA Testbed finite element results. The development of layerwise shell and beam finite elements is presented and these elements are used to perform the displacement field, stress, and first-ply failure analyses. The layerwise shell elements are used to model the shell skin and the layerwise beam elements are used to model the stiffeners. This arrangement allows the beam stiffeners to be assembled directly into the global stiffness matrix. A series of analytical studies are made to compare the response of geodesically stiffened shells as a function of loading, shell geometry, shell radii, shell laminate thickness, stiffener height, and geometric nonlinearity. Comparisons of the structural response of geodesically stiffened shells, axial and ring stiffened shells, and unstiffened shells are provided. In addition, interlaminar stress results near the stiffener intersection are presented. First-ply failure analyses for geodesically stiffened shells utilizing the Tsai-Wu failure criterion are presented for a few selected cases.
Dynamic stability of simply supported composite cylindrical shells under partial axial loading
NASA Astrophysics Data System (ADS)
Dey, Tanish; Ramachandra, L. S.
2015-09-01
The parametric vibration of a simply supported composite circular cylindrical shell under periodic partial edge loadings is discussed in this article. Donnell's nonlinear shallow shell theory considering first order shear deformation theory is used to model the shell. The applied partial edge loading is represented in terms of a Fourier series and stress distributions within the cylindrical shell are determined by prebuckling analysis. The governing equations of the dynamic instability of shells are derived in terms of displacements (u-v-w) and rotations (φx, φθ). Employing the Galerkin and Bolotin methods the dynamic instability regions are computed. Using the expression for the stress function derived in this paper, the pre-buckling stresses in the cylindrical shell due to partial loading can be calculated explicitly. Numerical results are presented to show the influence of radius-to-thickness ratio, different partial edge loading distributions and shear deformation on the dynamic instability regions. The linear and nonlinear responses in the stable and unstable regions are presented to bring out the characteristic features of the dynamic instability regions, such as the existence of beats, its dependence on forcing frequency and effect of nonlinearity on the response. The effect of dynamic load amplitude on the nonlinear response is also studied. It is found that for higher values of dynamic loading, the shell exhibits chaotic behavior.
Sound Transmission through a Cylindrical Sandwich Shell with Honeycomb Core
NASA Technical Reports Server (NTRS)
Tang, Yvette Y.; Robinson, Jay H.; Silcox, Richard J.
1996-01-01
Sound transmission through an infinite cylindrical sandwich shell is studied in the context of the transmission of airborne sound into aircraft interiors. The cylindrical shell is immersed in fluid media and excited by an oblique incident plane sound wave. The internal and external fluids are different and there is uniform airflow in the external fluid medium. An explicit expression of transmission loss is derived in terms of modal impedance of the fluids and the shell. The results show the effects of (a) the incident angles of the plane wave; (b) the flight conditions of Mach number and altitude of the aircraft; (c) the ratios between the core thickness and the total thickness of the shell; and (d) the structural loss factors on the transmission loss. Comparisons of the transmission loss are made among different shell constructions and different shell theories.
Broadband sound absorption by lattices of microperforated cylindrical shells
NASA Astrophysics Data System (ADS)
García-Chocano, Victor M.; Cabrera, Suitberto; Sánchez-Dehesa, José
2012-10-01
Absorption of broadband noise by sonic crystals consisting of microperforated cylindrical shells is proposed and experimentally demonstrated. The theoretical study has been performed in the framework of multiple scattering method, where a model for the T matrix of the microperforated shells has been developed. It has been predicted an extraordinary broadband sound absorption that is explained in terms of the multiple scattering phenomena occurring at the surfaces of the absorptive units—the microperforated panels. Our proposal has been supported by experiments performed on a structure consisting of 3 rows of cylindrical shells 3 meters height.
Active Constrained Layer Damping of Thin Cylindrical Shells
NASA Astrophysics Data System (ADS)
RAY, M. C.; OH, J.; BAZ, A.
2001-03-01
The effectiveness of the active constrained layer damping (ACLD) treatments in enhancing the damping characteristics of thin cylindrical shells is presented. A finite element model (FEM) is developed to describe the dynamic interaction between the shells and the ACLD treatments. Experiments are performed to verify the numerical predictions. The obtained results suggest the potential of the ACLD treatments in controlling the vibration of cylindrical shells which constitute the major building block of many critical structures such as cabins of aircrafts, hulls of submarines and bodies of rockets and missiles.
Developments in Cylindrical Shell Stability Analysis
NASA Technical Reports Server (NTRS)
Knight, Norman F., Jr.; Starnes, James H., Jr.
1998-01-01
Today high-performance computing systems and new analytical and numerical techniques enable engineers to explore the use of advanced materials for shell design. This paper reviews some of the historical developments of shell buckling analysis and design. The paper concludes by identifying key research directions for reliable and robust methods development in shell stability analysis and design.
Sound Transmission through Two Concentric Cylindrical Sandwich Shells
NASA Technical Reports Server (NTRS)
Tang, Yvette Y.; Silcox, Richard J.; Robinson, Jay H.
1996-01-01
This paper solves the problem of sound transmission through a system of two infinite concentric cylindrical sandwich shells. The shells are surrounded by external and internal fluid media and there is fluid (air) in the annular space between them. An oblique plane sound wave is incident upon the surface of the outer shell. A uniform flow is moving with a constant velocity in the external fluid medium. Classical thin shell theory is applied to the inner shell and first-order shear deformation theory is applied to the outer shell. A closed form for transmission loss is derived based on modal analysis. Investigations have been made for the impedance of both shells and the transmission loss through the shells from the exterior into the interior. Results are compared for double sandwich shells and single sandwich shells. This study shows that: (1) the impedance of the inner shell is much smaller than that of the outer shell so that the transmission loss is almost the same in both the annular space and the interior cavity of the shells; (2) the two concentric sandwich shells can produce an appreciable increase of transmission loss over single sandwich shells especially in the high frequency range; and (3) design guidelines may be derived with respect to the noise reduction requirement and the pressure in the annular space at a mid-frequency range.
Effect of damage on the modal parameters of a cylindrical shell
Srinivasan, M.G.; Kot, C.A.
1992-02-01
The objective of the study was to investigate the feasibility of assessing damage to structural systems by measuring the changes in the dynamic characteristics of a thin circular cylindrical shell with both ends open. Theoretical and experimental modal analyses were performed for the shell. Subsequently, a notch was machined into the shell simulating a small amount of damage. The shell with the notch was again subjected to experimental modal analysis. A comparison of the modal parameters determined from the tests before and after the shell was damaged showed that the natural frequencies were not sensitive to the crack introduced. However, some of the mode shapes showed significant changes, establishing that the mode shapes were the more sensitive parameters for damage detection.
Effect of damage on the modal parameters of a cylindrical shell
Srinivasan, M.G.; Kot, C.A.
1992-01-01
The objective of the study was to investigate the feasibility of assessing damage to structural systems by measuring the changes in the dynamic characteristics of a thin circular cylindrical shell with both ends open. Theoretical and experimental modal analyses were performed for the shell. Subsequently, a notch was machined into the shell simulating a small amount of damage. The shell with the notch was again subjected to experimental modal analysis. A comparison of the modal parameters determined from the tests before and after the shell was damaged showed that the natural frequencies were not sensitive to the crack introduced. However, some of the mode shapes showed significant changes, establishing that the mode shapes were the more sensitive parameters for damage detection.
Buckling of unstiffened and ring stiffened cylindrical shells under axial compression.
NASA Technical Reports Server (NTRS)
Pedersen, P. T.
1973-01-01
Bifurcation stresses and initial postbuckling behavior of both unstiffened and outside ring stiffened circular cylindrical shells under axial compression are analyzed. The shells are assumed to have axisymmetric sinusoidal imperfections with arbitrary wavelengths and amplitudes. It is found that for large imperfection amplitudes and wavelengths both the unstiffened and the stiffened shells have extremely small bifurcation loads. The postbuckling analysis shows that for small imperfection amplitudes the bifurcations from the axisymmetric state are initially unstable and collapse is associated with the bifurcation points. However, for larger values of the imperfection amplitudes the bifurcations are stable. For unstiffened shells the transition from unstable to stable bifurcations can take place at very small values of the load. On the other hand, for stiffened shells it is found that bifurcations at load levels less than about 40% of the classical buckling load have stable initial postbuckling behavior.
Arbitrarily laminated, anisotropic cylindrical shell under internal pressure
NASA Technical Reports Server (NTRS)
Chaudhuri, Reaz Z.; Balaraman, K.; Kunukkasseril, Vincent X.
1986-01-01
An arbitrarily laminated, anisotropic cylindrical shell of finite length, under uniform internal pressure, is analyzed using Love-Timoshenko's kinematic relations and under the framework of classical lamination theory. The previously obtained solutions for asymmetrically laminated orthotropic (cross-ply) as well as unbalanced-symmetric and balanced-unsymmetric (angle-ply) cylindrical shells under the same loading conditions have been shown to be special cases of the present closed-form solution. Numerical results have been presented for a two-layer cylindrical shell and compared with those obtained using finite element solutions based on the layerwise constant shear-angle theory. These are expected to serve as benchmark solutions for future comparisons and to facilitate the use of unsymmetric lamination in design.
Arbitrarily laminated, anisotropic cylindrical shell under internal pressure
NASA Technical Reports Server (NTRS)
Chaudhuri, Reaz Z.; Balaraman, K.; Kunukkasseril, Vincent X.
1986-01-01
An arbitrarily laminated, anisotropic cylindrical shell of finite length, under uniform internal pressure, is analyzed using Love-Timoshenko's kinematic relations and under the framework of classical lamination theory. The previously obtained solutions for asymmetrically laminated orthotropic (cross-ply) as well as unbalanced-symmetric and balanced-unsymmetric (angle-ply) cylindrical shells under the same loading conditions have been shown to be special cases of the present closed-form solution. Numerical results have been presented for a two-layer cylindrical shell and compared with those obtained using finite element solutions based on the layerwise constant shear-angle theory. These are expected to serve as benchmark solutions for future comparisons and to facilitate the use of unsymmetric lamination in design.
Far-field sound radiation of a submerged cylindrical shell at finite depth from the free surface.
Li, T Y; Miao, Y Y; Ye, W B; Zhu, X; Zhu, X M
2014-09-01
The far-field sound radiation behavior of a circular cylindrical shell submerged at finite depth from the free surface is studied. Based on the Flügge shell theory and the Helmholtz equation, the structure-acoustic coupling equation is established. An image method is applied so that the sound boundary condition of the free surface can be satisfied. Analytical expression of the far-field sound pressure is obtained using the stationary phase method and the Graf's addition theorem. In order to evaluate the effect of the submerged depth on sound radiation, the results of the submerged cylindrical shell at finite depth from the free surface are compared with those of the submerged cylindrical shell in the infinite fluid. The characteristics of the far-field sound pressure with the change of the depth are investigated. It is found that the submerged depth has a significant influence on the far-field sound pressure radiated from the submerged cylindrical shell due to the free surface effects. The work provides more understanding on the sound radiation properties of the submerged circular cylindrical shell without assuming infinite fluid field, which was commonly used in previous studies.
A higher order theory of laminated composite cylindrical shells
NASA Technical Reports Server (NTRS)
Krishna Murthy, A. V.; Reddy, T. S. R.
1986-01-01
A new higher order theory has been proposed for the analysis of composite cylindrical shells. The formulation allows for arbitrary variation of inplane displacements. Governing equations are presented in the form of a hierarchy of sets of partial differential equations. Each set describes the shell behavior to a certain degree of approximation. The natural frequencies of simply-supported isotropic and laminated shells and stresses in a ring loaded composite shell have been determined to various orders of approximation and compared with three dimensional solutions. These numerical studies indicate the improvements achievable in estimating the natural frequencies and the interlaminar shear stresses in laminated composite cylinders.
NASA Astrophysics Data System (ADS)
Kukudzhanov, S. N.
2008-10-01
We study the natural vibrations and the dynamic stability of nearly cylindrical orthotropic shells of revolution subjected to meridional forces uniformly distributed over the shell ends. We consider shells of medium length for which the shape of the midsurface generatrix is described by a parabolic function. Using the theory of shallow shells, we obtain the resolving equation for the vibrations of the corresponding prestressed shell. In the isotropic case, this equation differs from the well-known equation [1] by an additional term, which can be of the same order as the other terms taken into account. We consider shells of both positive and negative Gaussian curvature. We assumed that the shell ends are freely supported. The formulas and universal curves describing the dependence of the minimum frequency, the wave generation shape, and the dynamic instability domain boundaries on the orthotropy parameters, the preliminary stress, the Gaussian curvature, and the amplitude of the shell deviation from the cylinder are given in dimensionless form. We find that in the case of prestresses the orthotropy parameters and the shell deviation from the cylinder (of the order of thickness) can significantly change the least frequencies, the wave generation shape, and the dynamic instability domain boundaries of the corresponding prestressed orthotropic cylindrical shell. In this case, we note that for convex shells under preliminary compression the influence of the elastic parameter in the axial direction is stronger than the influence of the elastic parameter in the circular direction, while the situation is opposite in the case of concave shells. In the case of preliminary extension, the leading role of any orthotropy parameter can vary depending on the value of the preliminary stress and the Gaussian curvature.
Nicols, R.O.
1985-08-15
A 2-D optical analysis is described that allows determination of the intensity distribution on a circular cylinder located in the focal zone of nonperfect concentrators. We call nonperfect concentrators those in which the normal to each differential element of the specular surface departs from its correct position by an angle epsilon, the possible values of which follow a Gaussian distribution of mean value epsilon-bar and standard deviation sigma. The analysis is based on a previous one developed to calculate the intensity distribution at the receiver plane of nonperfect cylindrical concentrators. The analysis permits the consideration of circular receivers displaced from the focus by distance delta/sub f/ in any direction and directions of the incident rays nonparallel to the parabola's symmetry plane. Results for different sets of parameters characterizing the behavior of a given concentrator are shown and compared.
Evolution of bulk strain solitons in cylindrical inhomogeneous shells
Shvartz, A. Samsonov, A.; Dreiden, G.; Semenova, I.
2015-10-28
Bulk strain solitary waves in nonlinearly elastic thin-walled cylindrical shells with variable geometrical and physical parameters are studied, and equation for the longitudinal strain component with the variable coefficients is derived. A conservative finite difference scheme is proposed, and the results of numerical simulation of the strain soliton evolution in a shell with the abrupt variations of cross section and physical properties of the material are presented.
Limit analysis for combined edge and pressure loading on a cylindrical shell.
NASA Technical Reports Server (NTRS)
Ho, H. S.; Updike, D. P.
1971-01-01
Equations describing the stress field and velocity field occurring in a circular cylindrical shell at plastic collapse are derived corresponding to stress states lying on each face of a yield surface for a uniform shell of material obeying the Tresca yield condition. They are then applied to the case of a shell under combined axisymmetric loadings (moment, shear force, and axial force) at one end and uniform internal or external pressure on the lateral surface. For a sufficiently long shell, complete solutions are obtained for a fixed far end, and for a certain range of values of axial force and pressure, they are obtained for a free far end. All the solutions are represented by either closed form or by quadratures. It is shown that in many cases the radial velocity field is proportional to the shear force.
Strength reliability analysis of stiffened cylindrical shells considering failure correlation
NASA Astrophysics Data System (ADS)
Bai, Xu; Sun, Liping; Qin, Wei; Lv, Yongkun
2014-03-01
The stiffened cylindrical shell is commonly used for the pressure hull of submersibles and the legs of offshore platforms. There are various failure modes because of uncertainty with the structural size and material properties, uncertainty of the calculation model and machining errors. Correlations among failure modes must be considered with the structural reliability of stiffened cylindrical shells. However, the traditional method cannot consider the correlations effectively. The aim of this study is to present a method of reliability analysis for stiffened cylindrical shells which considers the correlations among failure modes. Firstly, the joint failure probability calculation formula of two related failure modes is derived through use of the 2D joint probability density function. Secondly, the full probability formula of the tandem structural system is given with consideration to the correlations among failure modes. At last, the accuracy of the system reliability calculation is verified through use of the Monte Carlo simulation. Result of the analysis shows the failure probability of stiffened cylindrical shells can be gained through adding the failure probability of each mode.
Finite deformations of an electroelastic circular cylindrical tube
NASA Astrophysics Data System (ADS)
Melnikov, Andrey; Ogden, Ray W.
2016-12-01
In this paper the theory of nonlinear electroelasticity is used to examine deformations of a pressurized thick-walled circular cylindrical tube of soft dielectric material with closed ends and compliant electrodes on its curved boundaries. Expressions for the dependence of the pressure and reduced axial load on the deformation and a potential difference between, or uniform surface charge distributions on, the electrodes are obtained in respect of a general isotropic electroelastic energy function. To illustrate the behaviour of the tube, specific forms of energy functions accounting for different mechanical properties coupled with a deformation independent quadratic dependence on the electric field are used for numerical purposes, for a given potential difference and separately for a given charge distribution. Numerical dependences of the non-dimensional pressure and reduced axial load on the deformation are obtained for the considered energy functions. Results are then given for the thin-walled approximation as a limiting case of a thick-walled cylindrical tube without restriction on the energy function. The theory described herein provides a general basis for the detailed analysis of the electroelastic response of tubular dielectric elastomer actuators, which is illustrated for a fixed axial load in the absence of internal pressure and fixed internal pressure in the absence of an applied axial load.
Vibration control of cylindrical shells using active constrained layer damping
NASA Astrophysics Data System (ADS)
Ray, Manas C.; Chen, Tung-Huei; Baz, Amr M.
1997-05-01
The fundamentals of controlling the structural vibration of cylindrical shells treated with active constrained layer damping (ACLD) treatments are presented. The effectiveness of the ACLD treatments in enhancing the damping characteristics of thin cylindrical shells is demonstrated theoretically and experimentally. A finite element model (FEM) is developed to describe the dynamic interaction between the shells and the ACLD treatments. The FEM is used to predict the natural frequencies and the modal loss factors of shells which are partially treated with patches of the ACLD treatments. The predictions of the FEM are validated experimentally using stainless steel cylinders which are 20.32 cm in diameter, 30.4 cm in length and 0.05 cm in thickness. The cylinders are treated with ACLD patches of different configurations in order to target single or multi-modes of lobar vibrations. The ACLD patches used are made of DYAD 606 visco-elastic layer which is sandwiched between two layers of PVDF piezo-electric films. Vibration attenuations of 85% are obtained with maximum control voltage of 40 volts. Such attenuations are attributed to the effectiveness of the ACLD treatment in increasing the modal damping ratios by about a factor of four over those of conventional passive constrained layer damping (PCLD) treatments. The obtained results suggest the potential of the ACLD treatments in controlling the vibration of cylindrical shells which constitute the major building block of many critical structures such as cabins of aircrafts, hulls of submarines and bodies of rockets and missiles.
A cylindrical shell with an arbitrarily oriented crack
NASA Technical Reports Server (NTRS)
Yahsi, O. S.; Erdogan, F.
1982-01-01
The general problem of a shallow shell with constant curvatures is considered. It is assumed that the shell contains an arbitrarily oriented through crack and the material is specially orthotropic. The nonsymmetric problem is solved for arbitrary self equilibrating crack surface tractions, which, added to an appropriate solution for an uncracked shell, would give the result for a cracked shell under most general loading conditions. The problem is reduced to a system of five singular integral equations in a set of unknown functions representing relative displacements and rotations on the crack surfaces. The stress state around the crack tip is asymptotically analyzed and it is shown that the results are identical to those obtained from the two dimensional in plane and antiplane elasticity solutions. The numerical results are given for a cylindrical shell containing an arbitrarily oriented through crack. Some sample results showing the effect of the Poisson's ratio and the material orthotropy are also presented.
Constitutive sensitivity of the oscillatory behaviour of hyperelastic cylindrical shells
NASA Astrophysics Data System (ADS)
Aranda-Iglesias, D.; Vadillo, G.; Rodríguez-Martínez, J. A.
2015-12-01
Free and forced nonlinear radial oscillations of a thick-walled cylindrical shell are investigated. The shell material is taken to be incompressible and isotropic within the framework of finite nonlinear elasticity. In comparison with previous seminal works dealing with the dynamic behaviour of hyperelastic cylindrical tubes, in this paper we have developed a broader analysis on the constitutive sensitivity of the oscillatory response of the shell. In this regard, our investigation is inspired by the recent works of Bucchi and Hearn (2013) [28,29], who carried out a constitutive sensitivity analysis of similar problem with hyperelastic cylindrical membranes subjected to static inflation. In the present paper we consider two different Helmholtz free-energy functions to describe the material behaviour: Mooney-Rivlin and Yeoh constitutive models. We carry out a systematic comparison of the results obtained by application of both constitutive models, paying specific attention to the critical initial and loading conditions which preclude the oscillatory response of the cylindrical tube. It has been found that these critical conditions are strongly dependent on the specific constitutive model selected, even though both Helmholtz free-energy functions were calibrated using the same experimental data.
Prakash, Vijay S; Sonti, Venkata R
2015-11-01
Nonlinear acoustic wave propagation is considered in an infinite orthotropic thin circular cylindrical waveguide. The modes are non-planar having small but finite amplitude. The fluid is assumed to be ideal and inviscid with no mean flow. The cylindrical waveguide is modeled using the Donnell's nonlinear theory for thin cylindrical shells. The approximate solutions for the acoustic velocity potential are found using the method of multiple scales (MMS) in space and time. The calculations are presented up to the third order of the small parameter. It is found that at some frequencies the amplitude modulation is governed by the Nonlinear Schrödinger Equation (NLSE). The first objective is to study the nonlinear term in the NLSE, as the sign of the nonlinear term determines the stability of the amplitude modulation. On the other hand, at other specific frequencies, interactions occur between the primary wave and its higher harmonics. Here, the objective is to identify the frequencies of the higher harmonic interactions. Lastly, the linear terms in the NLSE obtained using the MMS calculations are validated. All three objectives are met using an asymptotic analysis of the dispersion equation.
NASA Astrophysics Data System (ADS)
Kwak, Moon K.; Yang, Dong-Ho
2013-09-01
This paper is concerned with the suppression of vibrations and radiated sound of a ring-stiffened circular cylindrical shell in contact with unbounded external fluid by means of piezoelectric sensors and actuators. The dynamic model of a circular cylindrical shell based on the Sanders shell theory was considered together with a ring stiffener model. The mass and stiffness matrices for a ring stiffener were newly derived in this study and added to the mass and stiffness matrices of the cylindrical shell, respectively. The fluid-added mass matrix, which was derived by using the baffled shell theory, was also added to the mass matrix. Finally, the equations representing the piezoelectric sensor measurement and piezoelectric actuation complete the theoretical model for the addressed problem. The natural vibration characteristics of the ring-stiffened cylindrical shell both in air and in water were investigated both theoretically and experimentally. The theoretical predictions were in good agreement with the experimental results. An active vibration controller which can cope with a harmonic disturbance was designed by considering the modified higher harmonic control, which is, in fact, a band rejection filter. An active vibration control experiment on the submerged cylindrical shell was carried out in a water tank and the digital control system was used. The experimental results showed that both vibrations and radiation sound of the submerged cylindrical shell were suppressed by a pair of piezoelectric sensor and actuator.
Tunable cylindrical shell as an element in acoustic metamaterial.
Titovich, Alexey S; Norris, Andrew N
2014-10-01
Elastic cylindrical shells are fitted with an internal mechanism which is optimized so that, in the quasi-static regime, the combined system exhibits prescribed effective acoustic properties. The mechanism consists of a central mass supported by an axisymmetric distribution of elastic stiffeners. By appropriate selection of the mass and stiffness of the internal mechanism, the shell's effective acoustic properties (bulk modulus and density) can be tuned as desired. Subsonic flexural waves excited in the shell by the attachment of stiffeners are suppressed by including a sufficiently large number of such stiffeners. The effectiveness of the proposed metamaterial is demonstrated by matching the properties of a thin aluminum shell with a polymer insert to those of water. The scattering cross section in water is nearly zero over a broad range of frequencies at the lower end of the spectrum. By arranging the tuned shells in an array the resulting acoustic metamaterial is capable of steering waves. As an example, a cylindrical-to-plane wave lens is designed by varying the bulk modulus in the array according to the conformal mapping of a unit circle to a square.
Asymptotic approximations for pure bending of thin cylindrical shells
NASA Astrophysics Data System (ADS)
Coman, Ciprian D.
2017-08-01
A simplified partial wrinkling scenario for in-plane bending of thin cylindrical shells is explored by using several asymptotic strategies. The eighth-order boundary eigenvalue problem investigated here originates in the Donnel-Mushtari-Vlasov shallow shell theory coupled with a linear membrane pre-bifurcation state. It is shown that the corresponding neutral stability curve is amenable to a detailed asymptotic analysis based on the method of multiple scales. This is further complemented by an alternative WKB approximation that provides comparable information with significantly less effort.
Nonlinear stability of cylindrical shells subjected to axial flow: Theory and experiments
NASA Astrophysics Data System (ADS)
Karagiozis, K. N.; Païdoussis, M. P.; Amabili, M.; Misra, A. K.
2008-01-01
This paper, is concerned with the nonlinear dynamics and stability of thin circular cylindrical shells clamped at both ends and subjected to axial fluid flow. In particular, it describes the development of a nonlinear theoretical model and presents theoretical results displaying the nonlinear behaviour of the clamped shell subjected to flowing fluid. The theoretical model employs the Donnell nonlinear shallow shell equations to describe the geometrically nonlinear structure. The clamped beam eigenfunctions are used to describe the axial variations of the shell deformation, automatically satisfying the boundary conditions and the circumferential continuity condition exactly. The fluid is assumed to be incompressible and inviscid, and the fluid-structure interaction is described by linear potential flow theory. The partial differential equation of motion is discretized using the Galerkin method and the final set of ordinary differential equations are integrated numerically using a pseudo-arclength continuation and collocation techniques and the Gear backward differentiation formula. A theoretical model for shells with simply supported ends is presented as well. Experiments are also described for (i) elastomer shells subjected to annular (external) air-flow and (ii) aluminium and plastic shells with internal water flow. The experimental results along with the theoretical ones indicate loss of stability by divergence with a subcritical nonlinear behaviour. Finally, theory and experiments are compared, showing good qualitative and reasonable quantitative agreement.
An evaluation of active noise control in a cylindrical shell
NASA Technical Reports Server (NTRS)
Silcox, R. J.; Lester, H. C.; Abler, S. B.
1989-01-01
The physical mechanisms governing the use of active noise control in an extended volume of a cylindrical shell are discussed. Measured data was compared with computer results from a previously derived analytical model based on an infinite shell theory. For both the analytical model and experiment, the radiation of the external monopoles is coupled to the internal acoustic field through the radial displacement of the thin, elastic cylindrical shell. An active noise control system was implemented in the cylinder using a fixed array of discrete monopole sources, all of which lie in the plane of the exterior noise sources. Good agreement between measurement and prediction was obtained for both internal pressure response and overall noise reduction. Attenuations in the source plane greater than 15 dB were recorded along with a uniformly quieted noise environment over the entire length of the experimental model. Results indicate that for extended axial forcing distributions or very low shell damping, axial arrays of control sources may be required. Finally, the Nyquist criteria for the number of azimuthal control sources is shown to provide for effective control over the full cylinder cross section.
An evaluation of active noise control in a cylindrical shell
NASA Technical Reports Server (NTRS)
Silcox, R. J.; Lester, H. C.; Abler, S. B.
1987-01-01
The physical mechanisms governing the use of active noise control in an extended volume of a cylindrical shell are discussed. Measured data was compared with computer results from a previously derived analytical model based on an infinite shell theory. For both the analytical model and experiment, the radiation of the external monopoles is coupled to the internal acoustic field through the radial displacement of the thin, elastic cylindrical shell. An active noise control system was implemented in the cylinder using a fixed array of discrete monopole sources, all of which lie in the plane of the exterior noise sources. Good agreement between measurement and prediction was obtained for both internal pressure response and overall noise reduction. Attenuations in the source plane greater than 15 dB were recorded along with a uniformly quieted noise environment over the entire length of the experimental model. Results indicate that for extended axial forcing distributions or very low shell damping, axial arrays of control sources may be required. Finally, the Nyquist criteria for the number of azimuthal control sources is shown to provide for effective control over the full cylinder cross section.
An evaluation of active noise control in a cylindrical shell
NASA Technical Reports Server (NTRS)
Silcox, R. J.; Lester, H. C.; Abler, S. B.
1989-01-01
The physical mechanisms governing the use of active noise control in an extended volume of a cylindrical shell are discussed. Measured data was compared with computer results from a previously derived analytical model based on an infinite shell theory. For both the analytical model and experiment, the radiation of the external monopoles is coupled to the internal acoustic field through the radial displacement of the thin, elastic cylindrical shell. An active noise control system was implemented in the cylinder using a fixed array of discrete monopole sources, all of which lie in the plane of the exterior noise sources. Good agreement between measurement and prediction was obtained for both internal pressure response and overall noise reduction. Attenuations in the source plane greater than 15 dB were recorded along with a uniformly quieted noise environment over the entire length of the experimental model. Results indicate that for extended axial forcing distributions or very low shell damping, axial arrays of control sources may be required. Finally, the Nyquist criteria for the number of azimuthal control sources is shown to provide for effective control over the full cylinder cross section.
Stability of the cylindrical shell of variable curvature
NASA Technical Reports Server (NTRS)
Marguerre, Karl
1951-01-01
This report is a first attempt to devise a calculation method for representing the buckling behavior of cylindrical shells of variable curvature. The problem occurs, for instance, in dimensioning wing noses, the stability of which is decisively influenced by the variability of curvature. The calculation is made possible by simplifying the stability equations (permissible for the shell of small curvature) and by assuming that the curvature 1/R as a function of the arc lengths can be represented by a very few Fourier terms. The formulas for the special case of an ellipse-like half oval with an axis ratio 1/3 ?= e ?= 1 under compression in longitudinal direction,shear, and a combination of shear and compression were evaluated. However, the results can also be applied approximately to an unsymmetrical oval-shell segment under compression, shear, and bending so that the numerical values contained in the diagrams 10 to 12 represent directly dimensioning data for the wing nose.
Flow-Induced Vibration of Circular Cylindrical Structures
Chen, Shoei-Sheng
1985-06-01
of heat exchanger tube banks are typical examples. Recently, flow-induced vibration has been studied extensively for several reasons. First, with the use of high-strength materials, structures become more slender and more susceptible to vibration. Second, the development of advanced nuclear power reactors requires high-velocity fluid flowing through components, which can cause detrimental vibrations. Third, the dynamic interaction of structure and fluid is one of the most fascinating problems in engineering mechanics. The increasing study is evidenced by many conferences directed to this subject and numerous publications, including reviews and books. In a broad sense, flow-induced vibration encompasses all topics on the dynamic responses of structures submerged in fluid, containing fluid, or subjected to external flow. In this report, discussions focus on circular cylindrical structures with emphasis on nuclear reactor system components.
Free Vibrations Of Delaminated Composite Cylindrical Shell Roofs
NASA Astrophysics Data System (ADS)
Acharyya, A. Kumar; Chakraborty, Dipankar; Karmakar, Amit
Recently laminated composites are widely used in civil engineering, which may suffer from delamination damage resulting from improper fabrication and overloading at service. A review of literature that exists on composite shells reveals that the research reports on delaminated shells are very few in number. Hence the present endeavor is to work on delaminated simply supported cylindrical shell with different extents of delaminations. An eight noded isoparametric element with five degrees of freedom per node is used together with Sander's strain displacement relationships and multipoint constraint equations to satisfy the compatibility of displacements and rotations along the cracked edges. The study reveals that there is a consistent decrease in the fundamental frequency value as the area of the delamination damage increases. Further the fundamental frequency of angle ply shells undergo relatively more prominent decrease compared to that of cross ply shells. It seems that delamination damage brings about greater reduction in frequency values as the number of layers increases for angle ply shells, especially for symmetric ones.
Nonstationary Vibrations of Elliptic Cylindrical Sandwich Shells Reinforced with Discrete Stringers
NASA Astrophysics Data System (ADS)
Meish, V. F.; Pavlyuk, A. V.
2017-01-01
The equations of the vibration of elliptic cylindrical sandwich shells with equally spaced stringers under nonstationary loading are derived. Models based on the Timoshenko-type shell theory are used. The dynamic equations are solved numerically by the integro-interpolation finite-differencing method for equations with discontinuous coefficients. The dynamic problem for an elliptic cylindrical sandwich shell reinforced with stringers is solved
Preliminary analysis techniques for ring and stringer stiffened cylindrical shells
NASA Technical Reports Server (NTRS)
Graham, J.
1993-01-01
This report outlines methods of analysis for the buckling of thin-walled circumferentially and longitudinally stiffened cylindrical shells. Methods of analysis for the various failure modes are presented in one cohesive package. Where applicable, more than one method of analysis for a failure mode is presented along with standard practices. The results of this report are primarily intended for use in launch vehicle design in the elastic range. A Microsoft Excel worksheet with accompanying macros has been developed to automate the analysis procedures.
Experimental Investigations of Compressed Sandwich Composite/Honeycomb Cylindrical Shells
NASA Astrophysics Data System (ADS)
Muc, A.; Stawiarski, A.; Romanowicz, P.
2017-06-01
This article explains in some details the behaviour of thick, deep cylindrical sandwich panels subjected to compressive loads. In general, experimental results indicated that two different forms of failure have been observed - the first corresponds to the overall buckling and the second to the facesheet wrinkling. The obtained experimentally damages of shells are verified and validated with the use of the FE analysis, 2-D and 3-D both in the linear and non-linear approach. The unidirectional strain gauges were applied to detect the initiation of the overall buckling mode.
Preliminary analysis techniques for ring and stringer stiffened cylindrical shells
NASA Astrophysics Data System (ADS)
Graham, J.
1993-03-01
This report outlines methods of analysis for the buckling of thin-walled circumferentially and longitudinally stiffened cylindrical shells. Methods of analysis for the various failure modes are presented in one cohesive package. Where applicable, more than one method of analysis for a failure mode is presented along with standard practices. The results of this report are primarily intended for use in launch vehicle design in the elastic range. A Microsoft Excel worksheet with accompanying macros has been developed to automate the analysis procedures.
Noise radiated from a rotating submerged elastic cylindrical thin shell
NASA Astrophysics Data System (ADS)
Caspall, Jayme J.; Yoda, Minami; Rogers, Peter H.
2002-11-01
Although the aeroacoustics of high Reynolds number boundary layers is reasonably well understood, less is known about the hydroacoustics of such flows, and the effect of fluid loading. The noise generated by the turbulent boundary layer around an elastic, thin-walled and cylindrical shell rotating in quiescent water was studied in the Georgia Tech. Underwater Acoustic Tank for Reynolds numbers up to 200000. The steel shell, which is filled with air, has a diameter D of 0.625 m, a wall thickness of 0.004D, and an aspect ratio of unity; the tank dimensions are 19D by 12D by 11D. Extraneous noise sources (e.g., bearing and motor vibration) were isolated from the net signal to estimate flow noise. Radiated noise power was calculated from hydrophone data under a diffuse field assumption. To our knowledge, these results are unique in both their structural acoustics and fluid mechanics scaling.
Transverse shear effect in a circumferentially cracked cylindrical shell
NASA Technical Reports Server (NTRS)
Delale, F.; Erdogan, F.
1979-01-01
The objectives of the paper are to solve the problem of a circumferentially-cracked cylindrical shell by taking into account the effect of transverse shear, and to obtain the stress intensity factors for the bending moment as well as the membrane force as the external load. The formulation of the problem is given for a specially orthotropic material within the framework of a linearized shallow shell theory. The particular theory used permits the consideration of all five boundary conditions as to moment and stress resultants on the crack surface. The effect of Poisson's ratio on the stress intensity factors and the nature of the out-of-plane displacement along the edges of the crack, i.e., bulging, are also studied.
Effects of Shell-Buckling Knockdown Factors in Large Cylindrical Shells
NASA Technical Reports Server (NTRS)
Hrinda, Glenn A.
2012-01-01
Shell-buckling knockdown factors (SBKF) have been used in large cylindrical shell structures to account for uncertainty in buckling loads. As the diameter of the cylinder increases, achieving the manufacturing tolerances becomes increasingly more difficult. Knockdown factors account for manufacturing imperfections in the shell geometry by decreasing the allowable buckling load of the cylinder. In this paper, large-diameter (33 ft) cylinders are investigated by using various SBKF's. An investigation that is based on finite-element analysis (FEA) is used to develop design sensitivity relationships. Different manufacturing imperfections are modeled into a perfect cylinder to investigate the effects of these imperfections on buckling. The analysis results may be applicable to large- diameter rockets, cylindrical tower structures, bulk storage tanks, and silos.
Exact Solutions of Boundary-Value Problems for Noncircular Cylindrical Shells
NASA Astrophysics Data System (ADS)
Storozhuk, E. A.; Yatsura, A. V.
2016-07-01
Boundary-values problems for transversely isotropic infinitely long noncircular cylindrical shells under static loads are formulated and solved analytically. The system of basic equations is derived from a refined theory of deep shells with low shear stiffness. Expressions of the internal forces and generalized displacements for closed and open oval cylindrical shells under internal pressure and transverse force are derived. The effect of the aspect ratio and transverse-shear strains on the stress-strain state of these shells is analyzed
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.
2014-01-01
Nonlinear and bifurcation buckling equations for elastic, stiffened, geometrically perfect, right-circular cylindrical, anisotropic shells subjected to combined loads are presented that are based on Sanders' shell theory. Based on these equations, a three-parameter approximate Rayleigh-Ritz solution and a classical solution to the buckling problem are presented for cylinders with simply supported edges. Extensive comparisons of results obtained from these solutions with published results are also presented for a wide range of cylinder constructions. These comparisons include laminated-composite cylinders with a wide variety of shell-wall orthotropies and anisotropies. Numerous results are also given that show the discrepancies between the results obtained by using Donnell's equations and variants of Sanders' equations. For some cases, nondimensional parameters are identified and "master" curves are presented that facilitate the concise representation of results.
Elastoplastic state of spherical shells with cyclically symmetric circular holes
NASA Astrophysics Data System (ADS)
Storozhuk, E. A.; Chernyshenko, I. S.; Rudenko, I. B.
2012-09-01
The elastoplastic state of thin spherical shells with cyclically symmetric circular holes is considered. A numerical procedure for solving such nonlinear problems is proposed. The distribution of stresses, strains, and displacements over their concentration zones is studied. The stress-strain state of shells with four holes made of a plastic material and subjected to internal pressure of given intensity is analyzed. The numerical results are presented in the form of graphs and tables
Elastoplastic buckling analysis of cylindrical shells using a semi-analytical formulation
NASA Astrophysics Data System (ADS)
Deerenberg, E.
1994-10-01
In this thesis, a semi-analytical formulation for the buckling analysis of circular cylindrical shells is described that takes into account the combined effects of initial geometric imperfections, elastoplastic material behavior and boundary conditions. The model is based on small strains-moderate rotations shell theory. The governing equations are formulated as a coupled set of first-order ordinary differential and algebraic equations. The basic variables in these equations are the variables that can be prescribed at the shell edges. The model described in this thesis is valid for cylinders with a multi-layer wall construction that may be loaded by axial compression, external pressure and/or torsion. The governing differential/algebraic equations are solved using Newton-type iteration methods. Separate equations are formulated for the bifurcation analysis of axisymmetric prebuckling states and an efficient solution method for the eigenvalue problem is described. The correctness of the formulation is checked by analyzing a number of elastic and elastoplastic buckling problems of perfect and imperfect shells.
NASA Astrophysics Data System (ADS)
Talebitooti, R.; Daneshjou, K.; Kornokar, M.
2016-02-01
This paper proposes an extension of the full method to investigate sound transmission through poroelastic cylindrical shell. The "extended full method" is presented based on Biot theory with considering the 3-D wave propagation in a cylindrical shell. Contrary to previous methods, it could be applicable for both poroelastic cylindrical shells and double-walled cylindrical shells lined with poroelastic materials with an excellent accuracy. In the extended full method, the well-known Helmholtz decomposition is used to obtain the displacement fields, solid stresses and the fluid pressure. In order to verify the results of the poroelastic cylindrical shell the porosity goes into zero with eliminating the fluid phase of the poroelastic material. Thus, the results are compared with those of TLs for isotropic shell with high accuracy. The results also indicate that enhancing the porosity of the poroelastic cylindrical shells efficiently leads into decreasing the TL. It is also designated that with doubling the thickness of the poroelastic shell, the TL is improved about 6 dB in a broad-band frequency. Also, the present method is investigated for the case of a double-walled cylindrical shell composed of isotropic skins and poroelastic core. The first-order shear deformation theory is applied to modeling the isotropic shells. The results indicate that presented method is more accurate than simplified method, particularly in the case of small radius cylindrical shells. Moreover, the results indicate that with increasing the radius of the shell, the double-walled cylindrical shell behaves in a same trend as a double-walled flat plate.
Aspects of circumferential waves in determining buckling capacity of cylindrical shells
Xu, J.; Bandyopadhyay, K.K.
1996-12-01
In an effort to quantify the failure behavior of a cylindrical shell when geometric imperfections are present and is subjected to a combination of axial load and internal pressure, the authors have carried out a series of analyses to investigate the effects of various load combinations and material behavior on the shell`s buckling capacity. To complete the characterization of buckling behavior of cylindrical shells, an evaluation was performed to examine the deformation modes in terms of circumferential waves in relation to the shell`s buckling capacity. This paper presents the results of the investigation.
Stress Analysis of Composite Cylindrical Shells With an Elliptical Cutout
NASA Technical Reports Server (NTRS)
Nemeth, M. P.; Oterkus, E.; Madenci, E.
2005-01-01
A special-purpose, semi-analytical solution method for determining the stress and deformation fields in a thin laminated-composite cylindrical shell with an elliptical cutout is presented. The analysis includes the effects of cutout size, shape, and orientation; nonuniform wall thickness; oval-cross-section eccentricity; and loading conditions. The loading conditions include uniform tension, uniform torsion, and pure bending. The analysis approach is based on the principle of stationary potential energy and uses Lagrange multipliers to relax the kinematic admissibility requirements on the displacement representations through the use of idealized elastic edge restraints. Specifying appropriate stiffness values for the elastic extensional and rotational edge restraints (springs) allows the imposition of the kinematic boundary conditions in an indirect manner, which enables the use of a broader set of functions for representing the displacement fields. Selected results of parametric studies are presented for several geometric parameters that demonstrate that analysis approach is a powerful means for developing design criteria for laminated-composite shells.
Stress Analysis of Composite Cylindrical Shells with an Elliptical Cutout
NASA Technical Reports Server (NTRS)
Oterkus, E.; Madenci, E.; Nemeth, M. P.
2007-01-01
A special-purpose, semi-analytical solution method for determining the stress and deformation fields in a thin laminated-composite cylindrical shell with an elliptical cutout is presented. The analysis includes the effects of cutout size, shape, and orientation; non-uniform wall thickness; oval-cross-section eccentricity; and loading conditions. The loading conditions include uniform tension, uniform torsion, and pure bending. The analysis approach is based on the principle of stationary potential energy and uses Lagrange multipliers to relax the kinematic admissibility requirements on the displacement representations through the use of idealized elastic edge restraints. Specifying appropriate stiffness values for the elastic extensional and rotational edge restraints (springs) allows the imposition of the kinematic boundary conditions in an indirect manner, which enables the use of a broader set of functions for representing the displacement fields. Selected results of parametric studies are presented for several geometric parameters that demonstrate that analysis approach is a powerful means for developing design criteria for laminated-composite shells.
Analysis of different techniques to improve sound transmission loss in cylindrical shells
NASA Astrophysics Data System (ADS)
Oliazadeh, Pouria; Farshidianfar, Anooshiravan
2017-02-01
In this study, sound transmission through double- and triple-walled shells is investigated. The structure-acoustic equations based on Donnell's shell theory are presented and transmission losses calculated by this approach are compared with the transmission losses obtained according to Love's theory. An experimental set-up is also constructed to compare natural frequencies obtained from Donnell and Love's theories with experimental results in the high frequency region. Both comparisons show that Donnell's theory predicts the sound transmission characteristics and vibrational behavior better than Love's theory in the high frequency region. The transmission losses of the double- and triple-walled construction are then presented for various radii and thicknesses. Then the effects of air gap size as an important design parameter are studied. Sound transmission characteristics through a circular cylindrical shell are also computed along with consideration of the effects of material damping. Modest absorption is shown to greatly reduce the sound transmission at ring frequency and coincidence frequency. Also the effects of five common gases that are used for filling the gap are investigated.
NASA Astrophysics Data System (ADS)
Amabili, M.; Sarkar, A.; Païdoussis, M. P.
2003-09-01
The nonlinear (large-amplitude) response of perfect and imperfect, simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of some of their lowest natural frequencies is investigated. The shell is assumed to be completely filled with an incompressible and inviscid fluid at rest. Donnell's nonlinear shallow-shell theory is used, and the solution is obtained by the Galerkin method. The proper orthogonal decomposition (POD) method is used to extract proper orthogonal modes that describe the system behaviour from time-series response data. These time series have been obtained via the conventional Galerkin approach (using normal modes as a projection basis) with an accurate model involving 16 degrees of freedom, validated in previous studies. The POD method, in conjunction with the Galerkin approach, permits a lower-dimensional model as compared to those obtainable via the conventional Galerkin approach. Different proper orthogonal modes computed from time series at different excitation frequencies are used and solutions are compared. Some of these sets of modes are capable of describing the system behaviour over the whole frequency range around the fundamental resonance with good accuracy and with only 3 degrees of freedom. They allow a drastic reduction in the computational effort, as compared to using the 16 degree-of-freedom model necessary when the conventional Galerkin approach is used.
NASA Technical Reports Server (NTRS)
Smull, Leland K.
1943-01-01
Four circular cylindrical grids were tested under axial compression to investigate the validity of a theoretical formula for the critical load for such structures. The chief result of the investigation was to throw light on some difficulties connected with the experimental validation of such formulas.
Low frequency soundproof characteristics of orthotropic two-layered cylindrical shells
NASA Astrophysics Data System (ADS)
Chonan, S.
1988-11-01
This paper is concerned with the acoustic characteristics of infinitely long, two-layered orthotropic cylindrical shells excited by a low frequency plane sound wave travelling axially within the shells. The problem is studied based on a thick shell theory, in which each layer is modeled as a single orthotropic shell and the two sets of shell equations are combined together by the continuity conditions of the displacements and tractions at the shell interface. The sound transmission loss through the shell wall, TL, for the axisymmetric acoustic mode ( n = 0) is obtained and calculated for various values of the physical parameters involved.
Kozyreff, Gregory; Acharyya, Nirmalendu
2016-12-12
We derive formulas for whispering gallery mode resonances and bending losses in infinite cylindrical dielectric shells and sets of concentric cylindrical shells. The formulas also apply to spherical shells and to sections of bent waveguides. The derivation is based on a Wentzel-Kramers-Brillouin (WKB) treatment of Helmholtz equation and can in principle be extended to any number of concentric shells. A distinctive limit analytically arises in the analysis when two shells are brought at very close distance to one another. In that limit, the two shells act as a slot waveguide. If the two shells are sufficiently apart, we identify a structural resonance between the individual shells, which can either lead to a substantial enhancement or suppression of radiation losses.
Effects of Stiffening and Mechanical Load on Thermal Buckling of Stiffened Cylindrical Shells
NASA Technical Reports Server (NTRS)
Johnson, Theodore F.; Card, Michael F.
1995-01-01
A study of thermal buckling of stiffened cylindrical shells with the proportions of a preliminary supersonic transport fuselage design (1970) is presented. The buckling analysis is performed using an axisymmetric shell-of-revolution code, BOSOR4. The effects of combined mechanical (axial loading) and thermal loading (heated skins) are investigated. Results indicate that the location of longitudinal eccentric stiffening has a very large effect on the thermal buckling strength of longitudinally stiffened shells, and on longitudinally stiffened shells with rings.
Sohn, Jung Woo; Jeon, Juncheol; Choi, Seung-Bok
2014-10-01
Vibration control performance of the ring-stiffened cylindrical shell structure is experimentally evaluated in this work. In order to achieve high control performance, advanced flexible piezoelectric actuator whose commercial name is Macro-Fiber Composite (MFC) is adapted to the shell structure. Governing equation is derived by finite element method and dynamic characteristics are investigated from the modal analysis results. Ring-stiffened cylindrical shell structure is then manufactured and modal test is conducted to verify modal analysis results. An optimal controller is designed and experimentally realized to the proposed shell structure system. Vibration control performance is experimentally evaluated in time domain and verified by simulated control results.
Kim, Heung Soo; Sohn, Jung Woo; Jeon, Juncheol; Choi, Seung-Bok
2013-02-06
In this work, active vibration control of an underwater cylindrical shell structure was investigated, to suppress structural vibration and structure-borne noise in water. Finite element modeling of the submerged cylindrical shell structure was developed, and experimentally evaluated. Modal reduction was conducted to obtain the reduced system equation for the active feedback control algorithm. Three Macro Fiber Composites (MFCs) were used as actuators and sensors. One MFC was used as an exciter. The optimum control algorithm was designed based on the reduced system equations. The active control performance was then evaluated using the lab scale underwater cylindrical shell structure. Structural vibration and structure-borne noise of the underwater cylindrical shell structure were reduced significantly by activating the optimal controller associated with the MFC actuators. The results provide that active vibration control of the underwater structure is a useful means to reduce structure-borne noise in water.
NASA Astrophysics Data System (ADS)
Qiu, Q.; Fang, Z. P.; Wan, H. C.; Zheng, L.
2013-07-01
Based on the Donnell assumptions and linear visco-elastic theory, the constitutive equations of the cylindrical shell with multilayer Passive Constrained Layer Damping (PCLD) treatments are described. The motion equations and boundary conditions are derived by Hamilton principle. After trigonometric series expansion and Laplace transform, the state vector is introduced and the dynamic equations in state space are established. The transfer function method is used to solve the state equation. The dynamic performance including the natural frequency, the loss factor and the frequency response of clamped-clamped multi-layer PCLD cylindrical shell is obtained. The results show that multi-layer PCLD cylindrical shell is more effective than the traditional three-layer PCLD cylindrical shell in suppressing vibration and noise if the same amount of material is applied. It demonstrates a potential application of multi-layer PCLD treatments in many critical structures such as cabins of aircrafts, hulls of submarines and bodies of rockets and missiles.
Kim, Heung Soo; Sohn, Jung Woo; Jeon, Juncheol; Choi, Seung-Bok
2013-01-01
In this work, active vibration control of an underwater cylindrical shell structure was investigated, to suppress structural vibration and structure-borne noise in water. Finite element modeling of the submerged cylindrical shell structure was developed, and experimentally evaluated. Modal reduction was conducted to obtain the reduced system equation for the active feedback control algorithm. Three Macro Fiber Composites (MFCs) were used as actuators and sensors. One MFC was used as an exciter. The optimum control algorithm was designed based on the reduced system equations. The active control performance was then evaluated using the lab scale underwater cylindrical shell structure. Structural vibration and structure-borne noise of the underwater cylindrical shell structure were reduced significantly by activating the optimal controller associated with the MFC actuators. The results provide that active vibration control of the underwater structure is a useful means to reduce structure-borne noise in water. PMID:23389344
Active vibration control of a submerged cylindrical shell by piezoelectric sensors and actuators
NASA Astrophysics Data System (ADS)
Kwak, Moon K.; Yang, Dong-Ho; Lee, Jae-Ha
2012-04-01
The active vibration control of a submerged cylindrical shell by piezoelectric sensors and actuators is investigated. The fluid is assumed to be inviscid and irrotational in developing a theoretical model. The cylindrical shell is modelled by using the Rayleigh- Ritz method based on the Donnell-Mushtari shell theory. The fluid motion is modelled based on the baffled shell model, which is applied to the fluid-structure interaction problem. The kinetic energy of the fluid is derived by solving the boundary-value problem. The resulting equations of motion are expressed in matrix form, which enables us to design control easily. The natural vibration characteristics of the cylindrical shell in air and in water are investigated both theoretically and experimentally. The experimental results show that the natural frequencies of the submerged cylindrical shell decrease to a great extent compared the natural frequencies in air. However, the natural mode shapes for lower modes are not different from the mode shapes in air. Two MFC actuators were glued to the shell and the positive position feedback control was applied. Experiments on the active vibration control of the submerged cylindrical shell were carried out in water tank. Both theoretical and experimental results showed that both vibrations and sound radiation can be suppressed by piezoelectric actuators.
NASA Astrophysics Data System (ADS)
Zheng, Ling; Zhang, Dongdong; Wang, Yi
2011-02-01
In this paper, the application of active constrained layer damping (ACLD) treatments is extended to the vibration control of cylindrical shells. The governing equation of motion of cylindrical shells partially treated with ACLD treatments is derived on the basis of the constitutive equations of elastic, piezoelectric and visco-elastic materials and an energy approach. The damping of a visco-elastic layer is modeled by the complex modulus formula. A finite element model is developed to describe and predict the vibration characteristics of cylindrical shells partially treated with ACLD treatments. A closed-loop control system based on proportional and derivative feedback of the sensor voltage generated by the piezo-sensor of the ACLD patches is established. The dynamic behaviors of cylindrical shells with ACLD treatments such as natural frequencies, loss factors and responses in the frequency domain are further investigated. The effects of several key parameters such as control gains, location and coverage of ACLD treatments on vibration suppression of cylindrical shells are also discussed. The numerical results indicate the validity of the finite element model and the control strategy approach. The potential of ACLD treatments in controlling vibration and sound radiation of cylindrical shells used as major critical structures such as cabins of aircraft, hulls of submarines and bodies of rockets and missiles is thus demonstrated.
Nonlinear vibrations of cylindrical shells with initial imperfections in a supersonic flow
NASA Astrophysics Data System (ADS)
Kurilov, E. A.; Mikhlin, Yu. V.
2007-09-01
The paper studies the dynamics of nonlinear elastic cylindrical shells using the theory of shallow shells. The aerodynamic pressure on the shell in a supersonic flow is found using piston theory. The effect of the flow and initial deflections on the vibrations of the shell is analyzed in the flutter range. The normal modes of both perfect shells in a flow and shells with initial imperfections are studied. In the latter case, the trajectories of normal modes in the configuration space are nearly rectilinear, only one mode determined by the initial imperfections being stable
Free and Forced Vibrations of Thick-Walled Anisotropic Cylindrical Shells
NASA Astrophysics Data System (ADS)
Marchuk, A. V.; Gnedash, S. V.; Levkovskii, S. A.
2017-03-01
Two approaches to studying the free and forced axisymmetric vibrations of cylindrical shell are proposed. They are based on the three-dimensional theory of elasticity and division of the original cylindrical shell with concentric cross-sectional circles into several coaxial cylindrical shells. One approach uses linear polynomials to approximate functions defined in plan and across the thickness. The other approach also uses linear polynomials to approximate functions defined in plan, but their variation with thickness is described by the analytical solution of a system of differential equations. Both approaches have approximation and arithmetic errors. When determining the natural frequencies by the semi-analytical finite-element method in combination with the divide and conqure method, it is convenient to find the initial frequencies by the finite-element method. The behavior of the shell during free and forced vibrations is analyzed in the case where the loading area is half the shell thickness
Su, Zhu; Jin, Guoyong
2016-11-01
This paper presents a Fourier spectral element method (FSEM) to analyze the free vibration of conical-cylindrical-spherical shells with arbitrary boundary conditions. Cylindrical-conical and cylindrical-spherical shells as special cases are also considered. In this method, each fundamental shell component (i.e., cylindrical, conical, and spherical shells) is divided into appropriate elements. The variational principle in conjunction with first-order shear deformation shell theory is employed to model the shell elements. Since the displacement and rotation components of each element are expressed as a linear superposition of nodeless Fourier sine functions and nodal Lagrangian polynomials, the global equations of the coupled shell structure can be obtained by adopting the assembly procedure. The Fourier sine series in the displacement field is introduced to enhance the accuracy and convergence of the solution. Numerical results show that the FSEM can be effectively applied to vibration analysis of the coupled shell structures. Numerous results for coupled shell structures with general boundary conditions are presented. Furthermore, the effects of geometric parameters and boundary conditions on the frequencies are investigated.
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Starnes, James H., Jr.
2004-01-01
The results of an experimental and numerical study of the effects of initial imperfections on the buckling response and failure of unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells are presented. The shells considered in the study have six different orthotropic or quasi-isotropic shell-wall laminates and two different shell-radius-to-thickness ratios. The numerical results include the effects of geometric shell-wall mid-surface imperfections, shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform end loads, and the effects of elastic boundary conditions. Selected cylinder parameter uncertainties were also considered. Results that illustrate the effects of imperfections and uncertainties on the nonlinear response characteristics, buckling loads and failure the shells are presented. In addition, a common failure analysis is used to predict material failures in the shells.
NASA Astrophysics Data System (ADS)
Lai, Changliang; Wang, Junbiao; Liu, Chuang
2014-10-01
Six typical composite grid cylindrical shells are constructed by superimposing three basic types of ribs. Then buckling behavior and structural efficiency of these shells are analyzed under axial compression, pure bending, torsion and transverse bending by finite element (FE) models. The FE models are created by a parametrical FE modeling approach that defines FE models with original natural twisted geometry and orients cross-sections of beam elements exactly. And the approach is parameterized and coded by Patran Command Language (PCL). The demonstrations of FE modeling indicate the program enables efficient generation of FE models and facilitates parametric studies and design of grid shells. Using the program, the effects of helical angles on the buckling behavior of six typical grid cylindrical shells are determined. The results of these studies indicate that the triangle grid and rotated triangle grid cylindrical shell are more efficient than others under axial compression and pure bending, whereas under torsion and transverse bending, the hexagon grid cylindrical shell is most efficient. Additionally, buckling mode shapes are compared and provide an understanding of composite grid cylindrical shells that is useful in preliminary design of such structures.
Dispersion analysis and measurement of circular cylindrical wedge-like acoustic waveguides.
Yu, Tai-Ho
2015-09-01
This study investigated the propagation of flexural waves along the outer edge of a circular cylindrical wedge, the phase velocities, and the corresponding mode displacements. Thus far, only approximate solutions have been derived because the corresponding boundary-value problems are complex. In this study, dispersion curves were determined using the bi-dimensional finite element method and derived through the separation of variables and the Hamilton principle. Modal displacement calculations clarified that the maximal deformations appeared at the outer edge of the wedge tip. Numerical examples indicated how distinct thin-film materials deposited on the outer surface of the circular cylindrical wedge influenced the dispersion curves. Additionally, dispersion curves were measured using a laser-induced guided wave, a knife-edge measurement scheme, and a two-dimensional fast Fourier transform method. Both the numerical and experimental results correlated closely, thus validating the numerical solution.
NASA Astrophysics Data System (ADS)
Meish, Yu. A.
2016-11-01
The forced vibrations of transversely reinforced elliptic cylindrical shells on an elastic foundation under nonstationary loads are studied using the Timoshenko-type theory of shells and rods. A numerical algorithm for solving problems of this class is developed. A numerical example for the case of distributed impulsive loading is given
The implosion of cylindrical shell structures in a high-pressure water environment
Ikeda, C. M.; Wilkerling, J.; Duncan, J. H.
2013-01-01
The implosion of cylindrical shell structures in a high-pressure water environment is studied experimentally. The shell structures are made from thin-walled aluminium and brass tubes with circular cross sections and internal clearance-fit aluminium end caps. The structures are filled with air at atmospheric pressure. The implosions are created in a high-pressure tank with a nominal internal diameter of 1.77 m by raising the ambient water pressure slowly to a value, Pc, just above the elastic stability limit of each shell structure. The implosion events are photographed with a high-speed digital movie camera, and the pressure waves are measured simultaneously with an array of underwater blast sensors. For the models with larger values of length-to-diameter ratio, L/D0, the tubes flatten during implosion with a two-lobe (mode 2) cross-sectional shape. In these cases, it is found that the pressure wave records scale primarily with Pc and the time scale (where Ri is the internal radius of the tube and ρ is the density of water), whereas the details of the structural design produce only secondary effects. In cases with smaller values of L/D0, the models implode with higher-mode cross-sectional shapes. Pressure signals are compared for various mode-number implosions of models with the same available energy, PcV , where V is the internal air-filled volume of the model. It is found that the pressure records scale well temporally with the time scale , but that the shape and amplitudes of the pressure records are strongly affected by the mode number. PMID:24353473
Stability of cylindrical shells with initial imperfections under the action of external pressure
NASA Astrophysics Data System (ADS)
Lopanitsyn, E. A.; Matveev, E. A.
2011-04-01
We use the equations of nonlinear theory of shallow shells to solve the problem of stability of thin elastic isotropic cylindrical shells, with small initial shape imperfections, that are under the action of external uniform pressure. The problem solution is constructed by the Rayleigh-Ritz method with the approximation of the shell midsurface displacement by double functional sums in trigonometric and beam functions. The system of nonlinear algebraic equations is solved by using the methods of continuation with respect to a close-to-best parameter. For the initial imperfections of the shells, we use their normalized deflections from the limit points of overcritical branches of the loading trajectories. We consider various cases of the shell fixation and support under loading by lateral and hydrostatic uniform pressure. We also construct the range of values of the critical pressure, which, with the maximal deviation of the shell shape from the cylindrical shape up to 30%, covers practically all known experimental data.
A cylindrical shell with an axial crack under skew-symmetric loading.
NASA Technical Reports Server (NTRS)
Yuceoglu, U.; Erdogan, F.
1973-01-01
The skew-symmetric problem for a cylindrical shell containing an axial crack is considered. It is assumed that the material has a special orthotropy - namely, that the shear modulus may be evaluated from the measured Young's moduli and Poisson ratios and is not an independent material constant. The problem is solved within the confines of an eighth-order linearized shallow shell theory. As numerical examples, the torsion of an isotropic cylinder and that of a specially orthotropic cylinder (titanium) are considered. The membrane and bending components of the stress intensity factor are calculated and are given as functions of a dimensionless shell parameter. In the torsion problem for the axially cracked cylinder the bending effects appear to be much more significant than that found for the circumferentially cracked cylindrical shell. Also, as the shell parameter increases, unlike the results found in the pressurized shell, the bending stresses around crack ends do not change sign.
NASA Astrophysics Data System (ADS)
Cao, Yin; Sun, Hongling; An, Fengyan; Li, Xiaodong
2012-05-01
A novel active control method of sound radiation from a cylindrical shell under axial excitations is proposed and theoretically analyzed. This control method is based on a pair of piezoelectric stack force actuators which are installed on the shell and parallel to the axial direction. The actuators are driven in phase and generate the same forces to control the vibration and the sound radiation of the cylindrical shell. The model considered is a fluid-loaded finite stiffened cylindrical shell with rigid end-caps and only low-frequency axial vibration modes are involved. Numerical simulations are performed to explore the required control forces and the optimal mounting positions of actuators under different cost functions. The results show that the proposed force actuators can reduce the radiated sound pressure of low-frequency axial modes in all directions.
A Simplified Method of Elastic-Stability Analysis for Thin Cylindrical Shells
NASA Technical Reports Server (NTRS)
Batdorf, S B
1947-01-01
This paper develops a new method for determining the buckling stresses of cylindrical shells under various loading conditions. In part I, the equation for the equilibrium of cylindrical shells introduced by Donnell in NACA report no. 479 to find the critical stresses of cylinders in torsion is applied to find critical stresses for cylinders with simply supported edges under other loading conditions. In part II, a modified form of Donnell's equation for the equilibrium of thin cylindrical shells is derived which is equivalent to Donnell's equation but has certain advantages in physical interpretation and in ease of solution, particularly in the case of shells having clamped edges. The question of implicit boundary conditions is also considered.
NASA Astrophysics Data System (ADS)
Latifov, F. S.; Seifullaev, F. A.; Alyev, Sh. Sh.
2016-07-01
This paper presents the results of determining the free vibration frequency of a structurally anisotropic, cylindrical fiberglass shell reinforced by annular ribs and containing flowing fluid. Boundary Navier conditions are imposed on the ends of the shell. Natural vibration frequencies are calculated as dependences of the frequency on the fiberglass winding angle and fluid flow velocity for different values of the wave formation parameters and the parameters characterizing the geometric dimensions of the shell.
A numerical algorithm of tooth profile of non-circular cylindrical gear
NASA Astrophysics Data System (ADS)
Wang, Xuan
2017-08-01
Non-circular cylindrical gear (NCCG) is a common form of non-circular gear. Different from the circular gear, the tooth profile equation of NCCG cannot be obtained. So it is necessary to use a numerical algorithm to calculate the tooth profile of NCCG. For this reason, this paper presents a simple and highly efficient numerical algorithm to obtain the tooth profile of NCCG. Firstly, the mathematical model of tooth profile envelope of NCCG is established based on the principle of gear shaping, and the tooth profile envelope of NCCG is obtained. Secondly, the polar radius and polar angle of shaper cutter tooth profile are chosen as the criterions, by which the points of NCCG tooth cogging can be screened out. Finally, the boundary of tooth cogging points is extracted by a distance criterion and correspondingly the tooth profile of NCCG is obtained.
Stress Analysis of Bolted, Segmented Cylindrical Shells Exhibiting Flange Mating-Surface Waviness
NASA Technical Reports Server (NTRS)
Knight, Norman F., Jr.; Phillips, Dawn R.; Raju, Ivatury S.
2009-01-01
Bolted, segmented cylindrical shells are a common structural component in many engineering systems especially for aerospace launch vehicles. Segmented shells are often needed due to limitations of manufacturing capabilities or transportation issues related to very long, large-diameter cylindrical shells. These cylindrical shells typically have a flange or ring welded to opposite ends so that shell segments can be mated together and bolted to form a larger structural system. As the diameter of these shells increases, maintaining strict fabrication tolerances for the flanges to be flat and parallel on a welded structure is an extreme challenge. Local fit-up stresses develop in the structure due to flange mating-surface mismatch (flange waviness). These local stresses need to be considered when predicting a critical initial flaw size. Flange waviness is one contributor to the fit-up stress state. The present paper describes the modeling and analysis effort to simulate fit-up stresses due to flange waviness in a typical bolted, segmented cylindrical shell. Results from parametric studies are presented for various flange mating-surface waviness distributions and amplitudes.
NASA Technical Reports Server (NTRS)
El-Raheb, M.; Wagner, P.
1985-01-01
In the first part of the present work concerning the coupled elastic and acoustic response of a system of cylindrical and toroidal shells enclosing an acoustic medium, the theoretical model for the cylindrical and toroidal segments' elastodynamics incorporates an elastic simulation based on transfer matrices, while the acoustic simulation adapts Green's function and curved surface elements. The coupled response is determined by the equilibrium of the acoustic pressure and internal elastic reactions of the shell, and compatibility between acoustic and elastic accelerations at the shell-fluid interface. The second part of this work obtains and discusses numerical results based on the theory for the cases of shell configurations having a plane of symmetry, as well as asymmetric ones. The inadequacy of beam theory in modeling the response of short, thin shell configurations at frequencies above the fundamental elastic resonance is demonstrated.
Electromagnetic Casimir densities for a cylindrical shell on de Sitter space
NASA Astrophysics Data System (ADS)
Saharian, A. A.; Manukyan, V. F.; Saharyan, N. A.
2016-12-01
Complete set of cylindrical modes is constructed for the electromagnetic field inside and outside a cylindrical shell in the background of (D + 1)-dimensional dS space-time. On the shell, the field obeys the generalized perfect conductor boundary condition. For the Bunch-Davies vacuum state, we evaluate the vacuum expectation values (VEVs) of the electric field squared and of the energy-momentum tensor. The shell-induced contributions are explicitly extracted. In this way, for points away from the shell, the renormalization is reduced to the one for the VEVs in the boundary-free dS bulk. As a special case, the VEVs are obtained for a cylindrical shell in the (D + 1)-dimensional Minkowski bulk. We show that the shell-induced contribution in the electric field squared is positive for both the interior and exterior regions. The corresponding Casimir-Polder forces are directed toward the shell. The vacuum energy-momentum tensor, in addition to the diagonal components, has a nonzero off-diagonal component corresponding to the energy flux along the direction normal to the shell. This flux is directed from the shell in both the exterior and interior regions. For points near the shell, the leading terms in the asymptotic expansions for the electric field squared and diagonal components of the energy-momentum tensor are obtained from the corresponding expressions in the Minkowski bulk replacing the distance from the shell by the proper distance in the dS bulk. The influence of the gravitational field on the local characteristics of the vacuum is essential at distances from the shell larger than the dS curvature radius. The results are extended for confining boundary conditions of flux tube models in QCD.
Higher-Order Thickness Expansions for Cylindrical Shells
1991-09-01
4-5 iv Page 4.4 Element Independent Stiffness Formulation ............. 4-9 4.5 Symbolic Generation of...Arbitrary Shell . . . . A-I v Page A.2 Midsurface Strain Components for the Arbitrary Shell with a General Quartic Displacement Field Assumption...MACSYMA Routine for Elemental Codes Generation .... G-1 Bibliography ........................................... BIB-1 Vita
Optimal design of geodesically stiffened composite cylindrical shells
NASA Technical Reports Server (NTRS)
Gendron, G.; Gurdal, Z.
1992-01-01
An optimization system based on general-purpose finite element code CSM Testbed and optimization program ADS is described. The system can be used to obtain minimum-mass designs of composite shell structures with complex stiffening arrangements. Ply thicknesses, ply orientations, and stiffener heights can be used as design variables. Buckling, displacement, and material failure constraints can be imposed on the design. The system is used to conduct a preliminary design study of geodesically stiffened shells. For comparison purposes, optimal designs of unstiffened shells, and ring and longitudinal stringer stiffened shells are also studied. Trends in the design of geodesically stiffened shells are identified. Features that enhance the capabilities and efficiency of the design system are described.
Analysis on Node Position of Imperfect Resonators for Cylindrical Shell Gyroscopes
Wang, Zidan; Wu, Yulie; Xi, Xiang; Zhang, Yongmeng; Wu, Xuezhong
2016-01-01
For cylindrical shell gyroscopes, node position of their operating eigenmodes has an important influence on the gyroscopes’ performance. It is considered that the nodes are equally separated from each other by 90° when the resonator vibrates in the standing wave eigenmode. However, we found that, due to manufacturing errors and trimming, the nodes may not be equally distributed. This paper mainly analyzes the influences of unbalanced masses on the cylindrical resonators’ node position, by using FEM simulation and experimental measurement. PMID:27483284
Dynamics of a Discretely Reinforced Cylindrical Shell Under a Local Impulsive Load
NASA Astrophysics Data System (ADS)
Lugovoi, P. Z.; Sirenko, V. N.; Skosarenko, Yu. V.; Batutina, T. Ya.
2017-03-01
A procedure and software for studying the dynamics of a reinforced cylindrical shell on an elastic foundation are developed. The shell is under local loads distributed over small areas and varying linearly during a short time. The stringers are described by a structurally orthotropic model and the ring ribs by a discrete model. The candidate solution is expanded into series of natural modes. The influence of a local load on the deformation parameters of the shell is studied using a test example. Conclusions on the effect of the pulse shape, the time of action of the external forces, and the reinforcement on the strain state of the shell are drawn
NASA Astrophysics Data System (ADS)
Semenyuk, N. P.; Trach, V. M.
2016-11-01
An approach to solving the problem of the nonlinear deformation of orthotropic cylindrical shells is proposed. On the surface of the shell, there is a local deflection bounded by segments of the coordinate lines. The Timoshenko-Mindlin shell theory, the Byskov-Hatchinson asymptotic method, and the continuous continuation method for solving nonlinear algebraic equations are used. To determine the critical loads and deformation paths, it is necessary to estimate the number of interacting modes sufficient to achieve satisfactory accuracy. Examples of analyzing composite shells with an initial local deflection of positive or negative amplitude are given
Stability and Post-Buckling Behavior of Orthotropic Cylindrical Shells With Local Deflections
NASA Astrophysics Data System (ADS)
Semenyuk, N. P.; Zhukova, N. B.
2016-05-01
A procedure for analytical solution of the problem of the stability and post-buckling behavior of orthotropic cylindrical shells under external pressure or axial compression with allowance for transverse shears is developed. The shells are geometrically imperfect due to the presence of a local deflection. The problem is solved by analyzing the interaction of the modes that represent the critical loads of the perfect shell and using the Byskov-Hutchinson method. Equilibrium curves for both shells are plotted using the method of continuous loading
Influence of transverse shear on an axial crack in a cylindrical shell
NASA Technical Reports Server (NTRS)
Krenk, S.
1978-01-01
An axial crack in a cylindrical shell is investigated by use of a 10th order shell theory, which accounts for transverse shear deformations as well as a special kind of orthotropy. The symmetric problem is formulated in terms of two coupled singular integral equations, which are solved numerically. The asymptotic membrane and bending stress fields ahead of the crack are found to be self similar. Stress intensity factors are given as a function of the shell parameter for various values of the ratio shell radius to shell thickness. Considerable differences from 8th order shell theory results are found for the bending stresses, while the membrane stresses of the 8th order theory seems to be a lower limit reached for very thin shells.
Instability of the vertically forced surface wave in a circular cylindrical container
NASA Astrophysics Data System (ADS)
Jian, Yong-Jun; E, Xue-Quan
2004-10-01
The nonlinear amplitude equation, which was derived by Jian Yongjun employing expansion of two-time scales in inviscid fluids in a vertically oscillating circular cylindrical vessel, is modified by introducing a damping term due to the viscous dissipation of this system. Instability of the surface wave is analysed and properties of the solutions of the modified equation are determined together with phase-plane trajectories. A necessary condition of forming a stable surface wave is obtained and unstable regions are illustrated. Research results show that the stable pattern of surface wave will not lose its stability to an infinitesimal disturbance.
Nonlinear propagation of coupled electromagnetic waves in a circular cylindrical waveguide
NASA Astrophysics Data System (ADS)
Valovik, D. V.; Smol'kin, E. Yu.
2017-08-01
The problem of the propagation of coupled surface electromagnetic waves in a two-layer cylindrical circular waveguide filled with an inhomogeneous nonlinear medium is considered. A nonlinear coupled TE-TM wave is characterized by two (independent) frequencies ωe and ωm and two propagation constants {\\widehat γ _e} and {\\widehat γ _m}. The physical problem reduces to a nonlinear two-parameter eigenvalue problem for a system of nonlinear ordinary differential equations. The existence of eigenvalues ({\\widehat γ _e}, {\\widehat γ _m}) in proven and intervals of their localization are determined.
Simultaneous and Running Impulsive Loading of Cylindrical Shells
1975-06-01
the cylindrical tesi fixture at one of its ends, and the load would run longitiiri-;: nally in the axial direction of the cylinder for those areas...LEAD CYLINDER - TEST 26 DAMAGE "RODUCED BY A SASH LOAD OF 4. S8 KILOTAPS ALMIU CYLINDER- TS :--j2 7~ DAMAG PR DU E BYASS O DOF44 ,LT 12
Casimir Forces for Robin Scalar Field on Cylindrical Shell in de Sitter Space
NASA Astrophysics Data System (ADS)
Setare, M. R.
2006-02-01
The Casimir stress on a cylindrical shell in background of conformally flat spacetime for massless scalar field is investigated. In the general case of Robin (mixed) boundary condition, formulae are derived for the vacuum expectation values of the energy momentum tensor and vacuum forces acting on boundaries. The special case of the dS bulk is considered then different cosmological constants are assumed for the space inside and outside of the shell to have general results applicable to the case of cylindrical domain wall formations in the early universe.
Schaden, Martin
2010-08-15
The leading semiclassical estimates of the electromagnetic Casimir stresses on a spherical and a cylindrical metallic shell are within 1% of the field theoretical values. The electromagnetic Casimir energy for both geometries is given by two decoupled massless scalars that satisfy conformally covariant boundary conditions. Surface contributions vanish for smooth metallic boundaries, and the finite electromagnetic Casimir energy in leading semiclassical approximation is due to quadratic fluctuations about periodic rays in the interior of the cavity only. Semiclassically, the nonvanishing Casimir energy of a metallic cylindrical shell is almost entirely due to Fresnel diffraction.
Non-axisymmetric Dynamic Buckling of Cylindrical Shells under Axial Step Load
NASA Astrophysics Data System (ADS)
Meng, Hao; Han, Zhi-Jun; Lu, Guo-Yun
2016-05-01
Considering the effects of first-order shear deformation theory (FSDT) and stress wave, the dynamic buckling governing equations of cylindrical shells under axial step load are derived. Based on the Ritz method and Variable Separation method, the analytical solution of the critical load on the dynamic buckling can be obtained. The influences of first-order shear deformation effect, boundary conditions, the number of circumferential waves, etc. on dynamic buckling load are discussed by using MATLAB software and the results show that dynamic buckling of cylindrical shells occuresmore easily when considering shear effect.
NASA Astrophysics Data System (ADS)
Ansari, R.; Rouhi, S.; Aryayi, M.
2016-01-01
The vibrational behavior of double-walled carbon nanotubes is studied by the use of the molecular structural and cylindrical shell models. The spring elements are employed to model the van der Waals interaction. The effects of different parameters such as geometry, chirality, atomic structure and end constraint on the vibration of nanotubes are investigated. Besides, the results of two aforementioned approaches are compared. It is indicated that by increasing the nanotube side length and radius, the computationally efficient cylindrical shell model gives rational results.
NASA Astrophysics Data System (ADS)
Lee, Min Jin; Hong, Helen; Chung, Jin Wook
2014-03-01
We propose an automatic vessel segmentation method of vertebral arteries in CT angiography using combined circular and cylindrical model fitting. First, to generate multi-segmented volumes, whole volume is automatically divided into four segments by anatomical properties of bone structures along z-axis of head and neck. To define an optimal volume circumscribing vertebral arteries, anterior-posterior bounding and side boundaries are defined as initial extracted vessel region. Second, the initial vessel candidates are tracked using circular model fitting. Since boundaries of the vertebral arteries are ambiguous in case the arteries pass through the transverse foramen in the cervical vertebra, the circle model is extended along z-axis to cylinder model for considering additional vessel information of neighboring slices. Finally, the boundaries of the vertebral arteries are detected using graph-cut optimization. From the experiments, the proposed method provides accurate results without bone artifacts and eroded vessels in the cervical vertebra.
NASA Technical Reports Server (NTRS)
Delale, F.; Erdogan, F.
1981-01-01
An approximate solution was obtained for a cylindrical shell containing a part-through surface crack. It was assumed that the shell contains a circumferential or axial semi-elliptic internal or external surface crack and was subjected to a uniform membrane loading or a uniform bending moment away from the crack region. A Reissner type theory was used to account for the effects of the transverse shear deformations. The stress intensity factor at the deepest penetration point of the crack was tabulated for bending and membrane loading by varying three dimensionless length parameters of the problem formed from the shell radius, the shell thickness, the crack length, and the crack depth. The upper bounds of the stress intensity factors are provided by the results of the elasticity solution obtained from the axisymmetric crack problem for the circumferential crack, and that found from the plane strain problem for a circular ring having a radial crack for the axial crack. The line-spring model gives the expected results in comparison with the elasticity solutions. Results also compare well with the existing finite element solution of the pressurized cylinder containing an internal semi-elliptic surface crack.
Liu, Chun-Chuan; Li, Feng-Ming; Chen, Zhao-Bo; Yue, Hong-Hao
2013-02-01
The method of reverberation ray matrix is extended to investigate the transient wave propagation and early short time transient responses of the ring stiffened laminated composite cylindrical shells subjected to impact loads. The ring stiffened laminated cylindrical shells are modeled as the continuous coupling systems between the vibration of the un-stiffened laminated cylindrical shell and the motion of the curved beams. The dynamic models of the laminated cylindrical shell and curved beams in the Laplace phase space are established on the basis of the first order shear deformation theory. The reverberation ray matrix can be determined by the boundary and continuous conditions of the ring stiffened laminated cylindrical shell. Using the fast Fourier transform algorithm, the dynamic responses of the ring stiffened laminated cylindrical shells can be computed. Through the numerical simulations, it can be seen that the early short time transient accelerations of the ring stiffened laminated cylindrical shells under impact loads are very large, while the early short time transient shear strains and displacements are very small. Furthermore, the influences of the ring stiffener number and impact load types on the early short time transient responses of the ring stiffened laminated cylindrical shells are also investigated.
Scattering of Cylindrical Electric Field Waves from an Elliptical Dielectric Cylindrical Shell.
1982-12-01
shell is thin when compared to wavelength. This will simplify the numerical analysis and is consistent with Schneider’s work [4:281. Scope This study...field from the line sources and the scattered field from the rest of the shell. The problem in the mathematical analysis of (2.8) is the...reference for the implementation of the simusoidal basis function is Richmond’s report, Computer Analysis of Three-Dimensional Wire Antennas from The Ohio
Kelker, D.; Langenberg, C.W.
1988-08-01
A folded surface can be represented by the orientation of normals to the surface measured at several locations. When plotted on the unit sphere, the pattern of normals determines the type of fold. Poles from a cylindrical fold give a great circle on the unit sphere, whereas poles of a circular conical fold give a small circle, and poles from an elliptical conical fold give the projection of an ellipse onto the surface of the sphere. Several statistical tests that appear in the literature for classifying folds are discussed and compared. All but one of the tests use quantities obtained from an iterative least-squares procedure that fits the appropriate curve on the sphere. The classification procedure is illustrated with folds from the Canadian Rocky Mountains and uses for examples a cylindrical fold and a circular conical fold from the Smoky River coal field near Grande Cache, Alberta, and an elliptical conical fold near Jasper, Alberta. This methodology has resulted in new coal reserves in the Grande Cache area.
Circular-cylindrical flux-rope analytical model for Magnetic Clouds
NASA Astrophysics Data System (ADS)
Nieves-Chinchilla, Teresa; Linton, Mark; Hidalgo, Miguel A.; Vourlidas, Angelos; Savani, Neel P.; Szabo, Adam; Farrugia, Charlie; Yu, Wenyuan
2016-05-01
We present an analytical model to describe magnetic flux-rope topologies. When these structures are observed embedded in Interplanetary Coronal Mass Ejections (ICMEs) with a depressed proton temperature, they are called Magnetic Clouds ( MCs). The model extends the circular-cylindrical concept of Hidalgo et al. (2000) by introducing a general form for the radial dependence of the current density. This generalization provides information on the force distribution inside the flux rope in addition to the usual parameters of MC geometrical information and orientation.The generalized model provides flexibility for implementation in 3D MHD simulations. Here, we evaluate its performance in the reconstruction of MCs in in-situ observations. Four Earth directed ICME events, observed by the Wind spacecraft, are used to validate the technique. The events are selected from the ICME Wind list with the magnetic obstacle boundaries chosen consistently with the magnetic fi eld and plasma in situ observations and with a new parameter (EPP, Electron Pitch angle distribution Parameter) which quantifies the bidirectionally of theplasma electrons. The goodness of the fit is evaluated with a single correlation parameter to enable comparative analysis of the events. In general, at first glance, the model fits the selected events very well. However, a detailed analysis of events with signatures of significant compression indicates the need to explore geometries other than the circular-cylindrical.
Influence of transverse shear on an axial crack in a cylindrical shell
NASA Technical Reports Server (NTRS)
Krenk, S.
1976-01-01
An axial crack in a cylindrical shell is investigated by use of a 10th order shell theory, which accounts for transverse shear deformations as well as a special kind of orthotropy. The symmetric problem is formulated in terms of two coupled singular integral equations, which are solved numerically. The asymptotic membrane and bending stress fields ahead of the crack are found to be self similar. Stress intensity factors are given as a function of the shell parameter for various values of the ratio crack length to shell thickness. considerable differences from 8th order shell theory results are found for the bending stresses, while the membrane stresses of the 8th order theory seem to be a lower limit reached for very thin shells.
Influence of transverse shear on an axial crack in a cylindrical shell
NASA Technical Reports Server (NTRS)
Krenk, S.
1977-01-01
An axial crack in a cylindrical shell is investigated by use of a 10th order shell theory, which accounts for transverse shear deformations as well as a special kind of orthotropy. The symmetric problem is formulated in terms of two coupled singular integral equations, which are solved numerically. The asymptotic membrane and bending stress fields ahead of the crack are found to be self similar. Stress intensity factors are given as a function of the shell parameter for various values of the ratio crack length to shell thickness. Considerable differences from 8th order shell theory results are found for the bending stresses, while the membrane stresses of the 8th order theory seems to be a lower limit reached for very thin shells.
NASA Technical Reports Server (NTRS)
Rose, Cheryl A.; Young, Richard D.; Starnes, James H., Jr.
1999-01-01
Results of a geometrically nonlinear finite element parametric study to determine curvature correction factors or "bulging factors" that account for increased stresses due to curvature for longitudinal cracks in unstiffened pressurized cylindrical shells are presented. Geometric parameters varied in the study include the shell radius, the shell wall thickness, and the crack length. The major results are presented in graphs of the bulging factor as a function of the applied load and as a function of geometric parameters that include the shell radius, the shell thickness and the crack length. The computed bulging factors are compared with solutions based on linear shallow shell theory, and with semi-empirical solutions that approximately account for the nonlinear deformation in the vicinity of the crack. The effect of biaxial loads on the computed bulging factors is also discussed.
The crack problem in a reinforced cylindrical shell
NASA Technical Reports Server (NTRS)
Yahsi, O. S.; Erdogan, F.
1986-01-01
A partially reinforced cylinder containing an axial through crack is considered. The reinforcement is assumed to be fully bonded to the main cylinder. The composite cylinder is thus modelled by a nonhomogeneous shell having a step change in the elastic properties at the z = 0 plane, z being the axial coordinate. Using a Reissner type transverse shear theory the problem is reduced to a pair of singular integral equations. In the special case of a crack tip touching the bimaterial interface it is shown that the dominant parts of the kernels of the integral equations associated with both membrane loading and bending of the shell reduce to the generalized Cauchy kernel obtained for the corresponding plane stress case. The integral equations are solved and the stress intensity factors are given for various crack and shell dimensions. A bonded fiberglass reinforcement which may serve as a crack arrestor is used as an example.
The crack problem in a reinforced cylindrical shell
NASA Technical Reports Server (NTRS)
Yahsi, O. S.; Erdogan, F.
1986-01-01
In this paper a partially reinforced cylinder containing an axial through crack is considered. The reinforcement is assumed to be fully bonded to the main cylinder. The composite cylinder is thus modelled by a nonhomogeneous shell having a step change in the elastic properties at the z=0 plane, z being the axial coordinate. Using a Reissner type transverse shear theory the problem is reduced to a pair of singular integral equations. In the special case of a crack tip touching the bimaterial interface it is shown that the dominant parts of the kernels of the integral equations associated with both membrane loading and bending of the shell reduce to the generalized Cauchy kernel obtained for the corresponding plane stress case. The integral equations are solved and the stress intensity factors are given for various crack and shell dimensions. A bonded fiberglass reinforcement which may serve as a crack arrestor is used as an example.
Cylindrical acoustic levitator/concentrator having non-circular cross-section
Kaduchak, Gregory; Sinha, Dipen N.
2003-11-11
A low-power, inexpensive acoustic apparatus for levitation and/or concentration of aerosols and small liquid/solid samples having particulates up to several millimeters in diameter in air or other fluids is described. It is constructed from a commercially available, hollow piezoelectric crystal which has been formed with a cylindrical cross-section to tune the resonance frequency of the breathing mode resonance of the crystal to that of the interior cavity of the cylinder. When the resonance frequency of the interior cylindrical cavity is matched to the breathing mode resonance of the cylindrical piezoelectric transducer, the acoustic efficiency for establishing a standing wave pattern in the cavity is high. By deforming the circular cross-section of the transducer, the acoustic force is concentrated along axial regions parallel to the axis of the transducer. The cylinder does not require accurate alignment of a resonant cavity. The concentrated regions of acoustic force cause particles in the fluid to concentrate within the regions of acoustic force for separation from the fluid.
Buckling Behavior of Compression-Loaded Composite Cylindrical Shells with Reinforced Cutouts
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Starnes, James H., Jr.
2002-01-01
Results from a numerical study of the response of thin-wall compression-loaded quasi-isotropic laminated composite cylindrical shells with reinforced and unreinforced square cutouts are presented. The effects of cutout reinforcement orthotropy, size, and thickness on the nonlinear response of the shells are described. A high-fidelity nonlinear analysis procedure has been used to predict the nonlinear response of the shells. The analysis procedure includes a nonlinear static analysis that predicts stable response characteristics of the shells and a nonlinear transient analysis that predicts unstable dynamic buckling response characteristics. The results illustrate how a compression-loaded shell with an unreinforced cutout can exhibit a complex nonlinear response. In particular, a local buckling response occurs in the shell near the cutout and is caused by a complex nonlinear coupling between local shell-wall deformations and in-plane destabilizing compression stresses near the cutout. In general, the addition of reinforcement around a cutout in a compression-loaded shell can retard or eliminate the local buckling response near the cutout and increase the buckling load of the shell, as expected. However, results are presented that show how certain reinforcement configurations can actually cause an unexpected increase in the magnitude of local deformations and stresses in the shell and cause a reduction in the buckling load. Specific cases are presented that suggest that the orthotropy, thickness, and size of a cutout reinforcement in a shell can be tailored to achieve improved response characteristics.
NASA Astrophysics Data System (ADS)
Cao, Xiongtao; Shi, Lei; Zhang, Xusheng; Jiang, Guohe
2013-06-01
Active control of sound radiation from piezoelectric laminated cylindrical shells is theoretically investigated in the wavenumber domain. The governing equations of the smart cylindrical shells are derived by using first-order shear deformation theory. The smart layer is divided into lots of actuator patches, each of which is coated with two very thin electrodes at its inner and outer surfaces. Proportional derivative negative feedback control is applied to the actuator patches and the stiffness of the controlled layer is derived in the wavenumber domain. The equivalent driving forces and moments generated by the piezoelectric layer can produce distinct sound radiation. Large actuator patches cause strong wavenumber conversion and fluctuation of the far-field sound pressure, and do not make any contribution to sound reduction. Nevertheless, suitable small actuator patches induce weak wavenumber conversion and play an important role in the suppression of vibration and acoustic power. The derivative gain of the active control can effectively suppress sound radiation from smart cylindrical shells. The effects of small proportional gain on the sound field can be neglected, but large proportional gain has a great impact on the acoustic radiation of cylindrical shells. The influence of different piezoelectric materials on the acoustic power is described in the numerical results.
A new stability criterion for general cylindrical thin-shell wormholes
NASA Astrophysics Data System (ADS)
Chakraborty, Subenoy
2017-03-01
The paper deals with a detailed study of the stability criteria for general static cylindrical thin-shell wormhole.The stability analysis is done under perturbations preserving the symmetry for two definitions of the throat of the wormhole separately. Finally, the stability conditions are discussed both geometrically and physically.
Dynamic Instability of an Elastic Cylindrical Shell Excited by a Transient Acoustic Wave.
1979-07-12
Aeronautics and Space Administra- tion., Washington, D.C., 1973. 21. Goodier , J. N., and Mclvor, I. K., "The Elastic Cylindrical Shell Under Nearly...8217. DISTRIBUTION LIST DEPARTMENT OF DEFENSE DEPARTMENT OF THE NAVY (Continued) Defense Advanced Rsch. Proj. Agency David Taylor Naval Ship R & D Ctr. ATTN
The Stability and Load-Carrying Capacity of Cylindrical Shells with Axisymmetric Dents
NASA Astrophysics Data System (ADS)
Gavrilenko, G. D.; Matsner, V. I.
2002-07-01
The classical method of stability analysis and the reduced-stiffness method are used to evaluate the critical loads and the lower bounds of sensitivity to imperfections in buckling of longitudinally loaded elastic cylindrical shells with local imperfections in the form of axisymmetric longitudinal dents.
Optimal design of geodesically stiffened composite cylindrical shells
NASA Technical Reports Server (NTRS)
Gendron, G.; Guerdal, Z.
1992-01-01
An optimization system based on the finite element code Computations Structural Mechanics (CSM) Testbed and the optimization program, Automated Design Synthesis (ADS), is described. The optimization system can be used to obtain minimum-weight designs of composite stiffened structures. Ply thickness, ply orientations, and stiffener heights can be used as design variables. Buckling, displacement, and material failure constraints can be imposed on the design. The system is used to conduct a design study of geodesically stiffened shells. For comparison purposes, optimal designs of unstiffened shells and shells stiffened by rings and stingers are also obtained. Trends in the design of geodesically stiffened shells are identified. An approach to include local stress concentrations during the design optimization process is then presented. The method is based on a global/local analysis technique. It employs spline interpolation functions to determine displacements and rotations from a global model which are used as 'boundary conditions' for the local model. The organization of the strategy in the context of an optimization process is described. The method is validated with an example.
Elastic wave propagation in a joined cylindrical-conical-cylindrical shell.
NASA Technical Reports Server (NTRS)
Rose, J. L.; Mortimer, R. W.; Blum, A.
1972-01-01
The problem of longitudinal impact of a thin finite joined shell, consisting of a cylinder-truncated cone-cylinder, is analyzed both experimentally and analytically. The model analyzed is a 1/100 scale replica of a portion of the Apollo/Saturn V vehicle. Experimental results were obtained from a drop-test system. Longitudinal and circumferential strain pulses were monitored on each section of the joined shell. The velocity of the impacter ring prior to impact was measured and used as a boundary condition in the solution of the governing partial differential equations. A bending theory, including transverse shear, radial inertia, and rotary inertia effects, was used to analyze the finite joined shell. Good agreement between analytical and experimental strain profiles was obtained.
Elastic wave propagation in a joined cylindrical-conical-cylindrical shell.
NASA Technical Reports Server (NTRS)
Rose, J. L.; Mortimer, R. W.; Blum, A.
1972-01-01
The problem of longitudinal impact of a thin finite joined shell, consisting of a cylinder-truncated cone-cylinder, is analyzed both experimentally and analytically. The model analyzed is a 1/100 scale replica of a portion of the Apollo/Saturn V vehicle. Experimental results were obtained from a drop-test system. Longitudinal and circumferential strain pulses were monitored on each section of the joined shell. The velocity of the impacter ring prior to impact was measured and used as a boundary condition in the solution of the governing partial differential equations. A bending theory, including transverse shear, radial inertia, and rotary inertia effects, was used to analyze the finite joined shell. Good agreement between analytical and experimental strain profiles was obtained.
Active Control of Vibrations and Noise of Double Wall Cylindrical Shells
NASA Astrophysics Data System (ADS)
Wang, C.-Y.; Vaicaitis, R.
1998-10-01
Active control of vibrations and noise transmissions of double wall composite cylindrical shells using pairs of spatially discrete piezoelectric actuators is investigated. The velocity feedback and sound pressure rate feedback control procedures are developed. The inner and outer shells which are separated by a soft core are modelled by Love's thin shell theory for laminate composite materials and the inputs are taken as stationary random pressures and/or random point forces. A galerkin-like procedure is used to obtain solutions of the governing structural-acoustic equations. Parametric studies are performed to demonstrate the effect of actuator placement, actuator size, control gains, spillover, structural and acoustic damping characteristics
Vibroacoustic Response of a Double-Walled Cylindrical FGM Shell with a Porous Sandwiched Layer
NASA Astrophysics Data System (ADS)
Ramezani, H.; Talebitooti, R.
2015-11-01
The transmission loss of sound through a cylindrical structure whose walls sandwich a layer of porous material is predicted on the basis of the classical shell theory for shells made of functionally graded materials (FGMs). FGM shells composed of metal and ceramic, with three different distributions (power-law, sigmoid, or exponential) of their volume fractions across the wall thickness, are considered. The porous layer is modeled as a fluid with equivalent properties. The transmission loss through the multilayered structure is obtained analytically in a broad frequency band. To validate the results found, they are compared with some known ones. The effects of variation in the volume fractions of materials are also studied.
NASA Astrophysics Data System (ADS)
Tryka, Stanislaw
2007-04-01
A general formula and some special integral formulas were presented for calculating radiative fluxes incident on a circular plane from a planar multiple point source within a coaxial cylindrical enclosure perpendicular to the source. These formula were obtained for radiation propagating in a homogeneous isotropic medium assuming that the lateral surface of the enclosure completely absorbs the incident radiation. Exemplary results were computed numerically and illustrated with three-dimensional surface plots. The formulas presented are suitable for determining fluxes of radiation reaching planar circular detectors, collectors or other planar circular elements from systems of laser diodes, light emitting diodes and fiber lamps within cylindrical enclosures, as well as small biological emitters (bacteria, fungi, yeast, etc.) distributed on planar bases of open nontransparent cylindrical containers.
Numerical Simulation of the Layer-Bylayer Destruction of Cylindrical Shells Under Explosive Loading
NASA Astrophysics Data System (ADS)
Abrosimov, N. A.; Novoseltseva, N. A.
2015-09-01
A technique of numerical analysis of the influence of reinforcement structure on the nature of the dynamic response and the process of layer-by-layer destruction of layered fiberglass cylindrical shells under an axisymmetric internal explosive loading is elaborated. The kinematic model of deformation of the laminate package is based on a nonclassical theory of shells. The geometric dependences are based on simple quadratic relations of the nonlinear theory of elasticity. The relationship between the stress and strain tensors are established by using Hooke's law for orthotropic bodies with account of degradation of stiffness characteristics of the multilayer composite due to the local destruction of some its elementary layers. An energetically consistent system of dynamic equations for composite cylindrical shells is obtained by minimizing the functional of total energy of the shell as a three-dimensional body. The numerical method for solving the formulated initial boundary-value problem is based on an explicit variational-difference scheme. Results confirming the reliability of the method used to analyze the influence of reinforcement structure on the character of destruction and the bearing capacity of pulse-loaded cylindrical shells are presented.
Free vibration of composite skewed cylindrical shell panel by finite element method
NASA Astrophysics Data System (ADS)
Haldar, Salil
2008-03-01
In this paper a composite triangular shallow shell element has been used for free vibration analysis of laminated composite skewed cylindrical shell panels. In the present element first-order shear deformation theory has been incorporated by taking transverse displacement and bending rotations as independent field variables. The interpolation function used to approximate transverse displacement is one order higher than for bending rotations. This has made the element free from locking in shear. Two types of mass lumping schemes have been recommended. In one of the mass lumping scheme the effect of rotary inertia has been incorporated in the element formulations. Free vibration of skewed composite cylindrical shell panels having different thickness to radius ratios ( h/R=0.01-0.2), length to radius ratios ( L/R), number of layers and fiber orientation angles have been analyzed following the shallow shell method. The results for few examples obtained in the present analysis have compared with the published results. Some new results of composite skewed cylindrical shell panels have been presented which are expected to be useful to future research in this direction.
Active structural acoustic control of a smart cylindrical shell using a virtual microphone
NASA Astrophysics Data System (ADS)
Loghmani, Ali; Danesh, Mohammad; Kwak, Moon K.; Keshmiri, Mehdi
2016-04-01
This paper investigates the active structural acoustic control of sound radiated from a smart cylindrical shell. The cylinder is equipped with piezoelectric sensors and actuators to estimate and control the sound pressure that radiates from the smart shell. This estimated pressure is referred to as a virtual microphone, and it can be used in control systems instead of actual microphones to attenuate noise due to structural vibrations. To this end, the dynamic model for the smart cylinder is derived using the extended Hamilton’s principle, the Sanders shell theory and the assumed mode method. The simplified Kirchhoff-Helmholtz integral estimates the far-field sound pressure radiating from the baffled cylindrical shell. A modified higher harmonic controller that can cope with a harmonic disturbance is designed and experimentally evaluated. The experimental tests were carried out on a baffled cylindrical aluminum shell in an anechoic chamber. The frequency response for the theoretical virtual microphone and the experimental actual microphone are in good agreement with each other, and the results show the effectiveness of the designed virtual microphone and controller in attenuating the radiated sound.
NASA Astrophysics Data System (ADS)
Abrosimov, N. A.; Novosel'tseva, N. A.
2017-05-01
A technique for numerically analyzing the dynamic strength of two-layer metal-plastic cylindrical shells under an axisymmetric internal explosive loading is developed. The kinematic deformation model of the layered package is based on a nonclassical theory of shells. The geometric relations are constructed using relations of the simplest quadratic version of the nonlinear elasticity theory. The stress and strain tensors in the composite macrolayer are related by Hooke's law for an orthotropic body with account of degradation of the stiffness characteristics of the multilayer package due to local failure of some its elementary layers. The physical relations in the metal layer are formulated in terms of a differential theory of plasticity. An energy-correlated resolving system of dynamic equations for the metal-plastic cylindrical shells is derived by minimizing the functional of total energy of the shells as three-dimensional bodies. The numerical method for solving the initial boundary-value problem formulated is based on an explicit variational-difference scheme. The reliability of the technique considered is verified by comparing numerical results with experimental data. An analysis of the ultimate strains and strength of one-layer basalt-and glass-fiber-reinforced plastic and two-layer metalplastic cylindrical shells is carried out.
Enhanced thermal stability of functionally graded sandwich cylindrical shells by shape memory alloys
NASA Astrophysics Data System (ADS)
Asadi, H.; Akbarzadeh, A. H.; Chen, Z. T.; Aghdam, M. M.
2015-04-01
The present paper deals with the nonlinear thermal instability of geometrically imperfect sandwich cylindrical shells under uniform heating. The sandwich shells are made of a shape memory alloy (SMA)-fiber-reinforced composite and functionally graded (FG) face sheets (FG/SMA/FG). The Brinson phenomenological model is used to express the constitutive characteristics of SMA fibers. The governing equations are established within the framework of the third-order shear deformation shell theory by taking into account the von Karman geometrical nonlinearity and initial imperfection. The material properties of constituents are assumed to be temperature dependent. The Galerkin technique is utilized to derive expressions of the bifurcation points and bifurcation paths of the sandwich cylindrical shells. Using the developed closed-form solutions, extensive numerical results are presented to provide an insight into the influence of the SMA fiber volume fraction, SMA pre-strain, core thickness, non-homogeneity index, geometrical imperfection, geometry parameters of sandwich shells and temperature dependency of materials on the stability of shells. The results reveal that proper application of SMA fibers postpones the thermal bifurcation point and dramatically decreases thermal post-buckling deflection. Moreover, the induced tensile recovery stress of SMA fibers could also stabilize the geometrically imperfect shells during the inverse martensite phase transformation.
An explicit model of expanding cylindrical shells subjected to high explosive detonations
Martineau, R.L.; Prime, M.B.; Anderson, C.A.; Smith, F.W.
1999-04-01
A viscoplastic constitutive model was formulated to model the high strain-rate expansion of thin cylindrical shells subjected to internal explosive detonations. This model provides insight into the development of plastic instabilities, which occur on the surface of the shells prior to failure. The effects of shock heating and damage in the form of microvoid nucleation, growth, and coalescence were incorporated using the Johnson-Cook strength model with the Mie-Grueneisen equation of state and a modified Gurson yield surface. This model was implemented into ABAQUS/Explicit as a user material subroutine. A cylindrical copper shell was modeled using both axisymmetric and plane strain elements. The high explosive material inside of the cylinder was simulated using the high explosive burn model in ABAQUS/Explicit. Two experiments were conducted involving explosive-filled, copper cylinders and good agreement was obtained between the numerical results and experimental data.
Convergence of a cylindrical liquid shell and the formation of a bore in a rotating fluid
NASA Astrophysics Data System (ADS)
Kedrinskii, V. K.; Nikulin, V. V.
1999-12-01
This paper presents the results of experimental studies of a collapsing cylindrical cavity (the convergence of a liquid shell) in a rotating fluid as well as the formation and propagation of a jump (bore) at the interface. The basic parameters of the liquid shell dynamics for a pulsed one-dimensional load are estimated using the equation of cylindrical cavity pulsation in an unbounded fluid. The theoretical model of a rotationally symmetric hydraulic jump moving along the free surface of a hollow vortex is constructed. The jump is simulated by a discontinuous solution of the equations in the long-wave approximation for tornado-like and hollow vortices. For comparison with the experimental data, basic theoretical results are obtained for flows in a hollow vortex with constant circulation and axial velocity varying along the radius of the rotating liquid shell.
NASA Technical Reports Server (NTRS)
Young, Richard D.; Rose, Cheryl A.; Starnes, James H., Jr.
2000-01-01
Results of a geometrically nonlinear finite element parametric study to determine curvature correction factors or bulging factors that account for increased stresses due to curvature for longitudinal and circumferential cracks in unstiffened pressurized cylindrical shells are presented. Geometric parameters varied in the study include the shell radius, the shell wall thickness, and the crack length. The major results are presented in the form of contour plots of the bulging factor as a function of two nondimensional parameters: the shell curvature parameter, lambda, which is a function of the shell geometry, Poisson's ratio, and the crack length; and a loading parameter, eta, which is a function of the shell geometry, material properties, and the applied internal pressure. These plots identify the ranges of the shell curvature and loading parameters for which the effects of geometric nonlinearity are significant. Simple empirical expressions for the bulging factor are then derived from the numerical results and shown to predict accurately the nonlinear response of shells with longitudinal and circumferential cracks. The numerical results are also compared with analytical solutions based on linear shallow shell theory for thin shells, and with some other semi-empirical solutions from the literature, and limitations on the use of these other expressions are suggested.
Buckling characteristic of multi-laminated composite elliptical cylindrical shells
NASA Astrophysics Data System (ADS)
Kassegne, Samuel Kinde; Chun, Kyoung-Sik
2015-03-01
Fiber-reinforced composite materials continue to experience increased adoption in aerospace, marine, automobile, and civil structures due to their high specific strength, high stiffness, and light weight. This increased use has been accompanied by applications involving non-traditional configurations such as compression members with elliptical cross-sections. To model such shapes, we develop and report an improved generalized shell element called 4EAS-FS through a combination of enhanced assumed strain and the substitute shear strain fields. A flat shell element has been developed by combining a membrane element with drilling degree-of-freedom and a plate bending element. We use the element developed to determine specifically buckling loads and mode shapes of composite laminates with elliptical cross-section including transverse shear deformations. The combined influence of shell geometry and elliptical cross-sectional parameters, fiber angle, and lay-up on the buckling loads of an elliptical cylinder is examined. It is hoped that the critical buckling loads and mode shapes presented here will serve as a benchmark for future investigations.
Rayleigh-Taylor and Richtmyer-Meshkov Instabilities and Mixing in Stratified Cylindrical Shells
Mikaelian, K O
2004-04-15
We study the linear stability of an arbitrary number N of cylindrical concentric shells undergoing a radial implosion or explosion.We derive the evolution equation for the perturbation {eta}{sub i} at interface i; it is coupled to the two adjacent interfaces via {eta}{sub i{+-}1}. For N=2, where there is only one interface, we verify Bell's conjecture as to the form of the evolution equation for arbitrary {rho}{sub 1} and {rho}{sub 2}, the fluid densities on either side of the interface. We obtain several analytic solutions for the N=2 and 3 cases. We discuss freeze-out, a phenomenon that can occur in all three geometries (planar, cylindrical, or spherical), and ''critical modes'' that are stable for any implosion or explosion history and occur only in cylindrical or spherical geometries. We present numerical simulations of possible gelatin-ring experiments illustrating perturbation feedthrough from one interface to another. We also develop a simple model for the evolution of turbulent mix in cylindrical geometry and define a geometrical factor G as the ratio h{sub cylindrical}/h{sub planar} between cylindrical and planar mixing layers. We find that G is a decreasing function of R/R{sub o}, implying that in our model h{sub cylindrical} evolves faster (slower) than h{sub planar} during an implosion (explosion).
Study of the vibration of bulkhead-stiffened cylindrical shells by laser-based methods
NASA Astrophysics Data System (ADS)
Zhu, Ninghui
The first part of this dissertation work deals with an experimental study of the vibration behavior of bulkhead stiffened cylindrical shells by using laser-based vibration measurement methods. Holographic interferometry and laser speckle photography are first demonstrated on revealing the dynamic behavior of a 22 ft long cylindrical shell. These methods are thereafter further explored to study the vibration characteristic of cylindrical shells with different stiffeners such as a full bulkhead or a partial bulkhead. Many experimentally obtained holograms and specklegrams reveal interesting features of the vibration of bulkhead stiffened cylindrical shells. The experimentally obtained results are compared with those obtained from a finite element model developed by General Dynamic Electric Boat Division, and the finite element model is generally validated. Mode localization theory is used to explain some interesting findings in experiments and the reason of some discrepancies between the finite element analysis and experiment results. The presence of irregularities in a weakly coupled structure such as a bulkhead-stiffened cylindrical shell is shown to be able to localize the modes of vibration and inhibit the propagation of vibration within the shell. A numerical simulation based on the finite element modal analysis indicates the validation of this explanation of the experimental findings. Thereafter, the eigensolutions of disordered, plate-stiffened cylindrical shell stiffened are derived by the use of receptance method. Numerical calculations are thereafter performed based upon this model and indeed reveal the exist of localized vibration in this kind of structure. This analytical study provides physical insights into the mode localization phenomenon in stiffened cylindrical shell type of structures from a more systematic manner. The conditions and the effect of mode localization on natural frequencies and mode shapes of cylindrical shell structure are also
Transverse circular-polarized Bessel beam generation by inward cylindrical aperture distribution.
Pavone, S C; Ettorre, M; Casaletti, M; Albani, M
2016-05-16
In this paper the focusing capability of a radiating aperture implementing an inward cylindrical traveling wave tangential electric field distribution directed along a fixed polarization unit vector is investigated. In particular, it is shown that such an aperture distribution generates a non-diffractive Bessel beam whose transverse component (with respect to the normal of the radiating aperture) of the electric field takes the form of a zero-th order Bessel function. As a practical implementation of the theoretical analysis, a circular-polarized Bessel beam launcher, made by a radial parallel plate waveguide loaded with several slot pairs, arranged on a spiral pattern, is designed and optimized. The proposed launcher performance agrees with the theoretical model and exhibits an excellent polarization purity.
Buckling Behavior of Compression-Loaded Composite Cylindrical Shells With Reinforced Cutouts
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Sarnes, James H., Jr.
2004-01-01
Results from a numerical study of the response of thin-walled compression-loaded quasi-isotropic laminated composite cylindrical shells with unreinforced and reinforced square cutouts are presented. The effects of cutout reinforcement orthotropy, size, and thickness on the nonlinear response of the shells are described. A nonlinear analysis procedure has been used to predict the nonlinear response of the shells. The results indicate that a local buckling response occurs in the shell near the cutout when subjected to load and is caused by a nonlinear coupling between local shell-wall deformations and in-plane destabilizing compression stresses near the cutout. In general, reinforcement around a cutout in a compression-loaded shell is shown to retard or eliminate the local buckling response near the cutout and increase the buckling load of the shell. However, some results show that certain reinforcement configurations can cause an unexpected increase in the magnitude of local deformations and stresses in the shell and cause a reduction in the buckling load. Specific cases are presented that suggest that the orthotropy, thickness, and size of a cutout reinforcement in a shell can be tailored to achieve improved buckling response characteristics.
Characterization of plasticity and fracture of shell casing of lithium-ion cylindrical battery
NASA Astrophysics Data System (ADS)
Zhang, Xiaowei; Wierzbicki, Tomasz
2015-04-01
Most of the literature on lithium-ion battery cells is concerned with modeling of jellyroll with little attention to properties of shell casing. However, shell casing provides substantial strength and fracture resistance under mechanical loading and therefore must be an important part of modeling of lithium-ion batteries. The paper reports on a comprehensive test program on commercially available empty shell casing of 18650 lithium-ion cylindrical cells. Part of the tests was used to determine plastic and fracture properties from sub-size specimens cut from lateral part of the cans. The other part served to validate plasticity and fracture models under various loading conditions. The associated flow rule was used to simulate plasticity behavior and Modified Mohr-Coulomb (MMC) fracture model was adopted to predict crack initiation and propagation of shell casing. Simulation results confirmed that present plasticity and fracture models could predict global plastic behavior of the cells under different loading conditions. The jellyroll model with volumetric hardening was introduced to compare the performance of empty shell casing, bare jellyroll and complete battery cell. It was shown that in many loading situations, for example, three point bending of the cylindrical cells, the metallic shell casing provides most of mechanical resistance.
Design and Fabrication of a Ring-Stiffened Graphite-Epoxy Corrugated Cylindrical Shell
NASA Technical Reports Server (NTRS)
Johnson, R., Jr.
1978-01-01
Design and fabrication of supplement test panels that represent key portions of the cylinder are described, as are supporting tests of coupons, sample joints, and stiffening ring elements. The cylindrical shell is a ring-stiffened, open corrugation design that uses T300/5208 graphite-epoxy tape as the basic material for the shell wall and stiffening rings. The test cylinder is designed to withstand bending loads producing the relatively low maximum load intensity in the shell wall of 1,576 N/cm. The resulting shell wall weight, including stiffening rings and fasteners, is 0.0156 kg/m. The shell weight achieved in the graphite-epoxy cylinder represents a weight saving of approximately 23 percent, compared to a comparable aluminum shell. A unique fabrication approach was used in which the cylinder wall was built in three flat segments, which were then wrapped to the cylindrical shape. Such an approach, made possible by the flexibility of the thin corrugated wall in a radial direction, proved to be a simple approach to building the test cylinder. Based on tooling and fabrication methods in this program, the projected costs of a production run of 100 units are reported.
Bifurcation theory applied to buckling states of a cylindrical shell
NASA Astrophysics Data System (ADS)
Chaskalovic, J.; Naili, S.
1995-01-01
Veins, bronchii, and many other vessels in the human body are flexible enough to be capable of collapse if submitted to suitable applied external and internal loads. One way to describe this phenomenon is to consider an inextensible elastic and infinite tube, with a circular cross section in the reference configuration, subjected to a uniform external pressure. In this paper, we establish that the nonlinear equilibrium equation for this model has nontrivial solutions which appear for critical values of the pressure. To this end, the tools we use are the Liapunov-Schmidt decomposition and the bifurcation theorem for simple multiplicity. We conclude with the bifurcation diagram, showing the dependence between the cross-sectional area and the pressure.
Adaptive control of radiated noise from a cylindrical shell using active fiber composite actuators
NASA Astrophysics Data System (ADS)
Goddu, Gregory; McDowell, Donald; Bingham, Brian S.
2000-06-01
This paper describes the application of Active Fiber Composite (AFC) actuators, a hybrid piezoelectric device, to the reduction of acoustic radiation from a cylindrical shell by active control methods. AFCs were developed to provide a mechanically robust method for large-area, orthotropic actuation and sensing in active structures. The actuation layer is formed by small diameter piezoelectric fibers that are unidirectionally aligned and imbedded in a resin matrix system. By the nature of its structure, an AFC actuator allows use of the primary piezoelectric effect in the plane of the composite. A cylindrical shell testbed is used for this experiment due to the predominance of this structure, and the resulting general interest, within the field of underwater acoustics. To control acoustic radiation from the cylindrical shell, the AFC actuators, placed at optimal locations determined using numerical models, are used to generate a strain field that counteracts the strain associated with acoustically efficient shell motions. Using an end-mounted accelerometer as the error measurement, an adaptive LMS algorithm is used to minimize the error signal in real-time. Experimental are supplied to validate both the device and the methodology in a complex, real-world environment.
NASA Astrophysics Data System (ADS)
Li, Yuyin; Zhang, Yahui; Kennedy, David
2017-10-01
A random vibration analysis of an axially compressed cylindrical shell under a turbulent boundary layer (TBL) is presented in the symplectic duality system. By expressing the cross power spectral density (PSD) of the TBL as a Fourier series in the axial and circumferential directions, the problem of structures excited by a random distributed pressure due to the TBL is reduced to solving the harmonic response function, which is the response of structures to a spatial and temporal harmonic pressure of unit magnitude. The governing differential equations of the axially compressed cylindrical shell are derived in the symplectic duality system, and then a symplectic eigenproblem is formed by using the method of separation of variables. Expanding the excitation vector and unknown state vector in symplectic space, decoupled governing equations are derived, and then the analytical solution can be obtained. In contrast to the modal decomposition method (MDM), the present method is formulated in the symplectic duality system and does not need modal truncation, and hence the computations are of high precision and efficiency. In numerical examples, harmonic response functions for the axially compressed cylindrical shell are studied, and a comparison is made with the MDM to verify the present method. Then, the random responses of the shell to the TBL are obtained by the present method, and the convergence problems induced by Fourier series expansion are discussed. Finally, influences of the axial compression on random responses are investigated.
Cylindrical Shells Made of Stainless Steel - Investigation of Postbuckling
NASA Astrophysics Data System (ADS)
Stehr, Sebastian; Stranghöner, Natalie
2017-06-01
The relevant load case of open thin-walled shells is often wind loading during construction. Because of the missing stabilization effect of the roof they show a very high sensitivity to buckling which results into higher wall thicknesses. As part of the European RFCS research project BiogaSS the Institute for Metal and Lightweight Structures of the University of Duisburg-Essen carried out investigations on open thin-walled tanks made of austenitic and duplex stainless steels under wind load to study a possible economic advantage which might be gained from the consideration of the elastic postbuckling behaviour. This contribution presents not only experimental and numerical results but also first recommendations regarding the range of possible buckling reduction factors which might be incorporated in future revisions of EN 1993-1-6 and EN 1993-4-2.
NASA Astrophysics Data System (ADS)
Villalobos Mendoza, Brenda; Cordero Dávila, Alberto; González García, Jorge
2011-01-01
This paper describes the construction of an elliptical-cylindrical model without spherical aberration using vertical rotating tools. The engine of the circular tool is placed on one arm so that the tool fits on the surface and this in turn is moved by an X-Y table. The test method and computer algorithms that predict the desired wear are described.
Plane stress-strain state of a circular cylindrical bushing due to a finite out-of-plane shear
NASA Astrophysics Data System (ADS)
Zhukov, B. A.
2017-01-01
The paper deals with the determination of the stress-strain state due to a finite longitudinal shear in a circular cylindrical bushing manufactured from the Mooney-Rivlin material. Some expressions for the internal stresses and displacements in the plane perpendicular to the longitudinal shear are obtained.
Flutter of a sandwich cylindrical shell supported with annular ribs and loaded with axial forces
NASA Astrophysics Data System (ADS)
Bakulin, V. N.; Volkov, E. N.; Nedbaj, A. Ya.
2015-08-01
The supersonic flutter of a sandwich cylindrical shell supported from within with annular ribs and loaded with axial forces on the end faces is investigated. The shell motion is described by the equations of the theory of sandwich orthotropic shells. The solution of the equations is sought as a trigonometric series with respect to the axial coordinate. With the help of the Bubnov—Galerkin method, this problem is reduced to the set of algebraic equations for the analysis of the stability of which one uses the Routh—Hurwits criterion. By a numerical example, the effect of the number and the heights of the ribs on the critical velocity of the flow around the shell is shown.
Buckling and Failure of Compression-loaded Composite Cylindrical Shells with Reinforced Cutouts
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Nemeth, Michael P.
2005-01-01
Results from a numerical and experimental study that illustrate the effects of selected cutout reinforcement configurations on the buckling and failure response of compression-loaded composite cylindrical shells with a cutout are presented. The effects of reinforcement size, thickness, and orthotropy on the overall response of compression-loaded shells are described. In general, reinforcement around a cutout in a compression-loaded shell can retard or eliminate the local buckling response and material failure near the cutout and increase the buckling load of the shell. However, some results show that certain reinforcement configurations can cause a significant increase in the local interlaminar failures that can accumulate near the free edges of a cutout during a local buckling event.
A cylindrical shell model of the NASA-MPE barium ion cloud experiment.
NASA Technical Reports Server (NTRS)
Grauer, A. D.; Prak, J. W. L.; Jenkins, A. W., Jr.
1973-01-01
A computer model is developed using infinitely long concentric cylindrical shells to represent the neutral atoms, ions and electrons in the barium cloud. The neutral shells are given a distribution of positions and velocities whose parameters are chosen to be consistent with the dynamics of the release. From this distribution, the ion and electron shells are generated at random using the observed time constant for photoionization. The ion and electron shells thus formed are followed using self-consistent equations of motion. Various averages which could be compared with observation of the actual cloud are calculated at regular time intervals. An unexpected result is the predicted very early return of the magnetic field within the cloud to its ambient value.
A robust approach for analysing dispersion of elastic waves in an orthotropic cylindrical shell
NASA Astrophysics Data System (ADS)
Kaplunov, J.; Nobili, A.
2017-08-01
Dispersion of elastic waves in a thin orthotropic cylindrical shell is considered, within the framework of classical 2D Kirchhoff-Love theory. In contrast to direct multi-parametric analysis of the lowest propagating modes, an alternative robust approach is proposed that simply requires evaluation of the evanescent modes (quasi-static edge effect), which, at leading order, do not depend on vibration frequency. A shortened dispersion relation for the propagating modes is then derived by polynomial division and its accuracy is numerically tested against the full Kirchhoff-Love dispersion relation. It is shown that the same shortened relation may be also obtained from a refined dynamic version of the semi-membrane theory for cylindrical shells. The presented results may be relevant for modelling various types of nanotubes which, according to the latest experimental findings, possess strong material anisotropy.
Application of fuzzy GA for optimal vibration control of smart cylindrical shells
NASA Astrophysics Data System (ADS)
Jin, Zhanli; Yang, Yaowen; Kiong Soh, Chee
2005-12-01
In this paper, a fuzzy-controlled genetic-based optimization technique for optimal vibration control of cylindrical shell structures incorporating piezoelectric sensor/actuators (S/As) is proposed. The geometric design variables of the piezoelectric patches, including the placement and sizing of the piezoelectric S/As, are processed using fuzzy set theory. The criterion based on the maximization of energy dissipation is adopted for the geometric optimization. A fuzzy-rule-based system (FRBS) representing expert knowledge and experience is incorporated in a modified genetic algorithm (GA) to control its search process. A fuzzy logic integrated GA is then developed and implemented. The results of three numerical examples, which include a simply supported plate, a simply supported cylindrical shell, and a clamped simply supported plate, provide some meaningful and heuristic conclusions for practical design. The results also show that the proposed fuzzy-controlled GA approach is more effective and efficient than the pure GA method.
Optical trapping of core-shell magnetic microparticles by cylindrical vector beams
Zhong, Min-Cheng; Gong, Lei; Li, Di; Zhou, Jin-Hua; Wang, Zi-Qiang; Li, Yin-Mei
2014-11-03
Optical trapping of core-shell magnetic microparticles is experimentally demonstrated by using cylindrical vector beams. Second, we investigate the optical trapping efficiencies. The results show that radially and azimuthally polarized beams exhibit higher axial trapping efficiencies than the Gaussian beam. Finally, a trapped particle is manipulated to kill a cancer cell. The results make possible utilizing magnetic particles for optical manipulation, which is an important advantage for magnetic particles as labeling agent in targeted medicine and biological analysis.
NASA Astrophysics Data System (ADS)
Gonçalves, P. B.; Silva, F. M. A.; Del Prado, Z. J. G. N.
2008-08-01
In formulating mathematical models for dynamical systems, obtaining a high degree of qualitative correctness (i.e. predictive capability) may not be the only objective. The model must be useful for its intended application, and models of reduced complexity are attractive in many cases where time-consuming numerical procedures are required. This paper discusses the derivation of discrete low-dimensional models for the nonlinear vibration analysis of thin cylindrical shells. In order to understand the peculiarities inherent to this class of structural problems, the nonlinear vibrations and dynamic stability of a circular cylindrical shell subjected to static and dynamic loads are analyzed. This choice is based on the fact that cylindrical shells exhibit a highly nonlinear behavior under both static and dynamic loads. Geometric nonlinearities due to finite-amplitude shell motions are considered by using Donnell's nonlinear shallow-shell theory. A perturbation procedure, validated in previous studies, is used to derive a general expression for the nonlinear vibration modes and the discretized equations of motion are obtained by the Galerkin method using modal expansions for the displacements that satisfy all the relevant boundary and symmetry conditions. Next, the model is analyzed via the Karhunen-Loève expansion to investigate the relative importance of each mode obtained by the perturbation solution on the nonlinear response and total energy of the system. The responses of several low-dimensional models are compared. It is shown that rather low-dimensional but properly selected models can describe with good accuracy the response of the shell up to very large vibration amplitudes.
NASA Astrophysics Data System (ADS)
Thernisien, A.
2011-06-01
The graduated cylindrical shell (GCS) model developed by Thernisien et al. has been used with the goal of studying the three-dimensional morphology, position, and kinematics of coronal mass ejections observed by coronagraphs. These studies focused more on the results rather than the details of the model itself. As more researchers begin to use the model, it becomes necessary to provide a deeper discussion on how it is derived, which is the purpose of this paper. The model is built using the following features and constraints: (1) the legs are conical, (2) the front is pseudo-circular, (3) the cross section is circular, and (4) it expands in a self-similar way. We derive the equation of the model from these constraints. We also show that the ice-cream cone model is a limit of the GCS when the two legs overlap completely. Finally, we provide formulae for the calculation of various geometrical dimensions, such as angular width and aspect ratio, as well as the pseudo-code that is used for its computer implementation.
Thernisien, A.
2011-06-01
The graduated cylindrical shell (GCS) model developed by Thernisien et al. has been used with the goal of studying the three-dimensional morphology, position, and kinematics of coronal mass ejections observed by coronagraphs. These studies focused more on the results rather than the details of the model itself. As more researchers begin to use the model, it becomes necessary to provide a deeper discussion on how it is derived, which is the purpose of this paper. The model is built using the following features and constraints: (1) the legs are conical, (2) the front is pseudo-circular, (3) the cross section is circular, and (4) it expands in a self-similar way. We derive the equation of the model from these constraints. We also show that the ice-cream cone model is a limit of the GCS when the two legs overlap completely. Finally, we provide formulae for the calculation of various geometrical dimensions, such as angular width and aspect ratio, as well as the pseudo-code that is used for its computer implementation.
NASA Technical Reports Server (NTRS)
Tang, Yvette Y.; Silcox, Richard J.; Robinson, Jay H.
1996-01-01
This paper examines sound transmission into two concentric cylindrical sandwich shells subject to turbulent flow on the exterior surface of the outer shell. The interior of the shells is filled with fluid medium and there is an airgap between the shells in the annular space. The description of the pressure field is based on the cross-spectral density formulation of Corcos, Maestrello, and Efimtsov models of the turbulent boundary layer. The classical thin shell theory and the first-order shear deformation theory are applied for the inner and outer shells, respectively. Modal expansion and the Galerkin approach are used to obtain closed-form solutions for the shell displacements and the radiation and transmission pressures in the cavities including both the annular space and the interior. The average spectral density of the structural responses and the transmitted interior pressures are expressed explicitly in terms of the summation of the cross-spectral density of generalized force induced by the boundary layer turbulence. The effects of acoustic and hydrodynamic coincidences on the spectral density are observed. Numerical examples are presented to illustrate the method for both subsonic and supersonic flows.
NASA Technical Reports Server (NTRS)
Young, Richard D.; Rose, Cheryl A.; Starnes, James H., Jr.
2000-01-01
Results of a geometrically nonlinear finite element parametric study to determine curvature correction factors or bulging factors that account for increased crack-tip stresses due to curvature for longitudinal and circumferential cracks in unstiffened cylindrical shells subjected to combined loads are presented. Nondimensional parameters varied in the study include the shell curvature parameter, l , which is a function of the shell radius, the shell wall thickness, and the crack length; a pressure loading parameter, h , which is a function of the shell geometry, material properties and the applied internal pressure; and a biaxial loading parameter, c , which is the ratio of the farfield axial stress to the farfield circumferential stress. The major results are presented in the form of contour plots of the bulging factor as a function of these three nondimensional parameters. These plots identify the ranges of the shell curvature and loading parameters for which the effects of geometric nonlinearity are significant, and show the effect of the biaxial loads on the value of the bulging factor. Simple empirical expressions for the bulging factor are then derived from the numerical results and are shown to predict accurately the nonlinear response of shells with longitudinal and circumferential cracks.
Vibration analysis of ring-stiffened cross-ply laminated cylindrical shells
NASA Astrophysics Data System (ADS)
Wang, Rong-Tyai; Lin, Zung-Xian
2006-08-01
This work presents the formulation of governing equations for a symmetric cross-ply laminated cylindrical shell with a circumferential stiffener. Two kinds of the circumferential stiffeners are considered: outer ring and inner ring. The effects of rotatory inertia and transverse shearing strain of both the cross-ply laminated shell and stiffener are considered. Further, the warping effect of stiffener also is included. An analytic method is presented to obtain the modal frequencies and their corresponding mode shape functions of the ring-stiffened laminated shell. The orthogonality of two distinct sets of mode shape functions is shown. The effects of inner ring and outer ring on modal frequencies of the ring-stiffened laminated shell are compared. Further, the effect of ply arrangement on modal frequencies of the ring-stiffened shell also is studied. The forced vibration of the ring-stiffened laminated shell due to a concentrated transient force is examined. The stress distributions in the plies of the ring-stiffened laminated shell due to the transient force are investigated.
NASA Astrophysics Data System (ADS)
Mahadev, Sthanu
Continued research and development efforts devoted in recent years have generated novel avenues towards the advancement of efficient and effective, slender laminated fiber-reinforced composite members. Numerous studies have focused on the modeling and response characterization of composite structures with particular relevance to thin-walled cylindrical composite shells. This class of shell configurations is being actively explored to fully determine their mechanical efficacy as primary aerospace structural members. The proposed research is targeted towards formulating a composite shell theory based prognosis methodology that entails an elaborate analysis and investigation of thin-walled cylindrical shell type laminated composite configurations that are highly desirable in increasing number of mechanical and aerospace applications. The prime motivation to adopt this theory arises from its superior ability to generate simple yet viable closed-form analytical solution procedure to numerous geometrically intense, inherent curvature possessing composite structures. This analytical evaluative routine offers to acquire a first-hand insight on the primary mechanical characteristics that essentially govern the behavior of slender composite shells under typical static loading conditions. Current work exposes the robustness of this mathematical framework via demonstrating its potential towards the prediction of structural properties such as axial stiffness and bending stiffness respectively. Longitudinal ply-stress computations are investigated upon deriving the global stiffness matrix model for composite cylindrical tubes with circular cross-sections. Additionally, this work employs a finite element based numerical technique to substantiate the analytical results reported for cylindrically shaped circular composite tubes. Furthermore, this concept development is extended to the study of thin-walled, open cross-sectioned, curved laminated shells that are geometrically
1991-03-04
term that describes inextensional motion. The first equation represents the normal stress at the midsurface of the shell, which is equal to the...that the normal velocity at the midsurface of the shell is proportional to the normal derivative of the total pressw e. The scattered pressure ps can
Stress concentration in a transversely isotropic spherical shell with two circular rigid inclusions
NASA Astrophysics Data System (ADS)
Chekhov, V. N.; Zakora, S. V.
2011-10-01
The refined Timoshenko-type theory that takes into account the transverse shear strains is used to find an analytic solution for the stress state of transversely isotropic shallow spherical shell with two circular rigid inclusions. The case of a shell with closely spaced rigid inclusions of unequal radii under internal pressure is analyzed numerically. The stresses in the shell increase considerably with decrease in the distance between the inclusions and increase in the transverse shear parameter
Multi-objective optimization of ring stiffened cylindrical shells using a genetic algorithm
NASA Astrophysics Data System (ADS)
Bagheri, M.; Jafari, A. A.; Sadeghifar, M.
2011-01-01
In this paper, the genetic algorithm (GA) method is used for the multi-objective optimization of ring stiffened cylindrical shells. The objective functions seek the maximum fundamental frequency and minimum structural weight of the shell subjected to four constraints including the fundamental frequency, the structural weight, the axial buckling load, and the radial buckling load. The optimization process contains six design variables including the shell thickness, the number of stiffeners, the width and height of stiffeners, the stiffeners eccentricity distribution order, and the stiffeners spacing distribution order. The real coding scheme is used for representing the solution string, while the generation number-based adaptive penalty function is applied for penalizing infeasible solutions. In analytical solution, the Ritz method is applied and the stiffeners are treated as discrete elements. Some examples of simply supported cylindrical shells with nonuniform eccentricity distribution and nonuniform rings spacing distribution are provided to demonstrate the optimality of the solution obtained by the GA technique. The effects of objective weighting coefficients and bounding values of the design variables on the optimum solution are studied for various cases. The results show that the optimal solution can vary with the weighting coefficients significantly. It is also found that extreme reduction and augmentation in turn in the structural weight and fundamental frequency can be simultaneously achieved by selecting suitable stiffeners' geometrical parameters and distributions. Furthermore, the bounding values of the design variables have great effects on the optimum results.
Influence of an asymmetric ring on the modeling of an orthogonally stiffened cylindrical shell
NASA Technical Reports Server (NTRS)
Rastogi, Naveen; Johnson, Eric R.
1994-01-01
Structural models are examined for the influence of a ring with an asymmetrical cross section on the linear elastic response of an orthogonally stiffened cylindrical shell subjected to internal pressure. The first structural model employs classical theory for the shell and stiffeners. The second model employs transverse shear deformation theories for the shell and stringer and classical theory for the ring. Closed-end pressure vessel effects are included. Interacting line load intensities are computed in the stiffener-to-skin joints for an example problem having the dimensions of the fuselage of a large transport aircraft. Classical structural theory is found to exaggerate the asymmetric response compared to the transverse shear deformation theory.
NASA Technical Reports Server (NTRS)
Palazotto, A. N.
1975-01-01
Results for cylindrical configurations using the STAGS computer program were presented. Discontinuities were imposed upon the shell's skin by incorporating symmetrical cutout openings. In addition, the surface is stiffened with both stringer and ring-stringer arrangements. The cutout problem has been shown to be highly nonlinear for smooth surface shells, but it was found that bifurcation and collapse loads are close when one is considering stiffened skin configurations. In order to arrive at this conclusion, it was necessary to evaluate the following: (1) comparison between smeared and discrete stiffener theory for linear solutions, (2) numerical finite difference convergence as directed toward buckling determination, (3) collapse load results with the various skin stiffeners. A linear bifurcation study relating to stiffening effects around cutout areas present within stringer and ring-stringer shell surfaces was included. Comparisons were made between a variety of geometric positions considering cutout frame and thickened skin additions.
A viscoplastic model of expanding cylindrical shells subject to internal explosive detonations
Martineau, R.L.; Anderson, C.A.; Smith, F.W.
1998-12-31
Thin cylindrical shells subjected to internal explosive detonations expand outwardly at strain-rates on the order 10{sup 4} s{sup {minus}1}. At approximately 150% strain, multiple plastic instabilities appear on the surface of these shells in a quasi-periodic pattern. These instabilities continue to develop into bands of localized shear and eventually form cracks that progress in a way that causes the shell to break into fragments. The entire process takes less than 100 microseconds from detonation to complete fragmentation. Modeling this high strain-rate expansion and generation of instabilities prior to fragmentation is the primary focus of this paper. Applications for this research include hypervelocity accelerators, flux compression generators, and explosive containment vessels for terrorist threats and power plants.
Dynamics and Stability of Pinned-Clamped and Clamped-Pinned Cylindrical Shells Conveying Fluid
NASA Astrophysics Data System (ADS)
Misra, A. K.; Wong, S. S. T.; Païdoussis, M. P.
2001-11-01
The paper examines the dynamics and stability of fluid-conveying cylindrical shells having pinned-clamped or clamped-pinned boundary conditions, where ``pinned'' is an abbreviation for ``simply supported''. Flügge's equations are used to describe the shell motion, while the fluid-dynamic perturbation pressure is obtained utilizing the linearized potential flow theory. The solution is obtained using two methods - the travelling wave method and the Fourier-transform approach. The results obtained by both methods suggest that the negative damping of the clamped-pinned systems and positive damping of the pinned-clamped systems, observed by previous investigators for any arbitrarily small flow velocity, are simply numerical artefacts; this is reinforced by energy considerations, in which the work done by the fluid on the shell is shown to be zero. Hence, it is concluded that both systems are conservative.
Experiments and analysis on chaotic vibrations of a shallow cylindrical shell-panel
NASA Astrophysics Data System (ADS)
Nagai, K.; Maruyama, S.; Murata, T.; Yamaguchi, T.
2007-08-01
Detailed experimental results and analytical results are presented on chaotic vibrations of a shallow cylindrical shell-panel subjected to gravity and periodic excitation. The shallow shell-panel with square boundary is simply supported for deflection. In-plane displacement at the boundary is elastically constrained by in-plain springs. In the experiment, the cylindrical shallow shell-panel with thickness 0.24 mm, square form of length 140 mm and mean radius 5150 mm is used for the test specimen. All edges around the shell boundary are simply supported by adhesive flexible films. First, to find fundamental properties of the shell-panel, linear natural frequencies and characteristics of restoring force of the shell-panel are measured. These results are compared with the relevant analytical results. Then, geometrical parameters of the shell-panel are identified. Exciting the shell-panel with lateral periodic acceleration, nonlinear frequency responses of the shell-panel are obtained by sweeping the frequency of periodic acceleration. In typical ranges of the exciting frequency, predominant chaotic responses are generated. Time histories of the responses are recorded for inspection of the chaos. In the analysis, the Donnell equation with lateral inertia force is introduced. Assuming mode functions, the governing equation is reduced to a set of nonlinear ordinary differential equations by the Galerkin procedure. Periodic responses are calculated by the harmonic balance method. Chaotic responses are integrated numerically by the Runge-Kutta-Gill method. The chaotic responses, which are obtained by the experiment and the analysis, are inspected with the Fourier spectra, the Poincaré projections, the maximum Lyapunov exponents and the Lyapunov dimension. It is found that the dominant chaotic responses of the shell-panel are generated from the responses of the sub-harmonic resonance of {1}/{2} order and of the ultra-sub-harmonic resonance of {2}/{3} order. By the
Generalized asymptotic expansions for coupled wavenumbers in fluid-filled cylindrical shells
NASA Astrophysics Data System (ADS)
Kunte, M. V.; Sarkar, Abhijit; Sonti, Venkata R.
2010-12-01
Analytical expressions are found for the coupled wavenumbers in an infinite fluid-filled cylindrical shell using the asymptotic methods. These expressions are valid for any general circumferential order ( n). The shallow shell theory (which is more accurate at higher frequencies) is used to model the cylinder. Initially, the in vacuo shell is dealt with and asymptotic expressions are derived for the shell wavenumbers in the high- and the low-frequency regimes. Next, the fluid-filled shell is considered. Defining a relevant fluid-loading parameter μ, we find solutions for the limiting cases of small and large μ. Wherever relevant, a frequency scaling parameter along with some ingenuity is used to arrive at an elegant asymptotic expression. In all cases, Poisson's ratio ν is used as an expansion variable. The asymptotic results are compared with numerical solutions of the dispersion equation and the dispersion relation obtained by using the more general Donnell-Mushtari shell theory ( in vacuo and fluid-filled). A good match is obtained. Hence, the contribution of this work lies in the extension of the existing literature to include arbitrary circumferential orders ( n).
Analysis of soft and hard strip-loaded horns using a circular cylindrical model
NASA Astrophysics Data System (ADS)
Lier, Erik
1990-06-01
Strip-loaded horns with transverse (soft) and longitudinal (hard) strips are analyzed theoretically. The method is based on a circular cylindrical and uniform waveguide model with a periodic strip structure. The field is represented by an infinite series of space harmonics (Floquet modes) in the air-filled central region and in the dielectrically filled wall region. The tangential field is forced to be continuous across the air-dielectric boundary. The propagation constant and the total field (including the hybrid factor) can be determined by solving the resulting matrix equations. The convergence of the solution has been accelerated by calculating the higher-order terms analytically. It is shown that the soft-strip-loaded horn in principle exhibits the same electrical behavior as a corrugated horn. The horn represents an interesting alternative to the corrugated horn in wide-band or dual-band applications, in particular for millimeter waves and for lightweight applications onboard satellites. The hard-strip-loaded horn has potentially high gain and low cross polarization over a certain frequency range, dependent on the horn dimensions, thickness of the dielectric wall and on how strongly the stripline modes are being excited.
Cylindrical matrix device with a circular release area with inhomogeneous diffusivity
NASA Astrophysics Data System (ADS)
Cuartas Velez, Carlos Alfredo
2013-05-01
A cylindrical matrix device with a circular release area with inhomogeneous diffusivity was analyzed using a Laplace transform-based method, using Bromwich integral and residue theorem. The two-dimensional model represented a pharmaceutical agent uniformly distributed in a polymeric matrix with a diffusivity spatially modulated, surrounded by an impermeable layer. The pharmaceutical agent could be transferred only through a small hole centered at the top surface of the cylinder. A closed-form solution was obtained in terms of Bessel functions with the aim to help study the effects of design parameters and geometries on the cumulative amount of pharmaceutical agent released. The cumulative flux of pharmaceutical agent increased with the mass transfer and diffusion coefficients and decreased with any increment in the device's length and variations of the diffusivity coefficients. The delivery rate was described by an effective time constant calculated from Laplace transforms and using Bessel functions and their zeros. Reducing the orifice diameter or fabricating a longer system would delay transport of the medication. Simplified expressions for the release profile and the time constant were derived for special design cases.
Extension, inflation and torsion of a residually stressed circular cylindrical tube
NASA Astrophysics Data System (ADS)
Merodio, José; Ogden, Ray W.
2016-03-01
In this paper, we provide a new example of the solution of a finite deformation boundary-value problem for a residually stressed elastic body. Specifically, we analyse the problem of the combined extension, inflation and torsion of a circular cylindrical tube subject to radial and circumferential residual stresses and governed by a residual-stress dependent nonlinear elastic constitutive law. The problem is first of all formulated for a general elastic strain-energy function, and compact expressions in the form of integrals are obtained for the pressure, axial load and torsional moment required to maintain the given deformation. For two specific simple prototype strain-energy functions that include residual stress, the integrals are evaluated to give explicit closed-form expressions for the pressure, axial load and torsional moment. The dependence of these quantities on a measure of the radial strain is illustrated graphically for different values of the parameters (in dimensionless form) involved, in particular the tube thickness, the amount of torsion and the strength of the residual stress. The results for the two strain-energy functions are compared and also compared with results when there is no residual stress.
Convective heat transfer from circular cylinders located within perforated cylindrical shrouds
NASA Technical Reports Server (NTRS)
Daryabeigi, K.; Ash, R. L.
1986-01-01
The influence of perforated cylindrical shrouds on the convective heat transfer to circular cylinders in transverse flow has been studied experimentally. Geometries studied were similar to those used in industrial platinum resistance thermometers. The influence of Reynolds number, ventilation factor (ratio of the open area to the total surface area of shroud), radius ratio (ratio of shroud's inside radius to bare cylinder's radius), and shroud orientation with respect to flow were studied. The experiments showed that perforated shrouds with ventilation factors in the range 0.1 to 0.4 and radius ratios in the range 1.1 to 2.1 could enhance the convective heat transfer to bare cylinders up to 50%. The maximum enhancement occurred for a radius ratio of 1.4 and ventilation factors between 0.2 and 0.3. It was found that shroud orientation influenced the heat transfer, with maximum heat transfer generally occurring when the shroud's holes were centered on either side of the stagnation line. However, the hole orientation effect is of second order compared to the influence of ventilation factor and radius ratio.
Optimization of circular orifice jets mixing into a heated cross flow in a cylindrical duct
NASA Technical Reports Server (NTRS)
Kroll, J. T.; Sowa, W. A.; Samuelsen, G. S.; Holdeman, J. D.
1993-01-01
To examine the mixing characteristics of circular jets in an axisymmetric can geometry, temperature measurements were obtained downstream of a row of cold jet injected into a heated cross stream. The objective was to obtain uniform mixing within one duct radius downstream of the leading edge of the jet orifices. An area weighted standard deviation of the mixture fraction was used to help quantify the degree of mixedness at a given plane. Non-reacting experiments were conducted to determine the influence of the number of jets on the mixedness in a cylindrical configuration. Results show that the number of orifices significantly impacts the mixing characteristics of jets injected from round hole orifices in a can geometry. Optimum mixing occurs when the mean jet trajectory aligns with the radius which divides the cross sectional area of the can into two equal parts at one mixer radius downstream of the leading edge of the orifice. The optimum number of holes at momentum-flux ratios of 25 and 52 is 10 and 15 respectively.
NASA Astrophysics Data System (ADS)
Bondaryk, Joseph E.
This thesis investigates array processing and forward modeling methods for the analysis of experimental, structural acoustic data to understand wave propagation on fluid-loaded, elastic, cylindrical shells in the mid -frequency range, 2 < ka < 12. The transient, acoustic, in-plane, bistatic scattering response to wideband, plane waves at various angles of incidence was collected by a synthetic array for three shells, a finite, air-filled, empty thin shell, a duplicate shell stiffened with four unequally spaced ring-stiffeners and a duplicate ribbed shell augmented by resiliently-mounted, wave-bearing, internal structural elements. Array and signal processing techniques, including source deconvolution, array weighting, conventional focusing and the removal of the geometrically scattered contribution, are used to transform the collected data to a more easily interpreted representation. The resulting waveforms show that part of the transient, dynamic, structural response of the shell surface which is capable of radiating to the far field. Compressional membrane waves are directly observable in this representation and evidence of flexural membrane waves is present. Comparisons between the shells show energy compartmentalized by the ring stiffeners and coupled into the wave-bearing internals. Energy calculations show a decay rate of 30dB/msec due to radiation for the Empty shell but only 10dB/msec for the other shells at bow incidence. The Radon Transform is used to estimate the reflection coefficient of compressional waves at the shell endcap as 0.2. The measurement array does not provide enough resolution to allow use of this technique to determine the reflection, transmission and coupling coefficients at the ring stiffeners. Therefore, a forward modeling technique is used to further analyze the 0^ circ incidence case. This modeling couples a Transmission Line model of the shell with a Simulated Annealing approach to multi-dimensional, parameter estimation. This
NASA Astrophysics Data System (ADS)
Lugovoi, P. Z.; Meish, V. F.; Meish, Yu. A.
2016-07-01
The problem of wave processes in a system consisting of a cylindrical shell and a soil medium of periodic structure under impulsive loading is solved numerically. The results obtained allow us to control the parameters of a compressional wave entering the soil and to predict the behavior of the wave processes, depending on geometrical and mechanical parameters of the shell and soil
Composite cylindrical shells under static and dynamic axial loading: An experimental campaign
NASA Astrophysics Data System (ADS)
Bisagni, Chiara
2015-10-01
The results of an experimental investigation performed at the Politecnico di Milano inside the European project DAEDALOS on three composite cylindrical shells are here presented. At first, static buckling tests were performed under axial compression. Then, two types of dynamic tests were carried out: modal tests at different load levels before buckling and dynamic buckling tests applying an axial shortening of short duration. At the end, one shell was statically tested until final failure. The tests allow to understand the behavior of thin-walled cylindrical shells subjected to axial compression both in static and dynamic conditions. The results show the strength capacity of these structures to work in the post-buckling range with a capacity to sustain a load that is about 40% of the buckling load. The modal tests at different load levels allowed to observe that an increase of the load determines a reduction of the modal frequency and an increase of the damping. Large deformations are obtained before the final failure with out-of-plane displacements of almost 40 mm and a shortening equal to about 26 times the buckling shortening.
Buckling failure of the axially pre-compressed cylindrical shell irradiated by CW CO2 laser beam
NASA Astrophysics Data System (ADS)
Chen, Yuze; Li, Sizhong
1993-07-01
The experimental study on the buckling failure of lateral surface of the axially pre-compressed cylindrical aluminum shell irradiated by CW CO2 laser beam is described in this paper. It has been shown from its results that the heat softening of the surface material will induce buckling failure of the pre-compressed cylindrical shell, the critical buckling load decreases with increase of incident laser energy and the persistent axial compression loading. The behavior of the post buckling may cause catastrophic collapse of the shell.
NASA Astrophysics Data System (ADS)
Guo, Wenjie; Li, Tianyun; Zhu, Xiang; Miao, Yuyue; Zhang, Guanjun
2017-04-01
The far-field acoustic radiation of a cylindrical shell with finite length submerged at finite depth from the water surface is studied. Two steps are utilized to solve the problem. The first step is to determine the vibration response of the submerged cylindrical shell by using an analytical method and the second one is to determine the far field sound radiation with the boundary element method. To address the vibration responses of the shell analytically, the cylindrical shell and surrounding fluid are described by the Flügge shell equations and Laplace equation in the cylindrical coordinate system respectively. The free surface effect is taken into consideration by using the image method and the Graf's addition theorem. The reliability and efficiency of the present method are validated by comparison with the finite element method. Then, based on the vibration responses of the shell obtained from the first step, the far-field sound pressure is computed by using the boundary element method. It is found that the vibration of the cylindrical shell submerged at finite depth from the free surface tends to be the same as that in infinite fluid when the submerged depth exceeds a certain value. The frequency and the submerged depth have crucial effects on the fluctuation of the far-field sound pressure, while for the curve of sound pressure level versus immersion depth, the ratio of the distance between the adjacent peak points of sound pressure to the wavelength is independent of the frequency. Moreover, the petal number of the directivity of the far-field sound pressure increases with the increase of the frequency and the submerged depth. The work provides more understanding on the vibration and acoustic radiation behavior of a finite cylindrical shell submerged at finite depth.
Scalar Casimir densities induced by a cylindrical shell in de Sitter spacetime
NASA Astrophysics Data System (ADS)
Saharian, A. A.; Manukyan, V. F.
2015-01-01
We evaluate the positive-frequency Wightman function, the vacuum expectation values (VEVs) of the field squared, and the energy-momentum tensor for a massive scalar field with general curvature coupling for a cylindrical shell in the background of de Sitter (dS) spacetime. The field is prepared in the Bunch-Davies vacuum state and on the shell, and the corresponding operator obeys the Robin boundary condition (BC). In the region inside the shell and for non-Neumann BC, the Bunch-Davies vacuum is a physically realizable state for all values of the mass and curvature coupling parameter. For both interior and exterior regions, the VEVs are decomposed into boundary-free dS and shell-induced parts. We show that the shell-induced part of the vacuum energy-momentum tensor has a nonzero off-diagonal component corresponding to the energy flux along the radial direction. Unlike in the case of a shell in Minkowski bulk, for the dS background, the axial stresses are not equal to the energy density. In dependence of the mass and the coefficient in the BC, the vacuum energy density and the energy flux can be either positive or negative. The influence of the background gravitational field on the boundary-induced effects is crucial at distances from the shell larger than the dS curvature scale. In particular, the decay of the VEVs with distance is power-law (monotonic or oscillatory with dependence of the mass) for both massless and massive fields. For the Neumann BC, the decay is faster than that for non-Neumann conditions.
A viscoplastic model of expanding cylindrical shells subjected to internal explosive detonations
Martineau, Rick L.
1998-04-01
Magnetic flux compression generators rely on the expansion of thin ductile shells to generate magnetic fields. These thin shells are filled with high explosives, which when detonated, cause the shell to expand to over 200% strain at strain-rates on the order of 10^{4} s^{-1}. Experimental data indicate the development and growth of multiple plastic instabilities which appear in a quasi-periodic pattern on the surfaces of the shells. These quasi-periodic instabilities are connected by localized zones of intense shear that are oriented approximately 45° from the outward radial direction. The quasi-periodic instabilities continue to develop and eventually become through-cracks, causing the shell to fragment. A viscoplastic constitutive model is formulated to model the high strain-rate expansion and provide insight into the development of plastic instabilities. The formulation of the viscoplastic constitutive model includes the effects of shock heating and damage in the form of microvoid nucleation, growth, and coalescence in the expanding shell. This model uses the Johnson-Cook strength model with the Mie-Grueneisen equation of state and a modified Gurson yield surface. The constitutive model includes the modifications proposed by Tvergaard and the plastic strain controlled nucleation introduced by Neeleman. The constitutive model is implemented as a user material subroutine into ABAQUS/Explicit, which is a commercially available nonlinear explicit dynamic finite element program. A cylindrical shell is modeled using both axisymmetric and plane strain elements. Two experiments were conducted involving plane wave detonated, explosively filled, copper cylinders. Instability, displacement, and velocity data were recorded using a fast framing camera and a Fabry-Perot interferometer. Good agreement is shown between the numerical results and experimental data. An additional explosively bulged cylinder experiment was also performed and a photomicrograph of an
Steady-state temperature distribution in living tissue modeled as cylindrical shells.
NASA Technical Reports Server (NTRS)
Shitzer, A.; Chato, J. C.
1971-01-01
Closed form, analytical solutions to the problem of steady-state heat transfer in living tissue modeled as cylindrical shells are presented and discussed. These solutions are particularly useful for the study of temperature distributions in the extremities. Metabolic heat generation, conduction, and heat transported by the blood perfusing the tissue are considered in the model. The results demonstrate the important role that the blood stream plays in the transfer of heat inside living tissue. Solutions are also presented for the limiting cases of diminishing blood flow that would occur during vasoconstriction or occlusion of blood by external means.
Some general aspects of thin-shell wormholes with cylindrical symmetry
Eiroa, Ernesto F.; Simeone, Claudio
2010-04-15
In this article we study a general class of nonrotating thin-shell wormholes with cylindrical symmetry. We consider two physically sound definitions of the flare-out condition and we show that the less restrictive one allows for the construction of wormholes with positive energy density at the throat. We also analyze the mechanical stability of these objects under perturbations preserving the symmetry, proving that previous results are particular cases of a general property. We present examples of wormholes corresponding to Einstein-Maxwell spacetimes.
Steady-state temperature distribution in living tissue modeled as cylindrical shells.
NASA Technical Reports Server (NTRS)
Shitzer, A.; Chato, J. C.
1971-01-01
Closed form, analytical solutions to the problem of steady-state heat transfer in living tissue modeled as cylindrical shells are presented and discussed. These solutions are particularly useful for the study of temperature distributions in the extremities. Metabolic heat generation, conduction, and heat transported by the blood perfusing the tissue are considered in the model. The results demonstrate the important role that the blood stream plays in the transfer of heat inside living tissue. Solutions are also presented for the limiting cases of diminishing blood flow that would occur during vasoconstriction or occlusion of blood by external means.
Vibration damping in cylindrical shells filled with low-density low-wave-speed media
NASA Astrophysics Data System (ADS)
Verdirame, Justin M.; Nayfeh, Samir A.
2005-05-01
Significant damping can be introduced to a closed structure by filling the structure with a moderately lossy, low-wave-speed medium, such as a foam or a low-density powder. In this paper, we study the damping in long, thin-walled, cylindrical tubes filled with a low-density powder. Experimental results show that significant damping can be attained in tube bending (n=1) modes as well as shell bending (n=2 and higher) modes. To predict the damping in such systems, we develop a model based on three-dimensional shell equations including shear deformation and in-plane inertia, and treat the powder as a compressible fluid with a complex speed of sound. By studying the spatial decay of steady harmonic motion in an infinitely long tube, we obtain estimates for the loss factor of vibration for various numbers of circumferential nodes as a function of driving frequency.
A simplified method of elastic-stability analysis for thin cylindrical shells I : Donnell's equation
NASA Technical Reports Server (NTRS)
Batdorf, S B
1947-01-01
The equation for the equilibrium of cylindrical shells introduced by Donnell in NACA Technical Report no. 479 to find the critical stresses of cylinders in torsion is applied to find critical stresses for cylinders with simply supported edges under other loading conditions. It is shown that by this method solutions may be obtained very easily and the results in each case may be expressed in terms of two nondimensional parameters, one dependent on the critical stress and the other essentially determined by the geometry of the cylinder. The influence of boundary conditions related to edge displacements in the shell median surface is discussed. The accuracy of the solutions found is established by comparing them with previous theoretical solutions and with test results. The solutions to a number of problems concerned with the buckling of cylinders with simply supported edges on the basis of a unified viewpoint are presented in a convenient form for practical use. (author)
Existence of axisymmetric modes of thin cylindrical shells with axial displacement restraint
NASA Technical Reports Server (NTRS)
El-Raheb, M.
1981-01-01
A necessary and sufficient condition is derived for the existence of the axisymmetric mode of cylindrical shells with a radial displacement having one half wave along the axis and axial displacement restrained at both ends. The condition is purely geometric and consists of an upper bound on the mean radius of thickness ratio for a given fixed value of the length to mean radius ratio, above which the mode with one half wave in radial displacement along the axis ceases to exist. The proof is based on enforcing two basic lemmas concerned with the simplicity of the eigenvalues of the shell and the uniform ordering of these eigenvalues with the number of nodes of their corresponding radial displacement eigenfunctions.
Effect of a cylindrical thin-shell of matter on the electrostatic self-force on a charge
NASA Astrophysics Data System (ADS)
Rubín de Celis, Emilio
2016-02-01
The electrostatic self-force on a point charge in cylindrical thin-shell space-times is interpreted as the sum of a bulk field and a shell field. The bulk part corresponds to a field sourced by the test charge placed in a space-time without the shell. The shell field accounts for the discontinuity of the extrinsic curvature {κ ^p}_q. An equivalent electric problem is stated, in which the effect of the shell of matter on the field is reconstructed with the electric potential produced by a non-gravitating charge distribution of total image charge Q, to interpret the shell field in both the interior and exterior regions of the space-time. The self-force on a point charge q in a locally flat geometry with a cylindrical thin-shell of matter is calculated. The charge is repelled from the shell if {κ p}p=κ <0 (ordinary matter) and attracted toward the shell if κ >0 (exotic matter). The total image charge is zero for exterior problems, while for interior problems Q/q=-κ r_e, with r_e the external radius of the shell. The procedure is general and can be applied to interpret self-forces in other space-times with shells, e.g., for locally flat wormholes we found Q_{∓}^{wh}/q=-1/ (κ_{wh} r_{± }).
NASA Astrophysics Data System (ADS)
Franco, Jamal Eli
The residual stress in a high alloy ultra thin cylindrical shell is studied. The objective of this research is to quantify and develop an understanding of the residual stress produced during the fabrication process. It is shown, with the application of finite element analysis and experimental measurements, that the residual stress can be predicted and quantified. This dissertation investigates the experimental and numerical methods to determine the residual stress in high alloy ultra thin cylindrical shells. Experimental measurements of the shell profiles are used to obtain stresses during manufacturing. Finite element analysis is used to verify the experimental results. These results compare favorably with theoretical values. This dissertation shows that the thermal process applied to the shell for separation does not contribute to the residual stress. A residual stress due to the bending moment caused by the conical geometry of the shell is evident in the finite element results.
A semi-analytical formulation for the elastoplastic analysis of imperfect cylindrical shells
NASA Astrophysics Data System (ADS)
Deerenberg, E.
1991-12-01
A semi-analytical formulation for the elastoplastic analysis of initially imperfect cylindrical shells under axial compression and lateral pressure was developed. The formulation is based on a small strain, moderate rotation shell theory and small strain incremental constitutive theory. The basic shell equations and the partially inverted constitutive relations in total form are reduced to a set of coupled nonlinear algebraic/ordinary differential equations by means of a Fourier decomposition of the state variables, imperfections and loads in circumferential direction of the shell, and application of Galerkin's method. The governing nonlinear equations are solved with an incremental iterative technique. The method of quasilinearization is used to generate the governing equations of the iterative procedure which consistently takes into account both geometrical and material nonlinearities. Plasticity effects are described using a layered approach. The classical flow theory based on the von Mises yield surface, associative flow rule, and the isotropic hardening law is used to describe the evolution of the plastic strains in the integration points. In every iteration a set of linear ordinary differential equations is solved numerically with a shooting method and a return mapping algorithm is used to integrate the constitutive equations locally. A number of elastic and elastoplastic buckling problems are solved for which results are known from literature. It is shown that the quadratic rate of convergence, characteristic for a Newton type iteration procedure, is retained even for large load steps. A comparison between the present results and the results from literature shows a good agreement.
A cylindrical shell with a stress-free end which contains an axial part-through or through crack
NASA Technical Reports Server (NTRS)
Erdogan, F.; Yahsi, O. S.
1983-01-01
The interaction problem of a through or a part through crack with a stress free boundary in a semi-infinite cylindrical shell is considered. It is assumed that the crack lies in a meridional plane which is a plane of symmetry with respect to the external loads as well as the geometry. The circular boundary of the semi-infinite cylinder is assumed to be stress free. By using a transverse shear theory the problem is formulated in terms of a system of singular integral equations. The line spring model is used to treat the part through crack problem. In the case of a through crack the interaction between the perturbed stress fields due to the crack and the free boundary is quite strong and there is a considerable increase in the stress intensity factors caused by the interaction. On the other hand in the problem of a surface crack the interaction appears to be much weaker and consequently the magnification in the stress intensity factors is much less significant.
NASA Astrophysics Data System (ADS)
Casado, Victor M.; Hinsch, Svend; Garcia, Jesus Gomez; Castro, Saullo G. P.
2014-06-01
The impact of geometrical imperfections on the general instability of laminated cylindrical sandwich shells was assessed by means of a numerical investigation. Five forms of 'ideal' initial geometrical imperfection patterns were studied: eigen-mode shaped, axisymmetric dimple, geometric dimple, single perturbation load and single stress-free dimple. Implementation of such imperfections, despite their simplicity, can provide a method for predicting lower-bound buckling loads during the preliminary design phase, when the structural defects of the real hardware are unknown. Numerical prediction of the non- linear instability of the cylinders under axial compression was performed using the finite element method. A typical launcher Inter Stage Skirt (ISS) structure is used as the basis for the chosen geometry and materials. In order to make design and qualification tests more affordable, it is common to use representative sub-scaled hardware. This paper verifies the validity of the chosen sub-scaling method of an ISS cylindrical shell. Buckling mechanisms are described and the different lower-bound methods are discussed.
Bandgap analysis of cylindrical shells of generalized phononic crystals by transfer matrix method
NASA Astrophysics Data System (ADS)
Shu, Hai-Sheng; Wang, Xing-Guo; Liu, Ru; Li, Xiao-Gang; Shi, Xiao-Na; Liang, Shan-Jun; Xu, Li-Huan; Dong, Fu-Zhen
2015-09-01
Based on the concept of generalized phononic crystals (GPCs), a type of 1D cylindrical shell of generalized phononic crystals (CS-GPCs) where two kinds of homogeneous materials are arranged periodically along radial direction was proposed in this paper. On the basis of radial, torsional shear and axial shear vibrational equations of cylindrical shell, the total transfer matrix of mechanical state vector were set up respectively, and the bandgap phenomena of these three type waves were disclosed by using the method of transfer matrix eigenvalue of mechanical state vector instead of the previous localized factor analyses and Bloch theorem. The characteristics and forming mechanism of these bandgaps of CS-GPCs, together with the influences of several important structure and material parameters on them were investigated and discussed in detail. Our results showed that, similar to the plane wave bandgaps, 1D CS-GPCs can also possess radial, torsional shear and axial shear wave bandgaps within high frequency region that conforms to the Bragg scattering effect; moreover, the radial vibration of CS-GPCs can generate low frequency bandgap (the start frequency near 0 Hz), as a result of the double effects of wavefront expansion and Bragg scattering effect, wherein the wavefront effect can be the main factor and directly determine the existence of the low frequency bandgaps, while the Bragg scattering effect has obvious enhancement effect to the attenuation. Additionally, the geometrical and material parameters of units have significant influences on the wave bandgaps of CS-GPCs.
Steel, Robin; Fish, Peter J
2002-02-01
Flow phantoms used in medical ultrasound usually employ a plastic tube as a blood vessel mimic. These tubes often have acoustic properties differing significantly from the tissue and blood-mimicking media, which results in distortion of the acoustic pressure field within the tubes and, hence, of the Doppler flow spectra. Previous analyses of this problem have used some form of the infinite plate transmission coefficient, although at least one ray-based analysis has considered a cylindrical interface but with zero wall thickness. In this paper, we compare these approximate pressure fields with the exact solution for oblique incidence on a viscoelastic cylindrical shell at 5 MHz to find for which materials the plate approximation is valid. The shell has water both inside and outside, but it can be modified to use a different fluid inside and also to include absorption in either fluid. We find the plate approximation is reasonable for soft tubes such as the copolymer Cflex (Cole-Palmer, Niles, IL) but much less so for hard tubes such as polymethylmethacrylate (PMMA).
Acoustic resonance scattering from a multilayered cylindrical shell with imperfect bonding.
Rajabi, M; Hasheminejad, Seyyed M
2009-12-01
The method of wave function expansion is adopted to study the three dimensional scattering of a time-harmonic plane progressive sound field obliquely incident upon a multi-layered hollow cylinder with interlaminar bonding imperfection. For the generality of solution, each layer is assumed to be cylindrically orthotropic. An approximate laminate model in the context of the modal state equations with variable coefficients along with the classical T-matrix solution technique is set up for each layer to solve for the unknown modal scattering and transmission coefficients. A linear spring model is used to describe the interlaminar adhesive bonding whose effects are incorporated into the global transfer matrix by introduction of proper interfacial transfer matrices. Following the classic acoustic resonance scattering theory (RST), the scattered field and response to surface waves are determined by constructing the partial waves and obtaining the non-resonance (backgrounds) and resonance components. The solution is first used to investigate the effect of interlayer imperfection of an air-filled and water submerged bilaminate aluminium cylindrical shell on the resonances associated with various modes of wave propagation (i.e., symmetric/asymmetric Lamb waves, fluid-borne A-type waves, Rayleigh and Whispering Gallery waves) appearing in the backscattered spectrum, according to their polarization and state of stress. An illustrative numerical example is also given for a multi-layered (five-layered) cylindrical shell for which the stiffness of the adhesive interlayers is artificially varied. The sensitivity of resonance frequencies associated with higher mode numbers to the stiffness coefficients is demonstrated to be a good measure of the bonding strength. Limiting cases are considered and fair agreements with solutions available in the literature are established.
NASA Astrophysics Data System (ADS)
Plattenburg, Joseph; Dreyer, Jason T.; Singh, Rajendra
2016-06-01
This paper proposes a new analytical model for a thin cylindrical shell that utilizes a homogeneous cardboard liner to increase modal damping. Such cardboard liners are frequently used as noise and vibration control devices for cylindrical shell-like structures in automotive drive shafts. However, most prior studies on such lined structures have only investigated the associated damping mechanisms in an empirical manner. Only finite element models and experimental methods have been previously used for characterization, whereas no analytical studies have addressed sliding friction interaction at the shell-liner interface. The proposed theory, as an extension of a prior experimental study, uses the Rayleigh-Ritz method and incorporates material structural damping along with frequency-dependent viscous and Coulomb interfacial damping formulations for the shell-liner interaction. Experimental validation of the proposed model, using a thin cylindrical shell with three different cardboard liner thicknesses, is provided to validate the new model, and to characterize the damping parameters. Finally, the model is used to investigate the effect of the liner and the damping parameters on the modal attenuation of the shell vibration, in particular for the higher-order coupled shell modes.
Redirection and Splitting of Sound Waves by a Periodic Chain of Thin Perforated Cylindrical Shells
NASA Astrophysics Data System (ADS)
Bozhko, Andrey; Sánchez-Dehesa, José; Cervera, Francisco; Krokhin, Arkadii
2017-06-01
The scattering of sound by finite and infinite chains of equally spaced perforated metallic cylindrical shells in an ideal (inviscid) and viscous fluid is theoretically studied using rigorous analytical and numerical approaches. Because of perforations, a chain of thin shells is practically transparent for sound within a wide range of frequencies. It is shown that strong scattering and redirection of sound by 90° may occur only for a discrete set of frequencies (Wood's anomalies) where the leaky eigenmodes are excited. The spectrum of eigenmodes consists of antisymmetric and symmetric branches with normal and anomalous dispersion, respectively. The antisymmetric eigenmode turns out to be a deaf mode, since it cannot be excited at normal incidence. However, at slightly oblique incidence, both modes can be resonantly excited at different but close frequencies. The symmetric mode, due to its anomalous dispersion, scatters sound in the "wrong" direction. This property may find an application for the splitting of the two resonant harmonics of the incoming signal into two beams propagating along the chain in the opposite directions. A chain of perforated cylinders may also be used as a passive antenna that detects the direction to the incoming signal by measuring the frequencies of the waves excited in the chain. Calculations are presented for aluminum shells in viscous air where the effects of anomalous scattering, redirection, and signal splitting are well manifested.
NASA Technical Reports Server (NTRS)
Hulcher, Anthony Bruce; McGowan, David M.; Grimsley, Brian W.; Johnston, Norman J.; Gordon, Gail H. (Technical Monitor)
2001-01-01
Two 61-cm-diameter eight-ply quasi-isotropic IM7/PEEK cylindrical shells were fabricated by automated fiber placement the NASA Langley Research Center using only infrared radiant heat to preheat the substrate and incoming composite uni-tape. The shells were characterized by ultrasonic c-scans for overall consolidation quality, and by optical microscopy and acid digestion for void content. Compression tests were also performed. Although the material used in the study was of generally poor quality due to numerous splits and dry fiber regions, the process was able to achieve a net reduction in void content in the as-placed component. Microscopy of the composite shells revealed well-consolidated, void-free interfaces. The two cylinders were then tested in uni-axial compression in a 1334 kN-capacity hydraulic test machine until buckling occurred. A geometrically nonlinear finite element analysis was conducted, and the differences between the predicted and measured values were 18.0 and 25.8%, respectively. Inclusion of measured imperfections of the cylinder into the analysis is expected to reduce these differences.
NASA Astrophysics Data System (ADS)
Plattenburg, Joseph; Dreyer, Jason T.; Singh, Rajendra
2017-07-01
This article extends a recent publication [MSSP (2016), 176-196] by developing a Rayleigh-Ritz model of a thin cylindrical shell to predict its response subject to concurrent active and passive damping treatments. These take the form of piezoelectric patches and a distributed cardboard liner, since the effects of such combined treatments are yet to be investigated. Furthermore, prior literature typically considers only the ;bimorph; active patch configuration (with patches on the inner and outer shell surfaces), which is not feasible with an interior passive liner treatment. Therefore, a novel configuration-termed as ;unimorph;-is proposed and included in the model. Experiments are performed on a shell with active patches (under harmonic excitation from 200 to 2000 Hz) in both the bimorph and unimorph configurations to provide evidence for the analytical model predictions. The proposed model is then employed to assess competing control system designs by examining local vs. global control schemes as well as considering several alternate active patch locations, both with and without the passive damping. Non-dimensional performance metrics are devised to facilitate comparisons of vibration attenuation among different designs. Finally, insertion loss values are measured under single-frequency excitation to evaluate several vibration control designs, and to compare the effects of alternate damping treatments.
Aeroelastic stability of cylindrical shells interacting with internal annular fluid flow
NASA Astrophysics Data System (ADS)
Bochkarev, S. A.; Lekomtsev, S. V.
2017-06-01
This paper is devoted to the analysis of the dynamic behavior of cylindrical shells, containing an internal annular layer of ideal fluid and subject to the external supersonic gas flow. The aerodynamic pressure is calculated based on the quasi-static aerodynamic theory. The behavior of the compressible fluid is described in terms of the perturbation velocity potential. A mathematical formulation of the problem is developed based on the classical theory of shells and virtual displacement principle. A solution of the problem involves computation of complex eigenvalues of the coupled system of equations. The paper presents the results of numerical experiments, which were performed to estimate the influence of the fluid flow velocity on the value of the static pressure in the unperturbed gas flow for shells, interacting with fluid layers of different thicknesses. The numerical simulation shows that a reduction of the fluid layer thickness and increase of the fluid velocity produce a stabilizing effect by virtue of increasing the threshold of aerodynamic stability. However, an essential reduction of the layer thickness can lead, depending on the preset combinations of boundary conditions, to a considerable growth of the stability threshold or to the onset of instability.
NASA Astrophysics Data System (ADS)
Abrosimov, N. A.; Elesin, A. V.
2016-07-01
On the basis of the applied theory of shells, a resolving system of equations is formulated and a method for the numerical solution of problems of nonlinear nonaxisymmetric deformation and fracture of composite cylindrical shells at explosive loadings of different intensity is developed. A model of progressive destruction of a composite shell based on the degradation of stiffness characteristics of individual layers in a multilayer package is elaborated, which depends on the fracture mode of the binder and fiber. The reliability of the technique considered is proved by comparing calculation results with known experimental data. Results of an analysis of the effect of nonaxisymmetric arrangement of an explosive charge on the fracture behavior of composite cylindrical shells with different reinforcement structures are presented.
NASA Technical Reports Server (NTRS)
Kriegesmann, Benedikt; Hilburger, Mark W.; Rolfes, Raimund
2012-01-01
Results from a numerical study of the buckling response of a thin-walled compressionloaded isotropic circular cylindrical shell with initial geometric and loading imperfections are used to determine a lower bound buckling load estimate suitable for preliminary design. The lower bound prediction techniques presented herein include an imperfection caused by a lateral perturbation load, an imperfection in the shape of a single stress-free dimple (similar to the lateral pertubation imperfection), and a distributed load imperfection that induces a nonuniform load in the shell. The ABAQUS finite element code is used for the analyses. Responses of the cylinders for selected imperfection amplitudes and imperfection types are considered, and the effect of each imperfection is compared to the response of a geometrically perfect cylinder. The results indicate that compression-loaded shells subjected to a lateral perturbation load or a single dimple imperfection, and a nonuniform load imperfection, exhibit similar buckling behavior and lower bound trends and the predicted lower bounds are much less conservative than the corresponding design recommendation NASA SP-8007 for the design of buckling-critical shells. In addition, the lateral perturbation technique and the distributed load imperfection produce response characteristics that are physically meaningful and can be validated via laboratory testing.
NASA Astrophysics Data System (ADS)
Asadi, Hamed
2017-09-01
Spacecraft and satellite are susceptible to aerothermoelastic flutter instability, which may jeopardize the mission of the spacecraft and satellite. This kind of instability may result from the coupling of the thermal radiation from the sun and the elastic deformations of aeronautical components. As a first endeavor, the aerothermoelastic flutter and buckling instabilities of functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shell under simultaneous actions of aerodynamic loading and elevated temperature conditions are investigated. The formulations are derived according to the first-order shear deformation theory, Donnell shell theory in conjunction with von Karman geometrical nonlinearity. Thermomechanical properties are assumed to be temperature-dependent and modified rule of mixture is used to determine the equivalent material properties of the FG-CNTRC cylindrical shell. The quasi-steady Krumhaar's modified piston theory by taking into account the effect of panel curvature, is used to determine the aerodynamic pressure. The nonlinear dynamic equations are discretized in the circumferential and longitudinal directions using the trigonometric expression and the harmonic differential quadrature method, respectively. Effects of various influential factors, including CNT volume fraction and distribution, boundary conditions, geometrical parameters, thermal environments, freestream static pressure and Mach number on the aerothermoelastic instabilities of the FG-CNTRC cylindrical shell are studied in details. It is found that temperature rise has a significant effect on the aerothermoelastic flutter characteristics of the FG-CNTRC cylindrical shell. It is revealed that cylindrical shells with intermediate CNT volume fraction have intermediate critical dynamic pressure, while do not have, necessarily, intermediate critical buckling temperature. It is concluded that the critical circumferential mode number (mCr) corresponding to the
Design Optimization and Residual Strength Assessment of a Cylindrical Composite Shell Structure
NASA Technical Reports Server (NTRS)
Rais-Rohani, Masoud
2000-01-01
A summary of research conducted during the specified period is presented. The research objectives included the investigation of an efficient technique for the design optimization and residual strength assessment of a semi-monocoque cylindrical shell structure made of composite materials. The response surface methodology is used in modeling the buckling response of individual skin panels under the combined axial compression and shear loading. These models are inserted into the MSC/NASTRAN code for design optimization of the cylindrical structure under a combined bending-torsion loading condition. The comparison between the monolithic and sandwich skin design cases indicated a 35% weight saving in using sandwich skin panels. In addition, the residual strength of the optimum design was obtained by identifying the most critical region of the structure and introducing a damage in the form of skin-stringer and skin-stringer-frame detachment. The comparison between the two skin design concepts indicated that the sandwich skin design is capable of retaining a higher residual strength than its monolithic counterpart. The results of this investigation are presented and discussed in this report.
NASA Astrophysics Data System (ADS)
Daneshjou, K.; Talebitooti, R.; Kornokar, M.
2017-04-01
This paper presents an analytical solution for sound transmission through a multilayered cylindrical shell with bonded-unbonded (BU) configuration. The multilayered cylindrical shell, which is composed of an outer layer of functionally graded material (FGM) and an inner isotropic layer with a poroelastic core and an air gap, is assumed to be infinitely long and is subjected to a plane wave on its external sidewall. To describe the poroelastic core, the extended full method (EFM) is applied based on Biot's theory. Contrary to previous methods, the EFM completely models the poroelastic cylindrical shell in three dimensions. In addition, the motions of both FGM and isotropic shells are described with the first order shear deformation theory (FSDT). Unlike the simplified method, the EFM does not need to identify the frequency ranges where one of the airborne or frame waves is dominant in BU configuration. In fact, utilizing the EFM for BU configuration permits obtaining the sound transmission loss (TL) irrespective of the dominant wave, which significantly reduces the computational work. Moreover, comparing with the previous models, the EFM provides more accurate results as it does not ignore any term in the modeling. Furthermore, the advantages of the BU-FGM shell in enhancing the TL are demonstrated with respect to the BB-isotropic configuration. It is shown that presence of the FGM in addition to the poroelastic material in a structure yields thermal insulation and improves soundproofing characteristics in a broadband frequency range.
NASA Astrophysics Data System (ADS)
Moriot, J.; Maxit, L.; Guyader, J. L.; Gastaldi, O.; Périsse, J.
2015-02-01
The acoustic detection of defects or leaks inside a cylindrical shell containing a fluid is of prime importance in the industry, particularly in the nuclear field. This paper examines the beamforming technique which is used to detect and locate the presence of an acoustic monopole inside a cylindrical elastic shell by measuring the external shell vibrations. In order to study the effect of fluid-structure interactions and the distance of the source from the array of sensors, a vibro-acoustic model of the fluid-loaded shell is first considered for numerical experiments. The beamforming technique is then applied to radial velocities of the shell calculated with the model. Different parameters such as the distance between sensors, the radial position of the source, the damping loss factor of the shell, or of the fluid, and modifications of fluid properties can be considered without difficulty. Analysis of these different results highlight how the behaviour of the fluid-loaded shell influences the detection. Finally, a test in a water-filled steel pipe is achieved for confirming experimentally the interest of the presented approach.
NASA Astrophysics Data System (ADS)
Honeycutt, T. E.; Roberts, T. G.
1986-05-01
Brass retainer rings are currently fastened to artillery shells by spinning each shell at a high rate and then jamming the ring on it so that it is fastened or welded by friction between the two objects. This is an energy-inefficient process which heats and weakens more material than is desirable. The shell spinning at a high rate is also potentially dangerous. A laser welder is provided that generates output energy focused on a circular or cylindrical shape for simultaneously welding around a 360 degs circumference without unnecessarily heating large amounts of material. The welder may be used to fasten cylindrical shaped objects, gears and shafts together, which is difficult to do by conventional means. The welder may also be used to fasten one cylinder to another. To accomplish the welding, a laser has an unstable optical cavity arranged with its feedback mirror centered to generate a circular output beam having an obscuration in the center. A circularly-symmetric, off-axis concave mirror focuses the output beam onto the objects being fastened and away from the center line or axis of the circular beam.
NASA Astrophysics Data System (ADS)
Kwak, Moon K.; Heo, Seok; Jeong, Moonsan
2009-04-01
This paper is concerned with the dynamic modelling, active vibration controller design and experiments for a cylindrical shell equipped with piezoelectric sensors and actuators. The dynamic model was derived by using Rayleigh-Ritz method based on the Donnel-Mushtari shell theory. The actuator equations which relate the applied voltages to the generalized force and sensor equations which relate the generalized displacements to the sensor output voltages for the piezoelectric wafer were derived based on the pin-force model. The equations of motion along with the piezoelectric sensor equations were then reduced to modal forms considering the modes of interest. An aluminium shell was fabricated to demonstrate the effectiveness of the modelling and control techniques. The boundary conditions at both ends of the shell were assumed to be a shear diaphragm in the numerical analysis. Theoretical natural frequencies of the aluminium shell were then calculated and compared to experimental result. They were in good agreement with experimental result for the first two free-vibration modes. The multi-input and multi-output positive position feedback controller, which can cope with the first two vibration modes, was designed based on the block-inverse theory and was implemented digitally using the DSP board. The experimental results showed that vibrations of the cylindrical shell can be successfully suppressed by the piezoelectric actuator and the proposed controller.
Cross-code comparisons of mixing during the implosion of dense cylindrical and spherical shells
NASA Astrophysics Data System (ADS)
Joggerst, C. C.; Nelson, Anthony; Woodward, Paul; Lovekin, Catherine; Masser, Thomas; Fryer, Chris L.; Ramaprabhu, P.; Francois, Marianne; Rockefeller, Gabriel
2014-10-01
We present simulations of the implosion of a dense shell in two-dimensional (2D) spherical and cylindrical geometry performed with four different compressible, Eulerian codes: RAGE, FLASH, CASTRO, and PPM. We follow the growth of instabilities on the inner face of the dense shell. Three codes employed Cartesian grid geometry, and one (FLASH) employed polar grid geometry. While the codes are similar, they employ different advection algorithms, limiters, adaptive mesh refinement (AMR) schemes, and interface-preservation techniques. We find that the growth rate of the instability is largely insensitive to the choice of grid geometry or other implementation details specific to an individual code, provided the grid resolution is sufficiently fine. Overall, all simulations from different codes compare very well on the fine grids for which we tested them, though they show slight differences in small-scale mixing. Simulations produced by codes that explicitly limit numerical diffusion show a smaller amount of small-scale mixing than codes that do not. This difference is most prominent for low-mode perturbations where little instability finger interaction takes place, and less prominent for high- or multi-mode simulations where a great deal of interaction takes place, though it is still present. We present RAGE and FLASH simulations to quantify the initial perturbation amplitude to wavelength ratio at which metrics of mixing agree across codes, and find that bubble/spike amplitudes are converged for low-mode and high-mode simulations in which the perturbation amplitude is more than 1% and 5% of the wavelength of the perturbation, respectively. Other metrics of small-scale mixing depend on details of multi-fluid advection and do not converge between codes for the resolutions that were accessible.
NASA Astrophysics Data System (ADS)
Bakulin, V. N.; Volkov, E. N.; Nedbai, A. Ya.
2016-05-01
The dynamic stability of a cylindrical orthotropic shell reinforced by longitudinal ribs and a hollow cylinder under the action of axial forces changing harmonically with time was investigated with regard for the axial contact interaction of the shell with the ribs. A solution of the differential equations defining this process has been obtained in the form of trigonometric series in the angular and time coordinates. A two-term approximation of the Mathieu-Hill equations of motion was used for construction of the main region of instability of the shell. As a result, the problem was reduced to a system of algebraic equations for components of displacements of the shell at the locations of the ribs. The problem for uniformly spaced ribs was solved in the explicit form. A numerical example of this solution is presented.
NASA Astrophysics Data System (ADS)
Dajun, Wang; Chunyan, Zhou; Li, Junbao; Shen, Song; Li, Min; Liu, Xijun
2013-07-01
This paper presents an experimental investigation on nonlinear low frequency gravity water waves in a partially filled cylindrical shell subjected to high frequency horizontal excitations. The characteristics of natural frequencies and mode shapes of the water-shell coupled system are discussed. The boundaries for onset of gravity waves are measured and plotted by curves of critical excitation force magnitude with respect to excitation frequency. For nonlinear water waves, the time history signals and their spectrums of motion on both water surface and shell are recorded. The shapes of water surface are also measured using scanning laser vibrometer. In particular, the phenomenon of transitions between different gravity wave patterns is observed and expressed by the waterfall graphs. These results exhibit pronounced nonlinear properties of shell-fluid coupled system.
NASA Technical Reports Server (NTRS)
Mindle, W. L.; Torvik, P. J.
1986-01-01
The natural frequencies and associated mode shapes for three thick open cantilevered cylindrical shells were determined both numerically and experimentally. The shells ranged in size from moderately to very thick with length to thickness ratios of 16, 8 and 5.6, the independent dimension being the shell thickness. The shell geometry is characterized by a circumferential angle of the 142 degrees and a ratio of length to inner radii arc length near 1.0. The finite element analysis was performed using NASTRAN's (COSMIC) triangular plate bending element CTRIA2, which includes membrane effects. The experimental results were obtained through holographic interferometry which enables one to determine the resonant frequencies as well as mode shapes from photographs of time-averaged holograms.
Zeng, Kai; Hu, Youwang; Deng, Guiling; Sun, Xiaoyan; Su, Wenyi; Lu, Yunpeng; Duan, Ji’an
2017-01-01
The eigenfrequency of a resonator plays a significant role in the operation of a cylindrical shell vibrating gyroscope, and trimming is aimed at eliminating the frequency split that is the difference of eigenfrequency between two work modes. In this paper, the effects on eigenfrequency under resonator-top trimming methods that trim the top of the resonator wall are investigated by simulation and experiments. Simulation results show that the eigenfrequency of the trimmed mode increases in the holes-trimming method, whereas it decreases in the grooves-trimming method. At the same time, the untrimmed modes decrease in both holes-trimming and grooves-trimming methods. Moreover, grooves-trimming is more efficient than holes-trimming, which indicates that grooves-trimming can be a primary trimming method, and holes-trimming can be a precision trimming method. The rigidity condition after grooves-trimming is also studied to explain the variation of eigenfrequency. A femtosecond laser is employed in the resonator trimming experiment by the precise ablation of the material. Experimental results are in agreement with the simulation results. PMID:28869507
HL-20 structural design comparison - Conformal shell versus cylindrical crew compartment
NASA Technical Reports Server (NTRS)
Bush, Lance B.; Wahls, Deborah M.; Robinson, James C.
1993-01-01
Extensive studies have been performed at NASA Langley Research Center (LaRC) on personnel launch systems (PLS) concepts. The primary mission of a PLS is the transport of Space Station crew members from Earth to the Space Station and return. The NASA LaRC PLS studies have led to the design of a lifting body configuration named the HL-20. In this study, two different HL-20 structural configurations are evaluated. The two configurations are deemed the conformal shell and the cylindrical crew compartment. The configurations are based on two different concerns for maintenance and operations. One configuration allows for access to subsystems while on-orbit from the interior, while the other allows for easy access to the subsystems during ground maintenance and operations. For each concept, the total structural weight required to sustain the applied loads is quantified through a structural evaluation. Structural weight for both configurations is compared along with the particular attributes of each. Analyses of both configurations indicate no appreciable weight or load relief advantage of one concept over the other. Maintainability and operability, therefore become the primary discriminator, leading to a choice of a crew compartment configuration.
HL-20 structural design comparison - Conformal shell versus cylindrical crew compartment
NASA Astrophysics Data System (ADS)
Bush, Lance B.; Wahls, Deborah M.; Robinson, James C.
1993-04-01
Extensive studies have been performed at NASA Langley Research Center (LaRC) on personnel launch systems (PLS) concepts. The primary mission of a PLS is the transport of Space Station crew members from Earth to the Space Station and return. The NASA LaRC PLS studies have led to the design of a lifting body configuration named the HL-20. In this study, two different HL-20 structural configurations are evaluated. The two configurations are deemed the conformal shell and the cylindrical crew compartment. The configurations are based on two different concerns for maintenance and operations. One configuration allows for access to subsystems while on-orbit from the interior, while the other allows for easy access to the subsystems during ground maintenance and operations. For each concept, the total structural weight required to sustain the applied loads is quantified through a structural evaluation. Structural weight for both configurations is compared along with the particular attributes of each. Analyses of both configurations indicate no appreciable weight or load relief advantage of one concept over the other. Maintainability and operability, therefore become the primary discriminator, leading to a choice of a crew compartment configuration.
HL-20 structural design comparison - Conformal shell versus cylindrical crew compartment
NASA Technical Reports Server (NTRS)
Bush, Lance B.; Wahls, Deborah M.; Robinson, James C.
1993-01-01
Extensive studies have been performed at NASA Langley Research Center (LaRC) on personnel launch systems (PLS) concepts. The primary mission of a PLS is the transport of Space Station crew members from Earth to the Space Station and return. The NASA LaRC PLS studies have led to the design of a lifting body configuration named the HL-20. In this study, two different HL-20 structural configurations are evaluated. The two configurations are deemed the conformal shell and the cylindrical crew compartment. The configurations are based on two different concerns for maintenance and operations. One configuration allows for access to subsystems while on-orbit from the interior, while the other allows for easy access to the subsystems during ground maintenance and operations. For each concept, the total structural weight required to sustain the applied loads is quantified through a structural evaluation. Structural weight for both configurations is compared along with the particular attributes of each. Analyses of both configurations indicate no appreciable weight or load relief advantage of one concept over the other. Maintainability and operability, therefore become the primary discriminator, leading to a choice of a crew compartment configuration.
NASA Astrophysics Data System (ADS)
Daxner, T.; Rammerstorfer, F. G.; Fischer, F. D.
2004-06-01
Pushing a conical die into a pipe, a forming process also known as `flaring', is a way of changing the shape of a thin cylindrical tube into that of a conical shell. Interest in predicting the forming limits for this specific process motivated the present study, in which experiments and Finite Element simulations were employed for the identification of two limiting mechanisms: (a) diffuse necking caused by local loss of material stability at the free, expanding end of the pipe, and (b) loss of global stability due to elasto-plastic `Concertina' buckling of the straight pipe part. The former mechanism leads to the formation of periodic necks and subsequent failure by strain localization and rupture, while the latter mechanism is characterized by a periodic buckling pattern that is similar to the one observed in typical crash elements. Whether collapse or rupture is the limiting factor depends on geometrical parameters and material parameters, such as, for example, the hardening exponent in the Ludwik law. There are some publications of analytical considerations of the flaring process, describing the load displacement behavior of the stamp and the development of plastic deformations in the tube. However, the aspect of material and structural instability requires a deeper insight into the problem, which is provided by the experimental results and the numerical studies presented here. It appears to be important to take the tridimensionality of the stress and strain states into account when reliable predictions of necking and rupture limits are to be made.
1983-12-01
A + f( (n xNxx Nx)6u + (nxNx 9 Nee)Sv )ds (19) s w1 where n are defined as the direction cosines between the normal and the y direction. To integrate...of a specific shell shape. Thus far, Eq (27) applies to all cylindrical shells with the only assumption being the thickness, h, is small as com - pared...results. For instance, after solving Eq (32) for its eight roots, one of them must be established as X1. While this choice is com - pletely arbitrary at
NASA Technical Reports Server (NTRS)
Banks, H. T.; Smith, R. C.
1993-01-01
A fully coupled mathematical model describing the interactions between a vibrating thin cylindrical shell and enclosed acoustic field is presented. Because the model will ultimately be used in control applications involving piezoceramic actuators, the loads and material contributions resulting from piezoceramic patches bonded to the shell are included in the discussion. Theoretical and computational issues lead to the consideration of a weak form of the modeling set of partial differential equations (PDE's) and through the use of a semigroup formulation, well-posedness results for the system model are obtained.
NASA Astrophysics Data System (ADS)
Krysko, V. A.; Vetsel', S. S.; Dobriyan, V. V.; Saltykova, O. A.
2017-05-01
This paper studies the chaotic dynamics of two cylindrical shells nested into each other with a gap and their reinforcing beam, also with a gap, which is subjected to a distributed alternating load. The problem is solved using methods of nonlinear dynamics and the qualitative theory of differential equations. The Novozhilov equations for geometrically nonlinear structures are used as the governing equations. Contact pressure is determined by Kantor's method. Using finite elements in spatial variables, the partial differential equations for the beam and shells are reduced to the Cauchy problem, which is solved by explicit integration (Euler's method). The chaotic synchronization of this system is studied.
Shin, Younghoon; Kwak, Hojeong; Moon, Songky; Lee, Sang-Bum; Yang, Juhee; An, Kyungwon
2016-12-13
We report observation of an exceptional point in circular shell ultrasonic cavities in both theory and experiment. In our theoretical analysis we first observe two interacting mode groups, fluid- and solid-based modes, in the acoustic cavities and then show the existence of an EP of these mode groups exhibiting a branch-point topological structure of eigenfrequencies around the EP. We then confirm the mode patterns as well as eigenfrequency structure around the EP in experiments employing the schlieren method, thereby demonstrating utility of ultrasound cavities as experimental platform for investigating non-Hermitian physics.
NASA Astrophysics Data System (ADS)
Shin, Younghoon; Kwak, Hojeong; Moon, Songky; Lee, Sang-Bum; Yang, Juhee; An, Kyungwon
2016-12-01
We report observation of an exceptional point in circular shell ultrasonic cavities in both theory and experiment. In our theoretical analysis we first observe two interacting mode groups, fluid- and solid-based modes, in the acoustic cavities and then show the existence of an EP of these mode groups exhibiting a branch-point topological structure of eigenfrequencies around the EP. We then confirm the mode patterns as well as eigenfrequency structure around the EP in experiments employing the schlieren method, thereby demonstrating utility of ultrasound cavities as experimental platform for investigating non-Hermitian physics.
Shin, Younghoon; Kwak, Hojeong; Moon, Songky; Lee, Sang-Bum; Yang, Juhee; An, Kyungwon
2016-01-01
We report observation of an exceptional point in circular shell ultrasonic cavities in both theory and experiment. In our theoretical analysis we first observe two interacting mode groups, fluid- and solid-based modes, in the acoustic cavities and then show the existence of an EP of these mode groups exhibiting a branch-point topological structure of eigenfrequencies around the EP. We then confirm the mode patterns as well as eigenfrequency structure around the EP in experiments employing the schlieren method, thereby demonstrating utility of ultrasound cavities as experimental platform for investigating non-Hermitian physics. PMID:27958315
NASA Astrophysics Data System (ADS)
Narasimhan, M. S.; Govind, K. R.
1988-08-01
The design and experimental studies on a corrugated circular cyclindrical waveguide antenna that is feed-excited in the TE11 mode with suppressed far-out sidelobes are reported. To reduce the spillover in the region theta = 90 deg - 180 deg, an attempt was made to introduce circumferential corrugations on the outer surface of the waveguide wall. The design criterion used was that a minimum of 11 corrugations per wavelength were used, and in all there were 25 corrugations. The reason for selecting 25 corrugations was to ensure that the conduction currents induced on the outer walls of the guide were attenuated substantially and did not contribute to the far-out sidelobes. Measured E-plane and H-plane radiation patterns of the feeds and the corrugated waveguide are presented.
On the Flutter of Cylindrical Shells and Panels Moving in a Flow of Gas
NASA Technical Reports Server (NTRS)
Stepanov, R. D.
1958-01-01
The equations of shells are taken in the form of the general technical theory of shallow shells and shells of medium length. The aerodynamic forces acting on a shell are taken into account only as forces of excess pressure according to the formula proposed by A.A. Iliushin in reference 3.
NASA Astrophysics Data System (ADS)
Roussos, N.; Mason, D. P.
2005-03-01
The Lie point symmetry structure of the second order differential equations which describe non-linear radial oscillations of thin-walled hyperelastic cylindrical and spherical shells is investigated. The differential equations depend on the strain-energy function and on the net applied surface pressure. If the net applied surface pressure is time independent, the differential equations admit the Lie point symmetry corresponding to time translational invariance for arbitrary strain-energy functions. Other Lie point symmetries exist for each equation only for special classes of strain-energy function. For the cylindrical shell the special class includes the Mooney-Rivlin strain-energy function and the differential equation reduces to the Ermakov-Pinney equation. A new solution is obtained for a specific time dependent net applied surface pressure. For the spherical shell the special class does not include the Mooney-Rivlin strain-energy function. For free oscillations the differential equation reduces to the Ermakov-Pinney equation but there also exists a special net applied surface pressure and for this pressure the differential equation is more general than the Ermakov-Pinney equation.
NASA Astrophysics Data System (ADS)
Meyer, V.; Maxit, L.; Renou, Y.; Audoly, C.
2017-09-01
The understanding of the influence of non-axisymmetric internal frames on the vibroacoustic behavior of a stiffened cylindrical shell is of high interest for the naval or aeronautic industries. Several numerical studies have shown that the non-axisymmetric internal frame can increase the radiation efficiency significantly in the case of a mechanical point force. However, less attention has been paid to the experimental verification of this statement. That is why this paper proposes to compare the radiation efficiency estimated experimentally for a stiffened cylindrical shell with and without internal frames. The experimental process is based on scanning laser vibrometer measurements of the vibrations on the surface of the shell. A transform of the vibratory field in the wavenumber domain is then performed. It allows estimating the far-field radiated pressure with the stationary phase theorem. An increase of the radiation efficiency is observed in the low frequencies. Analysis of the velocity field in the physical and wavenumber spaces allows highlighting the coupling of the circumferential orders at the origin of the increase in the radiation efficiency.
NASA Astrophysics Data System (ADS)
Biglar, Mojtaba; Mirdamadi, Hamid Reza; Danesh, Mohammad
2014-02-01
In this study, the active vibration control and configurational optimization of a cylindrical shell are analyzed by using piezoelectric transducers. The piezoelectric patches are attached to the surface of the cylindrical shell. The Rayleigh-Ritz method is used for deriving dynamic modeling of cylindrical shell and piezoelectric sensors and actuators based on the Donnel-Mushtari shell theory. The major goal of this study is to find the optimal locations and orientations of piezoelectric sensors and actuators on the cylindrical shell. The optimization procedure is designed based on desired controllability and observability of each contributed and undesired mode. Further, in order to limit spillover effects, the residual modes are taken into consideration. The optimization variables are the positions and orientations of piezoelectric patches. Genetic algorithm is utilized to evaluate the optimal configurations. In this article, for improving the maximum power and capacity of actuators for amplitude depreciation of negative velocity feedback strategy, we have proposed a new control strategy, called "Saturated Negative Velocity Feedback Rule (SNVF)". The numerical results show that the optimization procedure is effective for vibration reduction, and specifically, by locating actuators and sensors in their optimal locations and orientations, the vibrations of cylindrical shell are suppressed more quickly.
Effects of Thickness and Curvature on the Natural Frequencies of Cylindrical Composite Shells
1994-06-14
the midsurface ’P1 Rotation of the normal to the shell surface in the x direction ( about the s axis) TP2 Rotation of the normal to the shell surface...density Curvilinear coordinates of the surface Domain of the midsurface T, Rotation of the normal to the shell surface in the x direction ( about the s...undeformed shell midsurface remain straight and normal. In other words, transverse shear strains are neglected, resulting in overestimates of the natural
NASA Astrophysics Data System (ADS)
Qu, Yegao; Hua, Hongxing; Meng, Guang
2015-10-01
A semi-analytical method is developed to predict the vibration and acoustic responses of submerged coupled spherical-cylindrical-spherical shells stiffened by circumferential rings and longitudinal stringers. The structural model of the coupled stiffened shell is formulated using a modified variational method combined with a multi-segment partitioning technique, whereas a spectral Kirchhoff-Helmholtz integral formulation is employed to model the exterior fluid. The stiffened rings and stringers, which may be few or many in number, non-uniform or uniform in size, and non-uniformly or uniformly spaced, are treated as discrete elements. The displacement and sound pressure variables are expanded in the form of a double mixed series using Fourier series and Chebyshev orthogonal polynomials. This provides a flexible way for the present method to account for the individual contributions of circumferential wave modes to the vibration and acoustic responses of coupled stiffened shells in an analytical manner. The application of the method is illustrated with several numerical examples, and comparisons are made with available solutions obtained from the coupled finite element/boundary element method. The contributions of different circumferential wave modes to the vibration responses, sound power and the directivity of radiated sound pressure for coupled shells bounded by light or heavy fluid are examined. Effects of the rings and stringers on the vibration and acoustic responses of the coupled shells are investigated.
Yilmaz, M. F.; Safronova, A. S.; Esaulov, A. A.; Kantsyrev, V. L.; Quart, N. D.; Williamson, K. M.; Shrestha, I.
2009-01-21
K-shell radiation of Al and Mg and L-shell radiation of Mo from implosions of compact cylindrical wire arrays (CCWA) on the 1 MA UNR Zebra generator was studied. Specifically, radiation from implosions of 3 and 6 mm CCWA with (16-24) Al-5052 (95% Al and 5% Mg) and Al-5052 (97.5% Al and 2.5% Mg) and Mo wires was analyzed using the full set of diagnostics: PCD and current signals, and X-ray pinhole images and spectra. Previously developed non-LTE models were applied to model spatially resolved time integrated as well as time-gated spatially integrated spectra from Al, Mg, and Mo plasmas. Derived electron temperature and density spatial gradients as well as percentage of radiating mass were studied and compared. In addition, the novel Wire Dynamics Model (WDM) was used to analyze the implosion dynamics of compact wire array loads.
NASA Technical Reports Server (NTRS)
Block, D. L.
1972-01-01
Results of analytical study to determine desirable ring and stringer stiffener parameters and proportions for axially compressed stiffened isotropic cylinders with and without internal pressure are presented. This investigation examines the panel and general instability buckling modes of a stiffened cylindrical shell and from this determines desirable stiffener parameters and proportions. Classical buckling equations are used which retain the important effects of the stiffeners. The results determined by using the simpler classical buckling equations are then spot checked and verified using buckling equations which considered discrete ring stiffeners and nonlinear prebuckling deformations. For both rings and stringers, T-shaped stiffeners are preferable and the effects to stiffener shape are much more pronounced at low or zero values of the internal pressure parameter. Simple analytical expressions are developed and presented which express the stiffener area parameter, the ratio of stiffener area and elastics to shell wall area and elastic modulus, in terms of the cylinder geometry and internal pressure parameter.
NASA Technical Reports Server (NTRS)
Delale, F.; Erdogan, F.
1977-01-01
The problem of a cylindrical shell containing a circumferential through crack is considered by taking into account the effect of transverse shear deformations. The formulation is given for a specially orthotropic material within the confines of a linearized shallow shell theory. The particular theory used permits the consideration of all five boundary conditions regarding moment and stress resultants on the crack surface. Consequently, aside from multiplicative constants representing the stress intensity factors, the membrane and bending components of the asymptotic stress fields near the crack tip are found to be identical. The stress intensity factors are calculated separately for a cylinder under a uniform membrane load, and that under a uniform bending moment. Sample results showing the nature of the out-of-plane crack surface displacement and the effect of the Poisson's ratio are presented.
Hussey, T.W.
1987-09-01
A simple model for the target dynamics of a distributed, uniform density imploding gas puff plasma colliding with a thin, annular, cylindrical shell has been developed. This model is applicable to a pulse-power-driven, photoionization-pumped, recombination x-ray laser. By integrating the equation for momentum conservation it was possible to obtain target closure time, a quantity that may be compared to experiment. In addition, it was possible to find energy available as pump radiation as a function of target parameters. We find that this quantity is maximized when target mass approximately equals the gas mass times the thickness of the gas puff prior to stagnation divided by twice the target radius. We also find that this quantity is a relatively weak function of gas puff shell thickness prior to stagnation, a somewhat stronger function of target mass, and a very strong function of implosion velocity. 7 refs.
NASA Astrophysics Data System (ADS)
Zhou, Chunyan; Wang, Dajun
2014-04-01
In Part I of this work (Comm. Nonlin. Sci. Numer. Simulat. 18 (2013) 1710-1724), an experimental investigation on nonlinear low-frequency gravity water waves in a cylindrical shell subjected to high-frequency horizontal excitations was reported. To reveal the mechanism of this phenomenon, a theoretical analysis is now presented as Part II of the work. A set of nonlinear equations for two mode interactions is established based on variational principle of fluid-shell coupled system. Theory proofs that for high frequency mode of circumferential wave number m nonlinear interaction exits only with gravity wave modes of circumferential wave number zero or 2m. Multi-scale analysis reveals that appearance of such phenomenon is due to Hopf bifurcation of the dynamic system. Curves of critic excitation force with respect to excitation frequency are obtained by analysis. Theoretical results show good qualitative and quantitative agreement with experimental observations.
NASA Astrophysics Data System (ADS)
Amenzade, R. Yu.; Kiiko, I. A.
2007-06-01
It is commonly assumed that the theory based on the Kirchhoff hypotheses describes the properties inherent in the wave processes occurring in shells filled with fluids. But there are several new effects that cannot be described by this theory (in particular, the appearance of new types of waves). In this paper, we present a linearized description of axisymmetric wave motion of a perfect incompressible fluid in a multilayered cylindrical shell with allowance for shear strain; the shell is assumed to be infinite and simply supported. This description is aimed at finding new mechanical effects and hence at estimating the influence of the multiple layers and the shear strain on the wave characteristics. In a sense, it generalizes and develops well-known studies of this type. Practice necessitates deriving equations constructed under the assumption that the physical and mechanical properties of the shell material are inhomogeneous along the thickness direction or the shell is multilayered; the development of refined theories (compared with the classical theory based on the Kirchhoff—Love straight normal hypothesis) is also inspired by practice. This is primarily related to the fact that multilayered thin-walled shells made of composite materials are used in various fields of technology. It is of interest to note that, as a result of long evolution, the phenomenon of being multilayered also predominates in living organisms. For example, this is typical of big blood vessels [1] (arteries and veins). In [2], on the basis of a three-dimensional variational principle of mixed type, the equations of motion and physical relations for elastic anisotropic shells rigidly inhomogeneous in the thickness direction are derived under the assumptions of the theory of thin shells and with shear strains taken into account. It is also noted that the case of multilayered shells can be modeled by introducing functions with integrable singularities. When studying wave propagation in
1992-11-25
83 66 Bending Shell Transfer Surface With Soft Core; dB = 10 log ((Pi(3a/4)/Po)2) .................................................... 84...ILLUSTRATIONS (Cont’d) Figure Page 68 Bending Shell Transfer Surface (n = 1); dB = I log ((Pj(a/2)/P...90; dB = 101og((Pi(a/2)/Px)2) ....................................................... 90 72 Bending Shell Transfer Surface (Liquid-Filled); dB = I log
Velikovich, A. L.; Schmit, P. F.
2015-12-15
Bell-Plesset (BP) effects account for the influence of global convergence or divergence of the fluid flow on the evolution of the interfacial perturbations embedded in the flow. The development of the Rayleigh-Taylor instability in radiation-driven spherical capsules and magnetically-driven cylindrical liners necessarily includes a significant contribution from BP effects due to the time dependence of the radius, velocity, and acceleration of the unstable surfaces or interfaces. An analytical model is presented that, for an ideal incompressible fluid and small perturbation amplitudes, exactly evaluates the BP effects in finite-thickness shells through acceleration and deceleration phases. The time-dependent dispersion equations determining the “instantaneous growth rate” are derived. It is demonstrated that by integrating this approximate growth rate over time, one can accurately evaluate the number of perturbation e-foldings during the inward acceleration phase of the implosion. In the limit of small shell thickness, exact thin-shell perturbation equations and approximate thin-shell dispersion equations are obtained, generalizing the earlier results [E. G. Harris, Phys. Fluids 5, 1057 (1962); E. Ott, Phys. Rev. Lett. 29, 1429 (1972); A. B. Bud'ko et al., Phys. Fluids B 2, 1159 (1990)].
NASA Astrophysics Data System (ADS)
Velikovich, A. L.; Schmit, P. F.
2015-12-01
Bell-Plesset (BP) effects account for the influence of global convergence or divergence of the fluid flow on the evolution of the interfacial perturbations embedded in the flow. The development of the Rayleigh-Taylor instability in radiation-driven spherical capsules and magnetically-driven cylindrical liners necessarily includes a significant contribution from BP effects due to the time dependence of the radius, velocity, and acceleration of the unstable surfaces or interfaces. An analytical model is presented that, for an ideal incompressible fluid and small perturbation amplitudes, exactly evaluates the BP effects in finite-thickness shells through acceleration and deceleration phases. The time-dependent dispersion equations determining the "instantaneous growth rate" are derived. It is demonstrated that by integrating this approximate growth rate over time, one can accurately evaluate the number of perturbation e-foldings during the inward acceleration phase of the implosion. In the limit of small shell thickness, exact thin-shell perturbation equations and approximate thin-shell dispersion equations are obtained, generalizing the earlier results [E. G. Harris, Phys. Fluids 5, 1057 (1962); E. Ott, Phys. Rev. Lett. 29, 1429 (1972); A. B. Bud'ko et al., Phys. Fluids B 2, 1159 (1990)].
Velikovich, A. L.; Schmit, P. F.
2015-12-28
Bell-Plesset (BP) effects account for the influence of global convergence or divergence of the fluid flow on the evolution of the interfacial perturbations embedded in the flow. The development of the Rayleigh-Taylor instability in radiation-driven spherical capsules and magnetically-driven cylindrical liners necessarily includes a significant contribution from BP effects due to the time dependence of the radius, velocity, and acceleration of the unstable surfaces or interfaces. An analytical model is presented that, for an ideal incompressible fluid and small perturbation amplitudes, exactly evaluates the BP effects in finite-thickness shells through acceleration and deceleration phases. The time-dependent dispersion equations determining themore » “instantaneous growth rate” are derived. It is demonstrated that by integrating this approximate growth rate over time, one can accurately evaluate the number of perturbation e-foldings during the inward acceleration phase of the implosion. As a result, in the limit of small shell thickness, exact thin-shell perturbationequations and approximate thin-shell dispersion equations are obtained, generalizing the earlier results [E. G. Harris, Phys. Fluids 5, 1057 (1962); E. Ott, Phys. Rev. Lett. 29, 1429 (1972); A. B. Bud'ko et al., Phys. Fluids B 2, 1159 (1990)].« less
Velikovich, A. L.; Schmit, P. F.
2015-12-28
Bell-Plesset (BP) effects account for the influence of global convergence or divergence of the fluid flow on the evolution of the interfacial perturbations embedded in the flow. The development of the Rayleigh-Taylor instability in radiation-driven spherical capsules and magnetically-driven cylindrical liners necessarily includes a significant contribution from BP effects due to the time dependence of the radius, velocity, and acceleration of the unstable surfaces or interfaces. An analytical model is presented that, for an ideal incompressible fluid and small perturbation amplitudes, exactly evaluates the BP effects in finite-thickness shells through acceleration and deceleration phases. The time-dependent dispersion equations determining the “instantaneous growth rate” are derived. It is demonstrated that by integrating this approximate growth rate over time, one can accurately evaluate the number of perturbation e-foldings during the inward acceleration phase of the implosion. As a result, in the limit of small shell thickness, exact thin-shell perturbationequations and approximate thin-shell dispersion equations are obtained, generalizing the earlier results [E. G. Harris, Phys. Fluids 5, 1057 (1962); E. Ott, Phys. Rev. Lett. 29, 1429 (1972); A. B. Bud'ko et al., Phys. Fluids B 2, 1159 (1990)].
Nonlinear Breathing Vibrations and Chaos of a Circular Truss Antenna with 1:2 Internal Resonance
NASA Astrophysics Data System (ADS)
Zhang, W.; Chen, J.; Sun, Y.
This paper investigates the nonlinear breathing vibrations and chaos of a circular truss antenna under changing thermal environment with 1:2 internal resonance for the first time. A continuum circular cylindrical shell clamped by one beam along its axial direction on one side is proposed to replace the circular truss antenna composed of the repetitive beam-like lattice by the principle of equivalent effect. The effective stiffness coefficients of the equivalent circular cylindrical shell are obtained. Based on the first-order shear deformation shell theory and the Hamilton’s principle, the nonlinear governing equations of motion are derived for the equivalent circular cylindrical shell. The Galerkin approach is utilized to discretize the nonlinear partial governing differential equation of motion to the ordinary differential equation for the equivalent circular cylindrical shell. The case of the 1:2 internal resonance, primary parametric resonance and 1/2 subharmonic resonance is taken into account. The method of multiple scales is used to obtain the four-dimensional averaged equation. The frequency-response curves and force-response curves are obtained when considering the strongly coupled of two modes. The numerical results indicate that there are the hardening type and softening type nonlinearities for the circular truss antenna. Numerical simulation is used to investigate the influences of the thermal excitation on the nonlinear breathing vibrations of the circular truss antenna. It is demonstrated from the numerical results that there exist the bifurcation and chaotic motions of the circular truss antenna.
Scattering by a thin multicoated perfectly conducting spherical shell with a circular aperture
NASA Astrophysics Data System (ADS)
Said, R. A.; Hamid, M.
1992-03-01
An analytic solution is presented for the problem of an infinitely thin perfectly conducting spherical shell with a circular aperture of arbitrary angle cut into the shell, filled with a dielectric, and coated by different thicknesses of spherical dielectric layers. The fields in all regions are expanded in terms of spherical wave functions and the boundary conditions of the continuity of the tangential fields at the dielectric-dielectric and dielectric-free-space boundaries are applied to express the expansion coefficients of the first dielectric layer in terms of the scattering coefficients. To approximate the modal expansion coefficients, the least-square error method is applied to the equations resulting from matching the fields through the aperture. Different numerical results for the simple case of a single coating layer are obtained in the form of amplitude patterns for the aperture and scattered fields versus angle as well as the backward- and forward-scattering cross sections for different loadings as functions of cavity size.
NASA Technical Reports Server (NTRS)
Yahsi, O. S.; Erdogan, F.
1983-01-01
A cylindrical shell having a very stiff and plate or a flange is considered. It is assumed that near the end the cylinder contains an axial flaw which may be modeled as a part through surface crack or a through crack. The effect of the end constraining on the stress intensity factor which is the main fracture mechanics parameter is studied. The applied loads acting on the cylinder are assumed to be axisymmetric. Thus the crack problem under consideration is symmetric with respect to the plane of the crack and consequently only the Mode 1 stress intensity factors are nonzero. With this limitation, the general perturbation problem for a cylinder with a built in end containing an axial crack is considered. Reissner's shell theory is used to formulate the problem. The part through crack problem is treated by using a line spring model. In the case of a crack tip terminating at the fixed end it is shown that the integral equations of the shell problem has the same generalized Cauchy kernel as the corresponding plane stress elasticity problem.
NASA Astrophysics Data System (ADS)
Zhou, Qizheng; Wang, Deshi
2015-07-01
The vibro-acoustic coupling dynamics of a rotor-bearing-foundation-cylinder system are investigated. Using rotor dynamics, structure dynamics and acoustical theory, the vibro-acoustic coupling equation of a cylindrical shell under rotor-bearing-foundation system's nonlinear vibration excitations is derived based on variational principle. In order to solve the coupling equation, the influences of the shell's vibration to the rotor-bearing system are neglected, and then the dynamical equation is reduced. The nonlinear forces transmitted to the cylinder are fitted in the Fourier series by the fast Fourier translation and the harmonic balance method, and then the analytical solution of the vibro-acoustic coupling equation of the cylinder is derived. Based on inherent assumption, the analytical expressions of the acoustic radiation power and the surface velocity are given. Then bifurcation diagrams, phase diagrams, time history diagrams and spectrum graphs are employed to study the nonlinear vibration characteristics and the acoustic radiation characteristics. It is inferred that the present work proposes a semi-analytical and semi-numerical method for the nonlinear vibro-acoustic coupling system. The motions of the forces transmitted to the cylinder are periodic motions, quasi-periodic motions, and so on. The vibro-acoustic characteristics of shell are dominated by the rotation frequency of the rotor, while there are some harmonic components dominating the vibro-acoustic characteristics at resonant frequencies.
NASA Astrophysics Data System (ADS)
Sadamoto, S.; Ozdemir, M.; Tanaka, S.; Taniguchi, K.; Yu, T. T.; Bui, T. Q.
2017-02-01
The paper is concerned with eigen buckling analysis of curvilinear shells with and without cutouts by an effective meshfree method. In particular, shallow shell, cylinder and perforated cylinder buckling problems are considered. A Galerkin meshfree reproducing kernel (RK) approach is then developed. The present meshfree curvilinear shell model is based on Reissner-Mindlin plate formulation, which allows the transverse shear deformation of the curved shells. There are five degrees of freedom per node (i.e., three displacements and two rotations). In this setting, the meshfree interpolation functions are derived from the RK. A singular kernel is introduced to impose the essential boundary conditions because of the RK shape functions, which do not automatically possess the Kronecker delta property. The stiffness matrix is derived using the stabilized conforming nodal integration technique. A convected coordinate system is introduced into the formulation to deal with the curvilinear surface. More importantly, the RKs taken here are used not only for the interpolation of the curved geometry, but also for the approximation of field variables. Several numerical examples with shallow shells and full cylinder models are considered, and the critical buckling loads and their buckling mode shapes are calculated by the meshfree eigenvalue analysis and examined. To show the accuracy and performance of the developed meshfree method, the computed critical buckling loads and mode shapes are compared with reference solutions based on boundary domain element, finite element and analytical methods.
NASA Astrophysics Data System (ADS)
Sadamoto, S.; Ozdemir, M.; Tanaka, S.; Taniguchi, K.; Yu, T. T.; Bui, T. Q.
2017-06-01
The paper is concerned with eigen buckling analysis of curvilinear shells with and without cutouts by an effective meshfree method. In particular, shallow shell, cylinder and perforated cylinder buckling problems are considered. A Galerkin meshfree reproducing kernel (RK) approach is then developed. The present meshfree curvilinear shell model is based on Reissner-Mindlin plate formulation, which allows the transverse shear deformation of the curved shells. There are five degrees of freedom per node (i.e., three displacements and two rotations). In this setting, the meshfree interpolation functions are derived from the RK. A singular kernel is introduced to impose the essential boundary conditions because of the RK shape functions, which do not automatically possess the Kronecker delta property. The stiffness matrix is derived using the stabilized conforming nodal integration technique. A convected coordinate system is introduced into the formulation to deal with the curvilinear surface. More importantly, the RKs taken here are used not only for the interpolation of the curved geometry, but also for the approximation of field variables. Several numerical examples with shallow shells and full cylinder models are considered, and the critical buckling loads and their buckling mode shapes are calculated by the meshfree eigenvalue analysis and examined. To show the accuracy and performance of the developed meshfree method, the computed critical buckling loads and mode shapes are compared with reference solutions based on boundary domain element, finite element and analytical methods.
NASA Technical Reports Server (NTRS)
Koval, L. R.
1978-01-01
In the context of the transmission of airborne noise into an aircraft fuselage, a mathematical model is presented for the effects of internal cavity resonances on sound transmission into a thin cylindrical shell. The 'noise reduction' of the cylinder is defined and computed, with and without including the effects of internal cavity resonances. As would be expected, the noise reduction in the absence of cavity resonances follows the same qualitative pattern as does transmission loss. Numerical results show that cavity resonances lead to wide fluctuations and a general decrease of noise reduction, especially at cavity resonances. Modest internal absorption is shown to greatly reduce the effect of cavity resonances. The effects of external airflow, internal cabin pressurization, and different acoustical properties inside and outside the cylinder are also included and briefly examined.
Neto, M.M.; Miranda, C.A.J.; Silveira, H.C.K. da
1996-12-01
In this paper the collapse of a ring-stiffened cylindrical shell under external hydrostatic pressure is evaluated using code formulations (ASME (1992), BSI (1990), and GL (1988)) and nonlinear elastic-plastic finite element analysis. Some conclusions and comments are addressed from the comparison between the results obtained from the used approaches.
Inelastic Response of an Infinite Cylindrical Shell to a Transient Acoustic Wave.
1979-03-01
decomposition of shell and fluid response into circumferential Fourier harmonics yields v(e,t) - E vn(t) sin ne n-1 w(et) - a w(t) cos ne (1) n-O - *(r,e,t...number of Fourier harmonics ; Fourier superposition in accordance with (1) then produces response histories of interest. In prac- 5 tice, however
Forced vibrations of plates and cylindrical shells with regular orthogonal system of stiffeners
NASA Astrophysics Data System (ADS)
Efimtsov, B. M.; Lazarev, L. A.
2009-10-01
A wide range of engineering structures, such as aircraft fuselages or ship hulls have as the foundation a shell orthogonally strengthened by two sets of stiffeners. Solution of the task related to determining the vibrations of such complicated structures requires an application of special methods which permit accounting for the interaction between the shell and the two sets of discrete stiffeners correctly. The present work proposes an effective method of predicting the vibrations of a finite orthogonally stiffened structure as a part of an infinite one when the edge conditions permit. The prediction method proposed is based on the method of space-harmonic expansions when the shell displacements and forces are presented in the form of special double trigonometric series. The method allows the interconnection of all three components of displacement and rotation of the shell and the stiffeners to be taken into account. The vibration velocity of the construction is determined directly without a need for solving the task of eigen-values first. The vibration shapes are broken into a large number of non-interacting groups of shapes. The solution reduces to a system of equations relating to the generalized reactions at supports. All this allows predictions to be made for large parts of the investigated construction over practically the whole frequency range of sound.
1988-07-15
1969), Geib (1969), and Rijnja (1981). It has been reported that rectangular or elliptical hydrophones are less sensitive to flow noise if the largest...equation (21) is SVr + (k2 - k ]) A (r,kx) = 0 , (22) ,2 where V is the operator in cylindrical coordinates defined as V. r , drr dr 2 2 2’and k r k2 - k...W, (24) dr r= the constant A can be expressed as Jkpfcf (A° 0 , (25) U SkrJ o (kra) A aF 0 LIL22 where W = 2 hI (-jo)Sc 1 2nph det iLl Equation (23
NASA Technical Reports Server (NTRS)
Li, Yi-Wei; Elishakoff, Isaac; Starnes, James H., Jr.; Bushnell, David
1998-01-01
This study is an extension of a previous investigation of the combined effect of axisymmetric thickness variation and axisymmetric initial geometric imperfection on buckling of isotropic shells under uniform axial compression. Here the anisotropic cylindrical shells are investigated by means of Koiter's energy criterion. An asymptotic formula is derived which can be used to determine the critical buckling load for composite shells with combined initial geometric imperfection and thickness variation. Results are compared with those obtained by the software packages BOSOR4 and PANDA2.
Some applications of NASTRAN to the buckling of thin cylindrical shells with cutouts
NASA Technical Reports Server (NTRS)
Williams, J. G.; Starnes, J. H., Jr.
1972-01-01
The buckling of isotropic and waffle-stiffened circular cylinders with and without cutouts was studied using NASTRAN's Rigid Format 5 for the case of axial compressive loading. The results obtained for the cylinders without cutouts are compared with available reference solutions. The results for the isotropic cylinders containing a single circular cutout with selected radii are compared with available experimental data. For the waffle-stiffened cyclinder, the effect of two diametrically opposed rectangular cutouts was studied. A DMAP alter sequence was used to permit the necessary application of different prebuckling and buckling boundary conditions. Advantage was taken of available symmetry planes to formulate equivalent NASTRAN model segments which reduced the associated computational cost of performing the analyses. Limitations of the applicability of NASTRAN for the solution of problems with nonlinear characteristics are discussed.
NASA Astrophysics Data System (ADS)
Velikovich, A. L.; Schmit, P. F.
2015-11-01
Bell-Plesset effects accounting for the time dependence of the radius, velocity and acceleration of the Rayleigh-Taylor-unstable surface are ubiquitous in the instability of spherical laser targets and magnetically driven cylindrical liners. We present an analytical model that, for an ideal incompressible fluid and small perturbation amplitudes, exactly accounts for the Bell-Plesset effects in finite-thickness targets and liners through acceleration and deceleration phases. We derive the time-dependent dispersion equations determining the ``instantaneous growth rate'' and demonstrate that by integrating this growth rate over time (the WKB approximation) we accurately evaluate the number of perturbation e-foldings during the acceleration phase. In the limit of the small target/liner thickness, we obtain the exact thin-shell perturbation equations and approximate thin-shell dispersion relations, generalizing the earlier results of Harris (1962), Ott (1972) and Bud'ko et al. (1989). This research was supported by the US DOE/NNSA (A.L.V.), and in part by appointment to the Sandia National Laboratories Truman Fellowship in National Security Science and Engineering (P.F.S.), which is part of the Laboratory Directed Research and Development (LDRD) Program, Project No. 165746, and sponsored by Sandia Corporation (a wholly owned subsidiary of Lockheed Martin Corporation) as Operator of Sandia National Laboratories under its U.S. Department of Energy Contract No. DE-AC04-94AL85000.
Chen, Rongsheng; Hu, Liangsheng; Huo, Kaifu; Fu, Jijiang; Ni, Hongwei; Tang, Yan; Chu, Paul K
2011-12-16
Quasi-aligned cylindrical and conical core-shell nanofibers consisting of carbon shells and TiO(2) nanowire cores are produced in situ on Ti foils without using a foreign metallic catalyst and template. A cylindrical nanofiber has a TiO(2) nanowire core 30-50 nm in diameter and a 5-10 nm-thick cylindrical carbon shell, while in the conical nanostructure the TiO(2) nanowire core has a diameter of 20-40 nm and the thickness of the carbon shell varies from about 200 nm at the bottom to about 5 nm at the tip. Electrochemical analysis reveals well-defined redox peaks of the [Fe(CN)(6)](3-/4-) redox couple and heterogeneous charge-transfer rate constants of 0.010 and 0.062 cm s(-1) for the cylindrical and conical nanofibers, respectively. The coverage of exposed edge planes on the cylindrical and conical carbon shells is estimated to be 2.5 and 15.5 % respectively. The more abundant exposed edge planes on the conical nanofiber decrease the overpotential and increase the voltammetric resolution during electrochemical detection of uric acid and ascorbic acid. Our results suggest that the density of edge-plane sites estimated from Raman scattering is not necessarily equal to the density of exposed edge-plane sites, and only carbon electrodes with a large density of exposed edge planes or free graphene sheet ends exhibit better electrochemical performance.
Analysis of the Nonlinear Large Deformation Behavior of Composite Cylindrical Shells.
1983-01-01
Jun 30- 191 S. PERFORMING ONG. REPORT NUMSER 7. AUTHOR(*) S. CONTRACT OR GRANT NUMSER(s.) George J. Simitses Izhak Sheinman and AFOSR 81-0227 Dein... Sheinman , I., and Shaw, D. "Stability of Laminated Composite Shells Subjected to Uniform Axial Compression and Torsion" Interim Scienfific Report to the Air...Mechanical Engineering Science, Vol. 6, No. 1, 1963, pp. 23-27. 17. Sheinman , I., Shaw, D., and Simitses, G. J., "Nonlinear Analysis of Axially-Loaded
Validation of Lower-Bound Estimates for Compression-Loaded Cylindrical Shells
NASA Technical Reports Server (NTRS)
Haynie, Waddy T.; Hilburger, Mark W.; Bogge, Massimiliano; Kriegesmann, Benedikt
2012-01-01
The traditional approach used in the design of stability critical thin-walled circular cylin- ders, is to reduce unconservative buckling load predictions with an empirical knockdown factor. An alternative analysis-based approach to determine a lower bound buckling load for cylinders under axial compression is to use a lateral perturbation load to create an initial imperfection and determine the buckling load while that load is applied. This paper describes a preliminary e ort to develop a test capability to verify this approach. Results from tests of three aluminum alloy cylinders are described and compared to nite element predictions.
2008-03-28
and the ring stiffeners constructed of aluminum . Conversely, the skin could be an isotropic material such as aluminum or steel and the rings made of...from 7075-T6 aluminum bar stock with a nominal yield strength of 80,000 psi. A schematic of these shells is given in Figure 9. Each specimen had six...5741 0.949 5744 0.949 5559 6150 0.904 24 20-52 4500 IGI 5302 0.849 4874 0.923 5305 0.848 4595 5260 0.874 25 15-58 7050 IGI 6406 1.101 6891 1.023 6602
Tests on Stiffened Circular Cylinders
NASA Technical Reports Server (NTRS)
Holt, Marshall
1941-01-01
Compressive tests were made of two series of stiffened circular cylindrical shells under axial load. All the shells were 16 inches in diameter by 24 inches in length and were made of aluminum-alloy sheet curved to the proper radius and welded with one longitudinal weld. The ratios of diameter to thickness of shell wall in the two series of specimens were 258 and 572. Strains were measured with Huggenberger tensometers at a number of gage lines on the stiffeners and shell. The results of these tests indicate that a spacing of circumferential stiffeners equal to 0.67 times the radius is too great to strengthen the shell wall appreciably. The results are not inclusive enough to show the optimum in stiffeners. Plain cylinders without stiffeners developed ultimate strengths approximately half as great as the buckling strengths computed by the equation resulting from the classical theory and slightly greater than those computed by Donnell's large deflection theory.
NASA Astrophysics Data System (ADS)
Cruz, Philip Christopher S.; Bernardo, Reginald Christian S.; Esguerra, Jose Perico H.
2017-04-01
We calculate the energy levels of a quantum particle on a cylindrical surface with non-circular cross-section in uniform electric and magnetic fields. Using separation of variables method and a change of independent variable, we show that the problem can be reduced to a one-dimensional Schrödinger equation for a periodic potential. The effects of varying the shape of the cross-section while keeping the same perimeter and the strengths of the electric and magnetic fields are investigated for elliptical, corrugated, and nearly-rectangular tubes with radial dimensions of the order of a nanometer. The geometric potential has minima at the angular positions where there is a significant amount of curvature. For the elliptical and corrugated tubes, it is shown that as the tube departs from the circular shape of cross-section the double-degeneracy between the energy levels is lifted. For the nearly-rectangular tube, it is shown that energy level crossings occur as the horizontal dimension of the tube is varied while keeping the same perimeter and radius of circular corners. The interplay between the curvature and the strength of the electric and magnetic fields determines the overall behavior of the energy levels. As the strength of the electric field increases, the overall potential gets skewed creating a potential well on the side corresponding to the more negative electric potential. The energy levels of the first few excited states approach more positive values while the ground state energy level approaches a more negative value. For large electric fields, all bound state energy levels tend to more negative values. The contribution of weak magnetic fields to the overall potential behaves in the same way as the electric field contribution but with its sign depending on the direction of the component of the momentum parallel to the cylindrical axis. Large magnetic fields lead to pairing of energy levels reminiscent of 2D Landau levels for the elliptical and nearly
NASA Astrophysics Data System (ADS)
Zel'dovich, V. I.; Frolova, N. Yu.; Kheifets, A. E.; Dolgikh, S. M.; Gaan, K. V.; Shorokhov, E. V.
2015-03-01
An experiment has been performed on the collapse of a thick steel cylindrical shell into a continuous cylinder under the action of a sliding detonation wave. The process of the collapse has been recorded via X-ray photography, and it has been found that the time of collapse in one section is equal to 30 μs. The average degree of deformation is 77% and the rate of deformation is 104 s-1. The structure of steel 20 in the transverse section of the cylinder consists of three zones. In the outer zone, the initial ferrite-pearlite structure changes under the effect of compressive shock wave and localized shears. The shock wave leads to the formation of a high-pressure ɛ phase and twins. Upon the subsequent inertial collapse of the shell, substantial shear deformations arise in the surface layer, which are localized in directions located at angles of 60° to the cylindrical surface. The structure of the middle zone changes under the action of severe plastic deformation, which occurs predominantly in the radial direction. The deformation leads to the appearance of an internal pressure and to an increase in the temperature. As a result of the action of three factors (pressure, temperature, and deformation), the temperature of the formation of austenite decreases by several hundred kelvins. In the free ferrite, an α → γ transformation occurs and quenching takes place following a subsequent sharp decrease in pressure (barothermic quenching). The pearlitic regions suffer plastic deformation. The microhardness of the steel with this structure is equal to the microhardness of quenched steel. The structure of the third, i.e., central, zone, changes under the action of a significant increase in temperature caused by the further increase in the degree of deformation. The complete transformation of ferrite into austenite occurs at the center of this zone, which means that the temperature in this zone reaches 850-900°C or greater. The microhardness decreases to values typical
NASA Technical Reports Server (NTRS)
Agarwal, B. L.; Sobel, L. H.
1976-01-01
This work presents optimum designs for unstiffened, hat stringer-stiffened and honeycomb sandwich cylinders under axial compression. Optimization results for graphite-epoxy cylinders show about a 50 percent weight savings over corresponding optimized aluminum cylinders for a wide loading range. The inclusion of minimum gage considerations results in a significant weight penalty, especially for a lightly loaded cylinder. Effects of employing a smeared stiffener buckling theory in the optimization program are investigated through comparison of results obtained from a more accurate branched shell buckling computer code. It was found that the stiffener cross-sectional deformations, which are usually ignored in smeared stiffener theory, result in about a 30 percent lower buckling load for the graphite-epoxy hat stiffened cylinder.
A Study of Failure in Small Pressurized Cylindrical Shells Containing a Crack
NASA Technical Reports Server (NTRS)
Barwell, Craig A.; Eber, Lorenz; Fyfe, Ian M.
1998-01-01
The deformation in the vicinity of axial cracks in thin pressurized cylinders is examined using small experimental The deformation in the vicinity of axial cracks in thin pressurized cylinders is examined using small experimental models. The loading applied was either symmetric or unsymmetric about the crack plane, the latter being caused by structural constraints such as stringers. The objective was two fold - one, to provide the experimental results which will allow computer modeling techniques to be evaluated for deformations that are significantly different from that experienced by flat plates, and the other to examine the deformations and conditions associated with the onset of crack kinking which often precedes crack curving. The stresses which control crack growth in a cylindrical geometry depend on conditions introduced by the axial bulging, which is an integral part of this type of failure. For the symmetric geometry, both the hoop and radial strain just ahead off the crack, r = a, were measured and these results compared with those obtained from a variety of structural analysis codes, in particular STAGS [1], ABAQUS and ANSYS. In addition to these measurements, the pressures at the onset of stable and unstable crack growth were obtained and the corresponding crack deformations measured as the pressures were increased to failure. For the unsymmetric cases, measurements were taken of the crack kinking angle, and the displacements in the vicinity of the crack. In general, the strains ahead of the crack showed good agreement between the three computer codes and between the codes and the experiments. In the case of crack behavior, it was determined that modeling stable tearing with a crack-tip opening displacement fracture criterion could be successfully combined with the finite-element analysis techniques as used in structural analysis codes. The analytic results obtained in this study were very compatible with the experimental observations of crack growth
NASA Astrophysics Data System (ADS)
Shi, Tong; Wang, Yikang; Wan, Linfeng; Cheng, Xin; Ding, Mingde; Zhang, Jie
2015-06-01
Accurately predicting the arrival of coronal mass ejections (CMEs) to the Earth based on remote images is of critical significance for the study of space weather. In this paper, we make a statistical study of 21 Earth-directed CMEs, specifically exploring the relationship between CME initial speeds and transit times. The initial speed of a CME is obtained by fitting the CME with the Graduated Cylindrical Shell model and is thus free of projection effects. We then use the drag force model to fit results of the transit time versus the initial speed. By adopting different drag regimes, i.e., the viscous, aerodynamics, and hybrid regimes, we get similar results, with a least mean estimation error of the hybrid model of 12.9 hr. CMEs with a propagation angle (the angle between the propagation direction and the Sun-Earth line) larger than their half-angular widths arrive at the Earth with an angular deviation caused by factors other than the radial solar wind drag. The drag force model cannot be reliably applied to such events. If we exclude these events in the sample, the prediction accuracy can be improved, i.e., the estimation error reduces to 6.8 hr. This work suggests that it is viable to predict the arrival time of CMEs to the Earth based on the initial parameters with fairly good accuracy. Thus, it provides a method of forecasting space weather 1-5 days following the occurrence of CMEs.
Structural-acoustic modal analysis of cylindrical shells: application to MRI scanner systems.
Li, Gemin; Mechefske, Chris K
2009-12-01
The acoustic noise in a magnetic resonance imaging (MRI) scanner bore is mainly introduced by the vibration of gradient coils. The interaction between acoustic modes in the scanner bore and structure modes in the coil structure leads to structural-acoustic coupling. In order to implement quiet MRI design, the structural-acoustic coupling mechanism in MRI machines needs to be fully investigated. Structural analysis was first implemented using Love's classical shell theory. The concept of a "virtually closed cavity" was used in the acoustic modal analysis of the gradient coil duct. The dispersion curves and the number of modes per frequency band were used to reveal modal distribution properties for both structural modes and acoustic modes. Structural-acoustic coupling modes were identified by superposition of the dispersion diagrams of the structural waves and acoustic waves. Experimental validation was implemented separately for the structural analysis and acoustic analysis. Independent structural modes and acoustic modes and their distribution patterns were calculated up to 3000Hz with various boundary conditions. Coupling modes were clearly revealed using the analysis procedures presented in this paper and were found to be in agreement with the ones identified from experimental measurements. These methods are effective for coupled and uncoupled modal analysis of MRI scanner systems and can be used for quiet MRI design or sound absorber design for existing MRI systems.
NASA Technical Reports Server (NTRS)
Heard, W. L., Jr.; Anderson, M. S.; Slysh, P.
1976-01-01
An engineering procedure is presented for calculating the compressive buckling strength of isogrid cylinders using shell of revolution techniques and accounting for loading beyond the material proportional limit and/or local buckling of the skin prior to general buckling. A general nondimensional chart is presented which can be used in conjunction with formulas based on simple deformation plasticity theory to calculate postbuckling stiffnesses of the skin. The stiffening grid system is treated as an equivalent isotropic grid layer. Stiffnesses are determined for this grid layer, when loaded beyond the proportional limit, by the same plasticity theory used for the skin and a nonlinear stress-strain curve constructed from simple isogrid-handbook formulas and standard-reference-manual stress-strain curves for the material involved. Comparison of prebuckling strains and buckling results obtained by this procedure with data from a large isogrid-cylinder test is excellent with the calculated buckling load no more than 4 percent greater than the test value.
NASA Astrophysics Data System (ADS)
Ramezani, H.; Saghafi, A.
2014-03-01
A study on the optimization of sound transmission loss (TL) across a double-walled cylindrical laminated composite shell whose walls sandwich a layer of porous material is investigated using a genetic algorithm. First, an exact relation is presented by considering the effective wave component in the porous layer within the framework of the classic theory for laminated composite shells. The TL of the structure is estimated in a broadband frequency. Then, an acoustic optimization is considered for the sandwich structure with respect to the constraints of geometric properties.
Hoffman, E.L.; Ammerman, D.J.
1993-08-01
A series of tests investigating dynamic pulse buckling of a cylindrical shell under axial impact is compared to several finite element simulations of the event. The purpose of the study is to compare the performance of the various analysis codes and element types with respect to a problem which is applicable to radioactive material transport packages, and ultimately to develop a benchmark problem to qualify finite element analysis codes for the transport package design industry.
Translations of Russian research: Transition of a space vehicle , braked in the atmosphere of a planet, into the orbit of an artificial satellite; axially symmetric oscillations of cylindrical shells in supersonic flow of gas.
Zhang, Anqi; Xu, Guan; Daluwatte, Chathuri; Yao, Gang; Bunting, Charles F; Pogue, Brian W; Piao, Daqing
2011-02-01
This is Part II of the work that examines photon diffusion in a homogenous medium enclosed by a concave circular cylindrical applicator or enclosing a convex circular cylindrical applicator. Part I of this work [J. Opt. Soc. Am. A 27, 648 (2010)] analytically examined the steady-state photon diffusion between a source and a detector for two specific cases: (1) the detector is placed only azimuthally with respect to the source, and (2) the detector is placed only longitudinally with respect to the source, in the infinitely long concave and convex applicator geometries. For the first case, it was predicted that the decay rate of photon fluence would become smaller in the concave geometry and greater in the convex geometry than that in the semi-infinite geometry for the same source-detector distance. For the second case, it was projected that the decay rate of photon fluence would be greater in the concave geometry and smaller in the convex geometry than that in the semi-infinite geometry for the same source-detector distance. This Part II of the work quantitatively examines these predictions from Part I through several approaches, including (a) the finite-element method, (b) the Monte Carlo simulation, and (c) experimental measurement. Despite that the quantitative examinations have to be conducted for finite cylinder applicators with large length-to-radius ratio to approximate the infinite-length condition modeled in Part I, the results obtained by these quantitative methods for two concave and three convex applicator dimensions validated the qualitative trend predicted by Part I and verified the quantitative accuracy of the analytic treatment of Part I in the diffusion regime of the measurement, at a given set of absorption and reduced scattering coefficients of the medium.
NASA Technical Reports Server (NTRS)
Schmidt, J. M.; Cairns, Iver H.; Xie, Hong; St. Cyr, O. C.; Gopalswamy, N.
2016-01-01
Coronal mass ejections (CMEs) are major transient phenomena in the solar corona that are observed with ground-based and spacecraft-based coronagraphs in white light or with in situ measurements by spacecraft. CMEs transport mass and momentum and often drive shocks. In order to derive the CME and shock trajectories with high precision, we apply the graduated cylindrical shell (GCS) model to fit a flux rope to the CME directed toward STEREO A after about 19:00 UT on 29 November 2013 and check the quality of the heliocentric distance-time evaluations by carrying out a three-dimensional magnetohydrodynamic (MHD) simulation of the same CME with the Block Adaptive Tree Solar-Wind Roe Upwind Scheme (BATS-R-US) code. Heliocentric distances of the CME and shock leading edges are determined from the simulated white light images and magnetic field strength data. We find very good agreement between the predicted and observed heliocentric distances, showing that the GCS model and the BATS-R-US simulation approach work very well and are consistent. In order to assess the validity of CME and shock identification criteria in coronagraph images, we also compute synthetic white light images of the CME and shock. We find that the outer edge of a cloud-like illuminated area in the observed and predicted images in fact coincides with the leading edge of the CME flux rope and that the outer edge of a faint illuminated band in front of the CME leading edge coincides with the CME-driven shock front.
NASA Technical Reports Server (NTRS)
Schmidt, J. M.; Cairns, Iver H.; Xie, Hong; St. Cyr, O. C.; Gopalswamy, N.
2016-01-01
Coronal mass ejections (CMEs) are major transient phenomena in the solar corona that are observed with ground-based and spacecraft-based coronagraphs in white light or with in situ measurements by spacecraft. CMEs transport mass and momentum and often drive shocks. In order to derive the CME and shock trajectories with high precision, we apply the graduated cylindrical shell (GCS) model to fit a flux rope to the CME directed toward STEREO A after about 19:00 UT on 29 November 2013 and check the quality of the heliocentric distance-time evaluations by carrying out a three-dimensional magnetohydrodynamic (MHD) simulation of the same CME with the Block Adaptive Tree Solar-Wind Roe Upwind Scheme (BATS-R-US) code. Heliocentric distances of the CME and shock leading edges are determined from the simulated white light images and magnetic field strength data. We find very good agreement between the predicted and observed heliocentric distances, showing that the GCS model and the BATS-R-US simulation approach work very well and are consistent. In order to assess the validity of CME and shock identification criteria in coronagraph images, we also compute synthetic white light images of the CME and shock. We find that the outer edge of a cloud-like illuminated area in the observed and predicted images in fact coincides with the leading edge of the CME flux rope and that the outer edge of a faint illuminated band in front of the CME leading edge coincides with the CME-driven shock front.
NASA Technical Reports Server (NTRS)
Lin, H. C.
1976-01-01
The endochronic theory of plasticity originated by Valanis was applied to study the axially symmetric motion of circular cylindrical thick shells subjected to an arbitrary pressure transient applied at its inner surface. The constitutive equations for the thick shells were obtained. The governing equations are solved by means of the nearcharacteristics method.
NASA Astrophysics Data System (ADS)
Leblond, C.; Sigrist, J. F.; Auvity, B.; Peerhossaini, H.
2009-01-01
This paper deals with the transient motions experienced by an elastic circular cylinder in a cylindrical fluid domain initially at rest and subjected to small-amplitude imposed displacements. Three fluid models are considered, namely potential, viscous and acoustic, to cover different fluid-structure interaction regimes. They are derived here from the general compressible Navier-Stokes equations by a formal perturbation method so as to underline their links and ranges of validity a priori. The resulting fluid models are linear owing to the small-amplitude-displacement hypothesis. For simplicity, the elastic flexure beam model is chosen for the circular cylinder dynamics. The semi-analytical approach used here is based on the methods of Laplace transform in time, in vacuo eigenvector expansion with time-dependent coefficients for the transverse beam displacement and separation of variables for the fluid. Moreover, the viscous case is handled with a matched asymptotic expansion performed at first order. The projection of the fluid forces on the in vacuo eigenvectors leads to a fully coupled system involving the modal time-dependent displacement coefficients. These coefficients are then obtained by matrix inversion in the Laplace domain and fast numerical inversion of the Laplace transform. The three models, written in the form of convolution products, are described through the analysis of their kernels, involving both the wave propagation phenomena in the fluid domain and the beam elasticity. Last, the three models are illustrated for a specific imposed motion mimicking shock loading. It is shown that their combination permits coverage of a broad range of motions.
NASA Technical Reports Server (NTRS)
Mei, Chuh; Jaunky, Navin
1999-01-01
The goal of this research project is to develop modelling and analysis strategy for the penetration of aluminium plates impacted by titanium impactors. Finite element analysis is used to study the penetration of aluminium plates impacted by titanium impactors in order to study the effect of such uncontained engine debris impacts on aircraft-like skin panels. LS-DYNA3D) is used in the simulations to model the impactor, test fixture frame and target barrier plate. The effects of mesh refinement, contact modeling, and impactor initial velocity and orientation were studied. The research project also includes development of a design tool for optimum design of grid-stiffened non-circular shells or panels subjected to buckling.
Hoffman, E.L.; Ammerman, D.J.
1995-04-01
A series of tests investigating dynamic pulse buckling of a cylindrical shell under axial impact is compared to several 2D and 3D finite element simulations of the event. The purpose of the work is to investigate the performance of various analysis codes and element types on a problem which is applicable to radioactive material transport packages, and ultimately to develop a benchmark problem to qualify finite element analysis codes for the transport package design industry. During the pulse buckling tests, a buckle formed at each end of the cylinder, and one of the two buckles became unstable and collapsed. Numerical simulations of the test were performed using PRONTO, a Sandia developed transient dynamics analysis code, and ABAQUS/Explicit with both shell and continuum elements. The calculations are compared to the tests with respect to deformed shape and impact load history.
NASA Astrophysics Data System (ADS)
Liu, Yu; He, Chuanbo
2015-12-01
In this discussion, the corrections to the errors found in the derivations and the numerical code of a recent analytical study (Zhou et al. Journal of Sound and Vibration 333 (7) (2014) 1972-1990) on sound transmission through double-walled cylindrical shells lined with poroelastic material are presented and discussed, as well as the further effect of the external mean flow on the transmission loss. After applying the corrections, the locations of the characteristic frequencies of thin shells remain unchanged, as well as the TL results above the ring frequency where BU and UU remain the best configurations in sound insulation performance. In the low-frequency region below the ring frequency, however, the corrections attenuate the TL amplitude significantly for BU and UU, and hence the BB configuration exhibits the best performance which is consistent with previous observations for flat sandwich panels.
NASA Technical Reports Server (NTRS)
Livingood, J. N. B.; Gauntner, J. W.
1973-01-01
An experimental study was made of the local and average heat-transfer characteristics of a single turbulent air jet impinging on the concave surface of a hemisphere. Correlations were developed for expressing the effects of a number of dimensionless variables on the local and average Nusselt numbers. Results of the present study are compared with those from a similar study concerning a concave surface of a semicylindrical shell.
Martinez, Loïc; Morvan, Bruno; Izbicki, Jean Louis
2004-04-01
A new 4D space-time-wave number-frequency representation Z(x,t,k,f) is introduced. The Z(x,t,k,f) representation is used for processing 2D space-time signal collection issued from wave propagation along a 1D medium. This representation is an extension along the time dimension of the space-wave number-frequency representation. The Z(x,t,k,f) representation is obtained by short time-space 2D Fourier transforming the space-time collection. The Z(x,t,k,f) representation allows the characterization transient aspects of wave generation and propagation in both space and time dimensions. The Z(x,t,k,f) representation is used to experimentally investigate Lamb wave generation and propagation around a cylindrical shell (relative thickness is equal to 0.03) surrounded by water and excited by a pulse (0.1 micros duration with 1-5 MHz transducers). Three kinds of fluids have been used inside the shell: air, water, propanol. In all the cases, the Z(x,t,k,f) analysis clearly identify the reflected field on the insonified side of the shell and it allows the measurement of the local reflection coefficients R(x,t,k,f). The generation and the propagation of Lamb waves are also quantified. For the liquid filled shells, the multiple internal reflections are revealed by Z(x,t,k,f) analysis: the local transmission coefficients T(x,t,k,f) are also measured. When local matching conditions allows Lamb wave generation, the multiple regeneration of Lamb wave is observed. Based on these results, a link is establish toward the theoretical results obtained by steady state approach and Sommerfeld-Watson transform.
Small bending and stretching of sandwich-type shells
NASA Technical Reports Server (NTRS)
Reissner, Eric
1950-01-01
A theory has been developed for small bending and stretching of sandwich-type shells. This theory is an extension of the known theory of homogeneous thin elastic shells. It was found that two effects are important in the present problem, which are not normally of importance in the theory of curved shells: (1) the effect of transverse shear deformation and (2) the effect of transverse normal stress deformation. The first of these two effects has been known to be of importance in the theory of plates and beams. The second effect was found to occur in a manner which is typical for shells and has no counterpart in flat-plate theory. The general results of this report have been applied to the solution of problems concerning flat plates, circular rings, circular cylindrical shells, and spherical shells. In each case numerical examples have been given, illustrating the magnitude of the effects of transverse shear and normal stress deformation.
2011-01-01
A versatile anodization method was reported to anodize Ti wires into cylindrical core-shell-like and thermally crystallized TiO2 nanotube (TNT) arrays that can be directly used as the photoanodes for semi- and all-solid fiber-type dye-sensitized solar cells (F-DSSC). Both F-DSSCs showed higher power conversion efficiencies than or competitive to those of previously reported counterparts fabricated by depositing TiO2 particles onto flexible substrates. The substantial enhancement is presumably attributed to the reduction of grain boundaries and defects in the prepared TNT anodes, which may suppress the recombination of the generated electrons and holes, and accordingly lead to more efficient carrier-transfer channels. PMID:21711629
Dove, R.C.; Bennett, J.G.; Butler, T.A.
1982-01-01
The effect of the use of the area replacement method (ARM) for reinforcing circular penetrations in cylindrical steel shells has been studied both experimentally and analyticaly. How this type of reinforcement affects the buckling strength of a shell subjected to uniform axial compression is the specific area of investigation. In shells that are of such a quality that the penetration reduces the buckling strength, the use of the ARM will increase the bucking strength of the shell. In any case, the conservative knockdown factors suggested for buckling design by the American Society of Mechanical Engineer's (ASME) Boiler and Pressure Vessel Code should ensure an adequate margin to failure under this loading condition.
A note on the low-frequency noise reduction of cylindrical capsules (L).
Ungar, Eric E
2006-12-01
The noise reductions provided by capsules consisting of uniform cylindrical shells whose two ends are closed off by like circular plates are analyzed for the low-frequency regime in which a capsule acts quasi-statically, much like a pressure vessel. The change in the confined volume is determined from the structural deflections produced by a net pressure difference, taking account of the interactions of the shell and end plates. Expressions for the noise reduction of a single capsule and of two nested capsules are derived. Some insights into the noise reduction effects of interaction between the shell and end plates are discussed, as are the contributions of these components.
Cup Cylindrical Waveguide Antenna
NASA Technical Reports Server (NTRS)
Acosta, Roberto J.; Darby, William G.; Kory, Carol L.; Lambert, Kevin M.; Breen, Daniel P.
2008-01-01
The cup cylindrical waveguide antenna (CCWA) is a short backfire microwave antenna capable of simultaneously supporting the transmission or reception of two distinct signals having opposite circular polarizations. Short backfire antennas are widely used in mobile/satellite communications, tracking, telemetry, and wireless local area networks because of their compactness and excellent radiation characteristics. A typical prior short backfire antenna contains a half-wavelength dipole excitation element for linear polarization or crossed half-wavelength dipole elements for circular polarization. In order to achieve simultaneous dual circular polarization, it would be necessary to integrate, into the antenna feed structure, a network of hybrid components, which would introduce significant losses. The CCWA embodies an alternate approach that entails relatively low losses and affords the additional advantage of compactness. The CCWA includes a circular cylindrical cup, a circular disk subreflector, and a circular waveguide that serves as the excitation element. The components that make it possible to obtain simultaneous dual circular polarization are integrated into the circular waveguide. These components are a sixpost polarizer and an orthomode transducer (OMT) with two orthogonal coaxial ports. The overall length of the OMT and polarizer (for the nominal middle design frequency of 2.25 GHz) is about 11 in. (approximately equal to 28 cm), whereas the length of a commercially available OMT and polarizer for the same frequency is about 32 in. (approximately equal to 81 cm).
NASA Astrophysics Data System (ADS)
Kheifets, A. E.; Zel'dovich, V. I.; Frolova, N. Yu.; Dolgikh, S. M.; Gaan, K. V.; Shorokhov, E. V.
2017-07-01
An experiment has been performed on the collapse of a thick-walled shell (tube) made of steel 20 (Fe-0.2 wt % C) to a continuous cylinder under the action of explosion. The changes of the microstructure of the cylinder have been investigated that arise under the effect of two factors, i.e., a shock wave, which causes the initial pulse to the collapse, and high-strain-rate deformation upon the subsequent inertial convergence of the shell walls. Changes in the time-dependent temperature distribution in the cylinder have been calculated. As a result of the deformation, the new structure has been obtained in steel 20 due to barothermic quenching that consists of fine crystals of the α phase, which arise during the quenching at the place of free ferrite, and of regions of the retained initial pearlite. It has been shown that the uncommon order of the occurrence of the α → γ transformation is explained by the different degree of heating of the structural constituents of the steel (free ferrite; and pearlite). The conclusion has been drawn that the high-strain-rate deformation that occurs in this experiment can be used as the method that makes it possible not only to differently deform but also to differently heat the different structural components of multiphase materials.
Hoffman, E.L.; Ammerman, D.J.
1995-04-01
A series of tests investigating dynamic pulse buckling of a cylindrical shell under axial impact is compared to several 2D and 3D finite element simulations of the event. The purpose of the work is to investigate the performance of various analysis codes and element types on a problem which is applicable to radioactive material transport packages, and ultimately to develop a benchmark problem to qualify finite element analysis codes for the transport package design industry. Four axial impact tests were performed on 4 in-diameter, 8 in-long, 304 L stainless steel cylinders with a 3/16 in wall thickness. The cylinders were struck by a 597 lb mass with an impact velocity ranging from 42.2 to 45.1 ft/sec. During the impact event, a buckle formed at each end of the cylinder, and one of the two buckles became unstable and collapsed. The instability occurred at the top of the cylinder in three tests and at the bottom in one test. Numerical simulations of the test were performed using the following codes and element types: PRONTO2D with axisymmetric four-node quadrilaterals; PRONTO3D with both four-node shells and eight-node hexahedrons; and ABAQUS/Explicit with axisymmetric two-node shells and four-node quadrilaterals, and 3D four-node shells and eight-node hexahedrons. All of the calculations are compared to the tests with respect to deformed shape and impact load history. As in the tests, the location of the instability is not consistent in all of the calculations. However, the calculations show good agreement with impact load measurements with the exception of an initial load spike which is proven to be the dynamic response of the load cell to the impact. Finally, the PRONIT02D calculation is compared to the tests with respect to strain and acceleration histories. Accelerometer data exhibited good qualitative agreement with the calculations. The strain comparisons show that measurements are very sensitive to gage placement.
Experiments on shells under base excitation
NASA Astrophysics Data System (ADS)
Pellicano, Francesco; Barbieri, Marco; Zippo, Antonio; Strozzi, Matteo
2016-05-01
The aim of the present paper is a deep experimental investigation of the nonlinear dynamics of circular cylindrical shells. The specific problem regards the response of circular cylindrical shells subjected to base excitation. The shells are mounted on a shaking table that furnishes a vertical vibration parallel to the cylinder axis; a heavy rigid disk is mounted on the top of the shells. The base vibration induces a rigid body motion, which mainly causes huge inertia forces exerted by the top disk to the shell. In-plane stresses due to the aforementioned inertias give rise to impressively large vibration on the shell. An extremely violent dynamic phenomenon suddenly appears as the excitation frequency varies up and down close to the linear resonant frequency of the first axisymmetric mode. The dynamics are deeply investigated by varying excitation level and frequency. Moreover, in order to generalise the investigation, two different geometries are analysed. The paper furnishes a complete dynamic scenario by means of: (i) amplitude frequency diagrams, (ii) bifurcation diagrams, (iii) time histories and spectra, (iv) phase portraits and Poincaré maps. It is to be stressed that all the results presented here are experimental.
NASA Astrophysics Data System (ADS)
Martin, Matthew; McBride, Ryan; Greenly, John
2012-10-01
Recent experiments on the Z machine at Sandia National Laboratories have demonstrated the measurement of magnetic fields inside an imploding cylindrical liner. The aspect ratio six beryllium liner had a two micron thick aluminum radiographic tracer layer on its inner surface and was driven with approximately 20MA of current over a 100ns rise time. B-dot probes were placed at varying radial positions inside the liner and a time-dependent magnetic field was measured. We compare the results of these experiments to simulations performed with the multi-physics ALEGRA code. These simulations suggest that the measured magnetic field is due to flux frozen into the release from the liner's inner surface. In short pulse mode, the surface magnetic pressure drives a shock into the liner. This shock has a magnetic component which is then frozen into the release wave formed when the shock reaches the liner's free inner surface. Simulations suggest this magnetized low density release then flows past the B-dot probe and is the source of the measured magnetic field. We demonstrate how these experimental measurements could be utilized to infer the amount of magnetic field at the shock front just before it releases into the vacuum. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Zhang, Anqi; Piao, Daqing; Bunting, Charles F
2012-04-01
This is Part III of the work that examines photon diffusion in a scattering-dominant medium enclosed by a "concave" circular cylindrical applicator or enclosing a "convex" circular cylindrical applicator. In Part II of this work Zhang et al. [J. Opt. Soc. Am. A, 66 (2011)] predicted that, on the tissue-applicator interface of either "concave" or "convex" geometry, there exists a unique set of spiral paths, along which the steady-state photon fluence rate decays at a rate equal to that along a straight line on a planar semi-infinite interface, for the same line-of-sight source-detector distance. This phenomenon of steady-state photon diffusion is referred to as "straight-line-resembling-spiral paths" (abbreviated as "spiral paths"). This Part III study develops analytic approaches to the spiral paths associated with geometry of a large radial dimension and presents spiral paths found numerically for geometry of a small radial dimension. This Part III study also examines whether the spiral paths associated with a homogeneous medium are a good approximation for the medium containing heterogeneity. The heterogeneity is limited to an anomaly that is aligned azimuthally with the spiral paths and has either positive or negative contrast of the absorption or scattering coefficient over the background medium. For a weak-contrast anomaly the perturbation by it to the photon fluence rate along the spiral paths is found by applying a well-established perturbation analysis in cylindrical coordinates. For a strong-contrast anomaly the change by it to the photon fluence rate along the spiral paths is computed using the finite-element method. For the investigated heterogeneous-medium cases the photon fluence rate along the homogeneous-medium associated spiral paths is macroscopically indistinguishable from, and microscopically close to, that along a straight line on a planar semi-infinite interface.
NASA Astrophysics Data System (ADS)
Hussain, Muzamal; Naeem, M. Nawaz; Shahzad, Aamir; He, Maogang
2017-04-01
The vibration analysis, based on the Donnell thin shell theory, of single-walled carbon nanotubes (SWCNTs) has been investigated. The wave propagation approach in standard eigenvalue form has been employed in order to derive the characteristic frequency equation describing the natural frequencies of vibration in SWCNTs. The complex exponential functions, with the axial modal numbers that depend on the boundary conditions stated at edges of a carbon nanotube, have been used to compute the axial modal dependence. In our new investigations, the vibration frequency spectra are obtained and calculated for various physical parameters like length-to-diameter ratios for armchair and zigzag SWCNTs for different modes and in-plane rigidity and mass density per unit lateral area for armchair and zigzag SWCNTs on the vibration frequencies. The computer software MATLAB is used in order to compute these frequencies of the SWCNTs. The results obtained from wave propagation method are found to be in satisfactory agreement with that obtained through the previously known numerical molecular dynamics simulations.
Vibrations of cantilevered doubly-curved shallow shells
NASA Technical Reports Server (NTRS)
Leissa, A. W.; Lee, J. K.; Wang, A. J.
1983-01-01
Vibrational characteristics are determined for a previously unsolved class of problems, that of doubly-curved shallow shells having rectangular planforms, clamped along one edge and free on the other three. The solution procedure uses the Ritz method with algebraic polynomial trial functions. Convergence studies are made, and accurate frequencies and contour plots of mode shapes are presented for various curvature ratios, including spherical, circular cylindrical and hyperbolic paraboloidal shells. Particular emphasis is given to the effect of adding spanwise curvature to shells having chordwise curvature; numerous published references already exist for the case of zero spanwise curvature. The effects of changing aspect ratio, thickness ratio and Poisson's ratio are also studied.
NASA Technical Reports Server (NTRS)
Giltrud, M. E.; Lucas, D. S.
1979-01-01
The transient response of an elastic cylindrical shell immersed in an acoustic media that is engulfed by a plane wave is determined numerically. The method applies to the USA-STAGS code which utilizes the finite element method for the structural analysis and the doubly asymptotic approximation for the fluid-structure interaction. The calculations are compared to an exact analysis for two separate loading cases: a plane step wave and an exponentially decaying plane wave.
A high transmission broadband gradient index lens using elastic shell acoustic metamaterial elements
NASA Astrophysics Data System (ADS)
Titovich, Alexey S.; Norris, Andrew N.; Haberman, Michael R.
2016-06-01
The use of cylindrical elastic shells as elements in acoustic metamaterial devices is demonstrated through simulations and underwater measurements of a cylindrical-to-plane wave lens. Transformation acoustics (TA) of a circular region to a square dictates that the effective density in the lens remain constant and equal to that of water. Piecewise approximation to the desired effective compressibility is achieved using a square array with elements based on the elastic shell metamaterial concept developed in [30]. The size of the elements are chosen based on availability of shells, minimizing fabrication difficulties. The tested device is neutrally buoyant comprising 48 elements of nine different types of commercial shells made from aluminum, brass, copper, and polymers. Simulations indicate a broadband range in which the device acts as a cylindrical to plane wave lens. The experimental findings confirm the broadband quadropolar response from approximately 20 to 40 kHz, with positive gain of the radiation pattern in the four plane wave directions.
A Geometric Theory of Nonlinear Morphoelastic Shells
NASA Astrophysics Data System (ADS)
Sadik, Souhayl; Angoshtari, Arzhang; Goriely, Alain; Yavari, Arash
2016-08-01
Many thin three-dimensional elastic bodies can be reduced to elastic shells: two-dimensional elastic bodies whose reference shape is not necessarily flat. More generally, morphoelastic shells are elastic shells that can remodel and grow in time. These idealized objects are suitable models for many physical, engineering, and biological systems. Here, we formulate a general geometric theory of nonlinear morphoelastic shells that describes both the evolution of the body shape, viewed as an orientable surface, as well as its intrinsic material properties such as its reference curvatures. In this geometric theory, bulk growth is modeled using an evolving referential configuration for the shell, the so-called material manifold. Geometric quantities attached to the surface, such as the first and second fundamental forms, are obtained from the metric of the three-dimensional body and its evolution. The governing dynamical equations for the body are obtained from variational consideration by assuming that both fundamental forms on the material manifold are dynamical variables in a Lagrangian field theory. In the case where growth can be modeled by a Rayleigh potential, we also obtain the governing equations for growth in the form of kinetic equations coupling the evolution of the first and the second fundamental forms with the state of stress of the shell. We apply these ideas to obtain stress-free growth fields of a planar sheet, the time evolution of a morphoelastic circular cylindrical shell subject to time-dependent internal pressure, and the residual stress of a morphoelastic planar circular shell.
Heat conduction in plates and shells with emphasis on a conical shell
NASA Astrophysics Data System (ADS)
Rubin, M. B.
This paper is concerned with analyzing heat conduction in rigid shell-like bodies. The thermal equations of the theory of a Cosserat surface are used to calculate the average (through-the-thickness) temperature and temperature gradient directly, without resorting to integration of three-dimensional results. Specific attention is focused on a conical shell. The conical shell is particularly interesting because it has a converging geometry, so that the shell near its tip is 'thick' even though the shell near its base may be 'thin'. Generalized constitutive equations are developed here in a consistent manner which include certain geometrical features of shells. These equations are tested by considering a number of problems of plates, circular cylindrical shells and spherical shells, and comparing the results with exact solutions. In all cases, satisfactory results are predicted even in the thick-shell limit. Finally, a problem of transient heat conduction in a conical shell is solved. It is shown that the thermal bending moment produced by the average temperature gradient is quite severe near the tip, and it attains its maximum value in a relatively short time.
NASA Astrophysics Data System (ADS)
McBride, Ryan
2011-06-01
The Z accelerator delivers approximately 4-MV, 26-MA electrical pulses with adjustable current rise times of 100--600 ns, as well as adjustable pulse waveforms. The magnetic pressure produced is used for various applications, including magnetically-driven implosions. The Z-Beamlet Laser (ZBL) is a pulsed (0.3-1.5 ns), multi-kJ, TW-class Nd:glass laser system that provides x-ray radiography capabilities for Z experiments. This talk focuses primarily on the radiography diagnostic used to study the magnetically-driven implosions of initially solid cylindrical shells (also referred to as ``liners''). Specifically, we discuss the 6.151-keV monochromatic backlighting system and its use in obtaining radiographs of imploding beryllium (Be) liners. The high transmission efficiency of 6.151-keV photons in Be allowed us to obtain radiographs with finite transmission throughout the radial extent of the imploding liners. Abel inverting these data, we have obtained time-resolved measurements of the imploding liner's density as a function of both axial and radial location throughout the field of view. These data are allowing us to study magneto-Rayleigh-Taylor (MRT) growth for inertial-confinement-fusion applications, as well as compression-wave propagation for equation-of-state studies (see talks by R.L. Lemke and M.R. Martin). Additionally, Z's pulse-shaping capabilities have enabled us to obtain data for both shock- and quasi-isentropically-compressed Be. Example data from MRT, shock-compression, and quasi-isentropic-compression experiments will be shown. We will also discuss planned upgrades to 25-keV radiography that will allow us to study materials with opacities beyond that of beryllium. This work was done in collaboration with R.W. Lemke, M.R. Martin, J.-P. Davis, M.D. Knudson, D.B. Sinars, S.A. Slutz, C.A. Jennings, M.E. Cuneo, D.G. Flicker, and M.C. Herrmann. Sandia is a multi-program laboratory operated by Sandia Corporation, a Lockheed-Martin company, for the US
NASA Technical Reports Server (NTRS)
Saravanos, Dimitris A.
1996-01-01
Mechanics for the analysis of laminated composite shells with piezoelectric actuators and sensors are presented. A new mixed-field laminate theory for piezoelectric shells is formulated in curvilinear coordinates which combines single-layer assumptions for the displacements and a layerwise representation for the electric potential. The resultant coupled governing equations for curvilinear piezoelectric laminates are described. Structural mechanics are subsequently developed and an 8-node finite-element is formulated for the static and dynamic analysis of adaptive composite structures of general laminations containing piezoelectric layers. Evaluations of the method and comparisons with reported results are presented for laminated piezoelectric-composite plates, a closed cylindrical shell with a continuous piezoceramic layer and a laminated composite semi-circular cantilever shell with discrete cylindrical piezoelectric actuators and/or sensors.
Wang, Fei; Gong, Haoran; Chen, Xi; Chen, C Q
2016-09-14
Origami structures enrich the field of mechanical metamaterials with the ability to convert morphologically and systematically between two-dimensional (2D) thin sheets and three-dimensional (3D) spatial structures. In this study, an in-plane design method is proposed to approximate curved surfaces of interest with generalized Miura-ori units. Using this method, two combination types of crease lines are unified in one reprogrammable procedure, generating multiple types of cylindrical structures. Structural completeness conditions of the finite-thickness counterparts to the two types are also proposed. As an example of the design method, the kinematics and elastic properties of an origami-based circular cylindrical shell are analysed. The concept of Poisson's ratio is extended to the cylindrical structures, demonstrating their auxetic property. An analytical model of rigid plates linked by elastic hinges, consistent with numerical simulations, is employed to describe the mechanical response of the structures. Under particular load patterns, the circular shells display novel mechanical behaviour such as snap-through and limiting folding positions. By analysing the geometry and mechanics of the origami structures, we extend the design space of mechanical metamaterials and provide a basis for their practical applications in science and engineering.
NASA Astrophysics Data System (ADS)
Wang, Fei; Gong, Haoran; Chen, Xi; Chen, C. Q.
2016-09-01
Origami structures enrich the field of mechanical metamaterials with the ability to convert morphologically and systematically between two-dimensional (2D) thin sheets and three-dimensional (3D) spatial structures. In this study, an in-plane design method is proposed to approximate curved surfaces of interest with generalized Miura-ori units. Using this method, two combination types of crease lines are unified in one reprogrammable procedure, generating multiple types of cylindrical structures. Structural completeness conditions of the finite-thickness counterparts to the two types are also proposed. As an example of the design method, the kinematics and elastic properties of an origami-based circular cylindrical shell are analysed. The concept of Poisson’s ratio is extended to the cylindrical structures, demonstrating their auxetic property. An analytical model of rigid plates linked by elastic hinges, consistent with numerical simulations, is employed to describe the mechanical response of the structures. Under particular load patterns, the circular shells display novel mechanical behaviour such as snap-through and limiting folding positions. By analysing the geometry and mechanics of the origami structures, we extend the design space of mechanical metamaterials and provide a basis for their practical applications in science and engineering.
Wang, Fei; Gong, Haoran; Chen, Xi; Chen, C. Q.
2016-01-01
Origami structures enrich the field of mechanical metamaterials with the ability to convert morphologically and systematically between two-dimensional (2D) thin sheets and three-dimensional (3D) spatial structures. In this study, an in-plane design method is proposed to approximate curved surfaces of interest with generalized Miura-ori units. Using this method, two combination types of crease lines are unified in one reprogrammable procedure, generating multiple types of cylindrical structures. Structural completeness conditions of the finite-thickness counterparts to the two types are also proposed. As an example of the design method, the kinematics and elastic properties of an origami-based circular cylindrical shell are analysed. The concept of Poisson’s ratio is extended to the cylindrical structures, demonstrating their auxetic property. An analytical model of rigid plates linked by elastic hinges, consistent with numerical simulations, is employed to describe the mechanical response of the structures. Under particular load patterns, the circular shells display novel mechanical behaviour such as snap-through and limiting folding positions. By analysing the geometry and mechanics of the origami structures, we extend the design space of mechanical metamaterials and provide a basis for their practical applications in science and engineering. PMID:27624892
Bronnikov, K. A.; Lemos, Jose P. S.
2009-05-15
It is shown that the existence of static, cylindrically symmetric wormholes does not require violation of the weak or null energy conditions near the throat, and cylindrically symmetric wormhole geometries can appear with less exotic sources than wormholes whose throats have a spherical topology. Examples of exact wormhole solutions are given with scalar, spinor and electromagnetic fields as sources, and these fields are not necessarily phantom. In particular, there are wormhole solutions for a massless, minimally coupled scalar field in the presence of a negative cosmological constant, and for an azimuthal Maxwell electromagnetic field. All these solutions are not asymptotically flat. A no-go theorem is proved, according to which a flat (or string) asymptotic behavior on both sides of a cylindrical wormhole throat is impossible if the energy density of matter is everywhere nonnegative.
Response of long shallow cylindrical panels to radial line loads
NASA Technical Reports Server (NTRS)
Johnson, E. R.; Hyer, M. W.; Carper, D. M.
1984-01-01
The large displacement static response of shallow orthotropic panels subjected to lateral loading is examined both theoretically and experimentally. The panels are circular cylindrical open shells which are also thin and long. The straight edges are simply supported at a fixed distance apart, and the curved edges are free. The lateral load is a spatially uniform line load acting along the generator direction of the cylinder, and is directed radially inward toward the center of curvature. The load induces a circumferential thrust, and the panel can, and does, snap-through to an inverted configuration at the buckling load. The effect of load position on the response is also examined. The test panels discussed in the paper are /(90/0)3/S graphite-epoxy laminates. Nominal dimensions are a radius of 60 in., a thickness of 0.060 in., and an arc length of 12 in. Very good agreement between theory and experiment is achieved.
NASA Astrophysics Data System (ADS)
Soldatos, K. P.
1987-11-01
This paper is concerned with the influence of thickness shear deformation and rotatory inertia on the free vibrations of antisymmetric angle-ply laminated circular cylindrical panels. Two kinds of thickness shear deformable shell theories are considered. In the first one, uniformly distributed thickness shear strains through the shell thickness and, therefore, thickness shear correction factors are used. In the second theory a parabolic variation of thickness shear strains and stresses with zero values at the inner and outer shell surfaces is assumed. The analysis is mainly based on Love's approximations but, for purposes of comparison, Donnell's shallow shell approximations are also considered. For a simply supported panel, the equations of motion of the aforementioned theories, as well as of the corresponding classical theories, are solved by using Galerkin's method. For a family of graphite-epoxy angle-ply laminated plates and circular cylindrical panels, numerical results are obtained, compared and discussed and some interesting conclusions are made regarding the shell theories considered as well as the mathematical method employed.
GRIPPING DEVICE FOR CYLINDRICAL OBJECTS
Pilger, J.P.
1964-01-21
A gripping device is designed for fragile cylindrical objects such as for drawing thin-walled tubes. The gripping is done by multiple jaw members held in position by two sets of slots, one defined by keystone-shaped extensions of the outer shell of the device and the other in a movable sleeve held slidably by the extensions. Forward movement oi the sleeve advances the jaws, thereby exerting a controlled, radial pressure on the object being gripped. (AEC)
Hall, Thomas E.
1999-04-29
The CS system is designed to provide a very fast imaging system in order to search for weapons on persons in an airport environment. The Cylindrical Scanner moves a vertical transceiver array rapidly around a person standing stationary. The software can be segmented in to three specific tasks. The first task is data acquisition and scanner control. At the operator's request, this task commands the scanner to move and the radar transceiver array to send data to the computer system in a known and well-ordered manner. The array is moved over the complete aperture in 10 to 12 seconds. At the completion of the array movement the second software task automatically reconstructs the high-resolution image from the radar data utilizing the integrated DSP boards. The third task displays the resulting images, as they become available, to the computer screen for user review and analysis.
NASA Technical Reports Server (NTRS)
Rosu, Grigore; Goguen, Joseph; Norvig, Peter (Technical Monitor)
2001-01-01
Circular coinduction is a technique for behavioral reasoning that extends cobasis coinduction to specifications with circularities. Because behavioral satisfaction is not recursively enumerable, no algorithm can work for every behavioral statement. However. algorithms using circular coinduction can prove every practical behavioral result that we know. This paper proves the correctness of circular coinduction and some consequences.
Optimum rotationally symmetric shells for flywheel rotors
Blake, Henry W.
2000-01-01
A flywheel rim support formed from two shell halves. Each of the shell halves has a disc connected to the central shaft. A first shell element connects to the disc at an interface. A second shell element connects to the first shell element. The second shell element has a plurality of meridional slits. A cylindrical shell element connects to the second shell element. The cylindrical shell element connects to the inner surface of the flywheel rim. A flywheel rim support having a disc connected an outer diameter of a shaft. Two optimally shaped shell elements connect to the optimally shaped disc at an interface. The interface defines a discontinuity in a meridional slope of said support. A cylindrical shell element connects to the two shell elements. The cylindrical shell element has an outer surface for connecting to the inner surface of the flywheel rim. A flywheel rim casing includes an annular shell connected to the central shaft. The annular shell connects to the flywheel rim. A composite shell surrounds the shaft, annular shell and flywheel rim.
Optimum rotationally symmetric shells for flywheel rotors
Blake, H.W.
2000-04-04
A flywheel rim support formed from two shell halves. Each of the shell halves has a disc connected to the central shaft. A first shell element connects to the disc at an interface. A second shell element connects to the first shell element. The second shell element has a plurality of meridional slits. A cylindrical shell element connects to the second shell element. The cylindrical shell element connects to the inner surface of the flywheel rim. A flywheel rim support having a disc connected an outer diameter of a shaft. Two optimally shaped shell elements connect to the optimally shaped disc at an interface. The interface defines a discontinuity in a meridional slope of said support. A cylindrical shell element connects to the two shell elements. The cylindrical shell element has an outer surface for connecting to the inner surface of the flywheel rim. A flywheel rim casing includes an annular shell connected to the central shaft. The annular shell connects to the flywheel rim. A composite shell surrounds the shaft, annular shell and flywheel rim.
Cylindrical rotating triboelectric nanogenerator.
Bai, Peng; Zhu, Guang; Liu, Ying; Chen, Jun; Jing, Qingshen; Yang, Weiqing; Ma, Jusheng; Zhang, Gong; Wang, Zhong Lin
2013-07-23
We demonstrate a cylindrical rotating triboelectric nanogenerator (TENG) based on sliding electrification for harvesting mechanical energy from rotational motion. The rotating TENG is based on a core-shell structure that is made of distinctly different triboelectric materials with alternative strip structures on the surface. The charge transfer is strengthened with the formation of polymer nanoparticles on surfaces. During coaxial rotation, a contact-induced electrification and the relative sliding between the contact surfaces of the core and the shell result in an "in-plane" lateral polarization, which drives the flow of electrons in the external load. A power density of 36.9 W/m(2) (short-circuit current of 90 μA and open-circuit voltage of 410 V) has been achieved by a rotating TENG with 8 strip units at a linear rotational velocity of 1.33 m/s (a rotation rate of 1000 r/min). The output can be further enhanced by integrating more strip units and/or applying larger linear rotational velocity. This rotating TENG can be used as a direct power source to drive small electronics, such as LED bulbs. This study proves the possibility to harvest mechanical energy by TENGs from rotational motion, demonstrating its potential for harvesting the flow energy of air or water for applications such as self-powered environmental sensors and wildlife tracking devices.
Titovich, Alexey S; Norris, Andrew N; Haberman, Michael R
2016-06-01
The use of cylindrical elastic shells as elements in acoustic metamaterial devices is demonstrated through simulations and underwater measurements of a cylindrical-to-plane wave lens. Transformation acoustics of a circular region to a square dictate that the effective density in the lens remain constant and equal to that of water. Piecewise approximation to the desired effective compressibility is achieved using a square array with elements based on the elastic shell metamaterial concept developed by Titovich and Norris [J. Acoust. Soc. Am. 136(4), 1601-1609 (2014)]. The sizes of the elements are chosen based on availability of shells, minimizing fabrication difficulties. The tested device is neutrally buoyant comprising 48 elements of nine different types of commercial shells made from aluminum, brass, copper, and polymers. Simulations indicate a broadband range in which the device acts as a cylindrical to plane wave lens. The experimental findings confirm the broadband quadropolar response from approximately 20 to 40 kHz, with positive gain of the radiation pattern in the four plane wave directions.
Imperfection Insensitive Thin Shells
NASA Astrophysics Data System (ADS)
Ning, Xin
The buckling of axially compressed cylindrical shells and externally pressurized spherical shells is extremely sensitive to even very small geometric imperfections. In practice this issue is addressed by either using overly conservative knockdown factors, while keeping perfect axial or spherical symmetry, or adding closely and equally spaced stiffeners on shell surface. The influence of imperfection-sensitivity is mitigated, but the shells designed from these approaches are either too heavy or very expensive and are still sensitive to imperfections. Despite their drawbacks, these approaches have been used for more than half a century. This thesis proposes a novel method to design imperfection-insensitive cylindrical shells subject to axial compression. Instead of following the classical paths, focused on axially symmetric or high-order rotationally symmetric cross-sections, the method in this thesis adopts optimal symmetry-breaking wavy cross-sections (wavy shells). The avoidance of imperfection sensitivity is achieved by searching with an evolutionary algorithm for smooth cross-sectional shapes that maximize the minimum among the buckling loads of geometrically perfect and imperfect wavy shells. It is found that the shells designed through this approach can achieve higher critical stresses and knockdown factors than any previously known monocoque cylindrical shells. It is also found that these shells have superior mass efficiency to almost all previously reported stiffened shells. Experimental studies on a design of composite wavy shell obtained through the proposed method are presented in this thesis. A method of making composite wavy shells and a photogrametry technique of measuring full-field geometric imperfections have been developed. Numerical predictions based on the measured geometric imperfections match remarkably well with the experiments. Experimental results confirm that the wavy shells are not sensitive to imperfections and can carry axial compression
Computational procedures for postbuckling of composite shells
NASA Technical Reports Server (NTRS)
Stanley, G. M.; Felippa, Carlos A.
1989-01-01
A recently developed finite-element capability for general nonlinear shell analysis, featuring the use of three-dimensional constitutive equations within an efficient resultant-oriented framework, is employed to simulate the postbuckling response of an axially compressed composite cylindrical panel with a circular cutout. The problem is a generic example of modern composite aircraft components for which postbuckling strength (i.e., fail-safety) is desired in the presence of local discontinuities such as holes and cracked stiffeners. While the computational software does a reasonable job of predicting both the buckling load and the qualitative aspects of postbuckling (compared both with experiment and another code) there are some discrepancies due to: (1) uncertainties in the nominal layer material properties, (2) structural sensitivity to initial imperfections, and (3) the neglect of dynamic and local material delamination effects in the numerical model. Corresponding refinements are suggested for the realistic continuation of this type of analysis.
Yang, J
2008-05-01
A set of nonlinear two-dimensional equations for thin electroelastic shells in vibrations with moderately large shear deformation in the tangent plane are obtained from the three-dimensional equations of nonlinear electroelasticity. As an example for application, the equations are used to study nonlinear torsional vibration of a circular cylindrical piezoelectric shell. It is shown that torsion is nonlinearly coupled to axial extension and circumferential extension. The results of this paper emphasize the need for further study of mode coupling induced by nonlinearity.
NASA Astrophysics Data System (ADS)
Kingan, Michael J.; Yang, Yi; Mace, Brian R.
2016-09-01
This paper concerns the prediction of sound transmission through a cylindrical structure. The problem considered is that of sound generated by a line source located exterior to a two-dimensional circular cylinder which produces sound waves which transmit through the cylinder to an internal medium. An analytical solution is presented for the case of sound transmission through a thin cylindrical shell, by modelling the shell response using the Flugge- Byrne-Lur'ye equations. This solution is then compared to calculations where the response of the cylinder is calculated using the Wave and Finite Element (WFE) method. The WFE method involves modelling a small segment of a structure using traditional finite element (FE) methods. The mass and stiffness matrices of the segment are then used to calculate the response of the structure to excitation by an acoustic field. The WFE approach for calculating sound transmission is validated by comparison with the analytic solution. Formulating analytic solutions for more complicated structures can be cumbersome whereas using a numerical technique, such as the WFE method, is relatively straightforward.
NASA Technical Reports Server (NTRS)
Ko, William L.
1994-01-01
Thermocryogenic buckling and stress analyses were conducted on a horizontally oriented cryogenic tank using the finite element method. The tank is a finite-length circular cylindrical shell with its two ends capped with hemispherical shells. The tank is subjected to cylindrical strip heating in the region above the liquid-cryogen fill level and to cryogenic cooling below the fill level (i.e., under thermocryogenic loading). The effects of cryogen fill level on the buckling temperature and thermocryogenic stress field were investigated in detail. Both the buckling temperature and stress magnitudes were relatively insensitive to the cryogen fill level. The buckling temperature, however, was quite sensitive to the radius-to-thickness ratio. A mechanical stress analysis of the tank also was conducted when the tank was under: (1) cryogen liquid pressure loading; (2) internal pressure loading; and (3) tank-wall inertia loading. Deformed shapes of the cryogenic tanks under different loading conditions were shown, and high-stress domains were mapped on the tank wall for the strain-gage installations. The accuracies of solutions from different finite element models were compared.
Self-referenced interferometer for cylindrical surfaces.
Šarbort, Martin; Řeřucha, Šimon; Holá, Miroslava; Buchta, Zdeněk; Lazar, Josef
2015-11-20
We present a new interferometric method for shape measurement of hollow cylindrical tubes. We propose a simple and robust self-referenced interferometer where the reference and object waves are represented by the central and peripheral parts, respectively, of the conical wave generated by a single axicon lens. The interferogram detected by a digital camera is characterized by a closed-fringe pattern with a circular carrier. The interference phase is demodulated using spatial synchronous detection. The capabilities of the interferometer are experimentally tested for various hollow cylindrical tubes with lengths up to 600 mm.
Cylindrical Piezoelectric Fiber Composite Actuators
NASA Technical Reports Server (NTRS)
Allison, Sidney G.; Shams, Qamar A.; Fox, Robert L.
2008-01-01
The use of piezoelectric devices has become widespread since Pierre and Jacques Curie discovered the piezoelectric effect in 1880. Examples of current applications of piezoelectric devices include ultrasonic transducers, micro-positioning devices, buzzers, strain sensors, and clocks. The invention of such lightweight, relatively inexpensive piezoceramic-fiber-composite actuators as macro fiber composite (MFC) actuators has made it possible to obtain strains and displacements greater than those that could be generated by prior actuators based on monolithic piezoceramic sheet materials. MFC actuators are flat, flexible actuators designed for bonding to structures to apply or detect strains. Bonding multiple layers of MFC actuators together could increase force capability, but not strain or displacement capability. Cylindrical piezoelectric fiber composite (CPFC) actuators have been invented as alternatives to MFC actuators for applications in which greater forces and/or strains or displacements may be required. In essence, a CPFC actuator is an MFC or other piezoceramic fiber composite actuator fabricated in a cylindrical instead of its conventional flat shape. Cylindrical is used here in the general sense, encompassing shapes that can have circular, elliptical, rectangular or other cross-sectional shapes in the planes perpendicular to their longitudinal axes.
Stress Analysis of Circular Frames
NASA Technical Reports Server (NTRS)
Fahlbusch, H; Wegner, W
1941-01-01
The stresses in circular frames of constant bending stiffnesses, as encountered in thin-wall shells, are investigated from the point of view of finite depth of sectional area of frame. The solution is carried out for four fundamental load conditions. The method is illustrated on a worked out example.
NASA Astrophysics Data System (ADS)
Narita, Y.; Nitta, T.
1998-07-01
Free vibration and corresponding optimal design problems are solved for laminated composite shallow shells of rectangular planform. The shells have symmetric laminated construction and are supported by shear diaphragms along the edges. The first-order transverse shear deformation is assumed in the Donnell type shell theory to account for the thickness shear effect, and an analytical solution is presented which is exact for cross-ply laminates and is approximate for angle-ply laminates. A simplified formula is also derived by neglecting inplane inertia terms. Analytical solutions with/without the inplane inertia terms from the classical thin shell theory are also shown. In numerical examples, natural frequencies are presented for various types of shell curvature, e.g., circular cylindrical, spherical and hyperbolic paraboloidal shells. Fibre orientation angles, which cause the maximized fundamental frequencies of the alternating angle-ply shells, are determined, and effects of using the four different vibration solutions are discussed on the optimal frequencies and fibre orientation angles. Questions of how the different solutions quantitatively affect the optimal design results and which solution is recommended in the present type of optimization problems are clarified in the conclusions.
ERIC Educational Resources Information Center
Lee, Paul D.
1995-01-01
Provides a period-long activity using battery powered cars rolling in a circular motion on a tile floor. Students measure the time and distance as the car moves to derive the equation for centripetal acceleration. (MVL)
ERIC Educational Resources Information Center
Lee, Paul D.
1995-01-01
Provides a period-long activity using battery powered cars rolling in a circular motion on a tile floor. Students measure the time and distance as the car moves to derive the equation for centripetal acceleration. (MVL)
Mixed FE analysis of viscoelastic cylindrical helixes
NASA Astrophysics Data System (ADS)
Arıbaş, Ü. N.; Omurtag, M. H.
2012-09-01
In this study, analysis of viscoelastic cylindrical helixes with circular and square cross section is investigated by using the mixed FEM based on Timoshenko beam theory. The Kelvin model is used for the viscoelastic behavior. The analysis is performed in the Laplace domain and the results are transformed back to time domain numerically by Modified Durbin algorithm. The outcome is quite satisfactory besides the necessary engineering precision.
Beamtracking in cylindrical and cartesian coordinates
Schillinger, B.; Weiland, T.
1997-02-01
For the design of devices with circular optical axes, e.g. bending magnets or spectrometers, the use of cylindrical coordinates for field calculations could be favourable. Additionally, in case of applications like bending systems with nonorthogonal entry and exit faces, the coupling of cylindrical and cartesian coordinates improves the simulation of fringe fields. In this context we have implemented a consistent coupling between the two coordinate systems and have extended the tracking code of the electromagnetic simulator MAFIA to cylindrical coordinates. This extensions could be of interest for the calculation of transfer maps of ionoptical devices using the tracked particle orbit as reference trajectory and including fringe field effects in a more general manner. We will give a short introduction to the extensions and show some examples for bending systems with nonorthogonal entries. {copyright} {ital 1997 American Institute of Physics.}
Beamtracking in cylindrical and cartesian coordinates
Schillinger, B.; Weiland, T.
1997-02-01
For the design of devices with circular optical axes, e.g. bending magnets or spectrometers, the use of cylindrical coordinates for field calculations could be favourable. Additionally, in case of applications like bending systems with nonorthogonal entry and exit faces, the coupling of cylindrical and cartesian coordinates improves the simulation of fringe fields. In this context we have implemented a consistent coupling between the two coordinate systems and have extended the tracking code of the electromagnetic simulator MAFIA to cylindrical coordinates. This extensions could be of interest for the calculation of transfer maps of ionoptical devices using the tracked particle orbit as reference trajectory and including fringe field effects in a more general manner. We will give a short introduction to the extensions and show some examples for bending systems with nonorthogonal entries.
Encoding high-order cylindrically polarized light beams.
Moreno, Ignacio; Davis, Jeffrey A; Cottrell, Don M; Donoso, Ramiro
2014-08-20
In this work we present a setup for the experimental production of cylindrically polarized beams, as well as other variations of polarized light beams. The optical system uses a single transmissive phase-only spatial light modulator, which is used to apply different spatial phase modulation to two output collinear R and L circularly polarized components. Different cylindrically polarized light beams can be obtained by applying different phase shifts to these two circularly polarized components. The system is very efficient since modulation is directly applied to the light beam (as opposed to other common methods operating in the first order of encoded diffraction gratings). Different variations to the cylindrically polarized light beams are also reported, obtained by adding linear or quadratic relative phase shifts between the two circular polarization components of the light beam. Experimental results are provided in all cases.
Multipole Analysis of Circular Cylindircal Magnetic Systems
Selvaggi, Jerry P.
2005-12-01
This thesis deals with an alternate method for computing the external magnetic field from a circular cylindrical magnetic source. The primary objective is to characterize the magnetic source in terms of its equivalent multipole distribution. This multipole distribution must be valid at points close to the cylindrical source and a spherical multipole expansion is ill-equipped to handle this problem; therefore a new method must be introduced. This method, based upon the free-space Green's function in cylindrical coordinates, is developed as an alternative to the more familiar spherical harmonic expansion. A family of special functions, called the toroidal functions or Q-functions, are found to exhibit the necessary properties for analyzing circular cylindrical geometries. In particular, the toroidal function of zeroth order, which comes from the integral formulation of the free-space Green's function in cylindrical coordinates, is employed to handle magnetic sources which exhibit circular cylindrical symmetry. The toroidal functions, also called Q-functions, are the weighting coefficients in a ''Fourier series-like'' expansion which represents the free-space Green's function. It is also called a toroidal expansion. This expansion can be directly employed in electrostatic, magnetostatic, and electrodynamic problems which exhibit cylindrical symmetry. Also, it is shown that they can be used as an alternative to the Elliptic integral formulation. In fact, anywhere that an Elliptic integral appears, one can replace it with its corresponding Q-function representation. A number of problems, using the toroidal expansion formulation, are analyzed and compared to existing known methods in order to validate the results. Also, the equivalent multipole distribution is found for most of the solved problems along with its corresponding physical interpretation. The main application is to characterize the external magnetic field due to a six-pole permanent magnet motor in terms of
Fluid-structure interaction for nonlinear response of shells conveying pulsatile flow
NASA Astrophysics Data System (ADS)
Tubaldi, Eleonora; Amabili, Marco; Païdoussis, Michael P.
2016-06-01
Circular cylindrical shells with flexible boundary conditions conveying pulsatile flow and subjected to pulsatile pressure are investigated. The equations of motion are obtained based on the nonlinear Novozhilov shell theory via Lagrangian approach. The flow is set in motion by a pulsatile pressure gradient. The fluid is modeled as a Newtonian pulsatile flow and it is formulated using a hybrid model that contains the unsteady effects obtained from the linear potential flow theory and the pulsatile viscous effects obtained from the unsteady time-averaged Navier-Stokes equations. A numerical bifurcation analysis employs a refined reduced order model to investigate the dynamic behavior. The case of shells containing quiescent fluid subjected to the action of a pulsatile transmural pressure is also addressed. Geometrically nonlinear vibration response to pulsatile flow and transmural pressure are here presented via frequency-response curves and time histories. The vibrations involving both a driven mode and a companion mode, which appear due to the axial symmetry, are also investigated. This theoretical framework represents a pioneering study that could be of great interest for biomedical applications. In particular, in the future, a more refined model of the one here presented will possibly be applied to reproduce the dynamic behavior of vascular prostheses used for repairing and replacing damaged and diseased thoracic aorta in cases of aneurysm, dissection or coarctation. For this purpose, a pulsatile time-dependent blood flow model is here considered by applying physiological waveforms of velocity and pressure during the heart beating period. This study provides, for the first time in literature, a fully coupled fluid-structure interaction model with deep insights in the nonlinear vibrations of circular cylindrical shells subjected to pulsatile pressure and pulsatile flow.
Leung, Ka-Ngo
2005-06-14
A cylindrical neutron generator is formed with a coaxial RF-driven plasma ion source and target. A deuterium (or deuterium and tritium) plasma is produced by RF excitation in a cylindrical plasma ion generator using an RF antenna. A cylindrical neutron generating target is coaxial with the ion generator, separated by plasma and extraction electrodes which contain many slots. The plasma generator emanates ions radially over 360.degree. and the cylindrical target is thus irradiated by ions over its entire circumference. The plasma generator and target may be as long as desired. The plasma generator may be in the center and the neutron target on the outside, or the plasma generator may be on the outside and the target on the inside. In a nested configuration, several concentric targets and plasma generating regions are nested to increase the neutron flux.
Leung, Ka-Ngo [Hercules, CA
2008-04-22
A cylindrical neutron generator is formed with a coaxial RF-driven plasma ion source and target. A deuterium (or deuterium and tritium) plasma is produced by RF excitation in a cylindrical plasma ion generator using an RF antenna. A cylindrical neutron generating target is coaxial with the ion generator, separated by plasma and extraction electrodes which contain many slots. The plasma generator emanates ions radially over 360.degree. and the cylindrical target is thus irradiated by ions over its entire circumference. The plasma generator and target may be as long as desired. The plasma generator may be in the center and the neutron target on the outside, or the plasma generator may be on the outside and the target on the inside. In a nested configuration, several concentric targets and plasma generating regions are nested to increase the neutron flux.
Leung, Ka-Ngo
2009-12-29
A cylindrical neutron generator is formed with a coaxial RF-driven plasma ion source and target. A deuterium (or deuterium and tritium) plasma is produced by RF excitation in a cylindrical plasma ion generator using an RF antenna. A cylindrical neutron generating target is coaxial with the ion generator, separated by plasma and extraction electrodes which contain many slots. The plasma generator emanates ions radially over 360.degree. and the cylindrical target is thus irradiated by ions over its entire circumference. The plasma generator and target may be as long as desired. The plasma generator may be in the center and the neutron target on the outside, or the plasma generator may be on the outside and the target on the inside. In a nested configuration, several concentric targets and plasma generating regions are nested to increase the neutron flux.
Cylindrically symmetric wormholes
Kuhfittig, Peter K.F.
2005-05-15
This paper discusses traversable wormholes that differ slightly but significantly from those of the Morris-Thorne type under the assumption of cylindrical symmetry. The throat is a piecewise smooth cylindrical surface resulting in a shape function that is not differentiable at some value. It is proposed that the regular derivative be replaced by a one-sided derivative at this value. The resulting wormhole geometry satisfies the weak energy condition.
Cylindrical coordinate representation for multiband Hamiltonians
NASA Astrophysics Data System (ADS)
Takhtamirov, Eduard
2012-10-01
Rotationally invariant combinations of the Brillouin zone-center Bloch functions are used as basis function to express in cylindrical coordinates the valence-band and Kane envelope-function Hamiltonians for wurtzite and zinc-blende semiconductor heterostructures. For cylindrically symmetric systems, this basis allows to treat the envelope functions as eigenstates of the operator of projection of total angular momentum on the symmetry axis, with the operator's eigenvalue conventionally entering the Hamiltonians as a parameter. Complementing the Hamiltonians with boundary conditions for the envelope functions on the symmetry axis, we present for the first time a complete formalism for efficient modeling and description of multiband electron states in low-dimensional semiconductor structures with cylindrical symmetry. To demonstrate the potency of the cylindrical symmetry approximation and establish a criterion of its applicability for actual structures, we map the ground and several excited valence-band states in an isolated wurtzite GaN quantum wire of a hexagonal cross-section to the states in an equivalent quantum wire of a circular cross-section.
NASA Technical Reports Server (NTRS)
Cohen, Gerald A.; Haftka, Raphael T.
1989-01-01
Buckling load sensitivity calculations in the shell-of-revolution program FASOR are discussed. This development is based on Koiter's initial postbuckling theory, which has been generalized to include the effect of stiffness changes, as well as geometric imperfections. The implementation in FASOR is valid for anisotropic, as well as orthotropic, shells. Examples are presented for cylindrical panels under axial compression, complete cylindrical shells in torsion, and antisymmetric angle-ply cylindrical panels under edge shear.
Layzer type models for pressure driven shells
Hurricane, O A
2004-09-16
Models for the nonlinear instability of finite thickness shells driven by pressure are constructed in the style of Layzer. Equations for both Cartesian and cylindrically convergent/divergent geometries are derived. The resulting equations are appropriate for incompressible shells with unity Atwood number. Predictions from the equations compare well with two-dimensional simulations.
Layzer type models for pressure driven shells
Hurricane, O.A.
2005-05-01
Models for the nonlinear instability of finite thickness shells driven by pressure are constructed in the style of Layzer. Equations for both Cartesian and cylindrically convergent/divergent geometries are derived. The resulting equations are appropriate for incompressible shells with unity Atwood number. Predictions from the equations compare well with two-dimensional simulations.
Gravitational radiation from a cylindrical naked singularity
Nakao, Ken-ichi; Morisawa, Yoshiyuki
2005-06-15
We construct an approximate solution which describes the gravitational emission from a naked singularity formed by the gravitational collapse of a cylindrical thick shell composed of dust. The assumed situation is that the collapsing speed of the dust is very large. In this situation, the metric variables are obtained approximately by a kind of linear perturbation analysis in the background Morgan solution which describes the motion of cylindrical null dust. The most important problem in this study is what boundary conditions for metric and matter variables should be imposed at the naked singularity. We find a boundary condition that all the metric and matter variables are everywhere finite at least up to the first order approximation. This implies that the spacetime singularity formed by this high-speed dust collapse is very similar to that formed by the null dust and the final singularity will be a conical one. Weyl curvature is completely released from the collapsed dust.
Superhydrophobic cylindrical nanoshell array.
Park, Yong-Bum; Im, Maesoon; Im, Hwon; Choi, Yang-Kyu
2010-06-01
A superhydrophobic property was demonstrated on a cylindrical poly crystalline silicon nanoshell array due to its geometrical properties, even without a hydrophobic coating. The proposed structure showed superior water-repellency compared to a conventional pillar structure with an identical structural dimension. This superhydrophobic property is attributed to an air pillar that exists in the nanoshell. Through the calculation of capillary pressure, the stability of the air pillar was confirmed. Furthermore, a droplet impinging test was conducted on the fabricated cylindrical nanoshell array to verify the robust Cassie state of the proposed structure under a dynamic condition.
Mathematical model for characterizing noise transmission into finite cylindrical structures
NASA Astrophysics Data System (ADS)
Li, Deyu; Vipperman, Jeffrey S.
2005-02-01
This work presents a theoretical study of the sound transmission into a finite cylinder under coupled structural and acoustic vibration. Particular attention of this study is focused on evaluating a dimensionless quantity, ``noise reduction,'' for characterizing noise transmission into a small cylindrical enclosure. An analytical expression of the exterior sound pressure resulting from an oblique plane wave impinging upon the cylindrical shell is first presented, which is approximated from the exterior sound pressure for an infinite cylindrical structure. Next, the analytical solution of the interior sound pressure is computed using modal-interaction theory for the coupled structural acoustic system. These results are then used to derive the analytical formula for the noise reduction. Finally, the model is used to predict and characterize the sound transmission into a ChamberCore cylindrical structure, and the results are compared with experimental data. The effects of incidence angle and internal acoustic damping on the sound transmission into the cylinder are also parametrically studied. .
Thermal runaway and microwave heating in thin cylindrical domains
NASA Astrophysics Data System (ADS)
Ward, Michael J.
2002-04-01
The behaviour of the solution to two nonlinear heating problems in a thin cylinder of revolution of variable cross-sectional area is analysed using asymptotic and numerical methods. The first problem is to calculate the fold point, corresponding to the onset of thermal runaway, for a steady-state nonlinear elliptic equation that arises in combustion theory. In the limit of thin cylindrical domains, it is shown that the onset of thermal runaway can be delayed when a circular cylindrical domain is perturbed into a dumbell shape. Numerical values for the fold point for different domain shapes are obtained asymptotically and numerically. The second problem that is analysed is a nonlinear parabolic equation modelling the microwave heating of a ceramic cylinder by a known electric field. The basic model in a thin circular cylindrical domain was analysed in Booty & Kriegsmann (Meth. Appl. Anal. 4 (1994) p. 403). Their analysis is extended to treat thin cylindrical domains of variable cross-section. It is shown that the steady-state and dynamic behaviours of localized regions of high temperature, called hot-spots, depend on a competition between the maxima of the electric field and the maximum deformation of the circular cylinder. For a dumbell-shaped region it is shown that two disconnected hot-spot regions can occur. Depending on the parameters in the model, these regions, ultimately, either merge as time increases or else remain as disconnected regions for all time.
ERIC Educational Resources Information Center
Jones, Dustin L.
2009-01-01
The author describes an activity where prospective mathematics teachers made hypotheses about the dimensions of a fair cylindrical die and conducted experiments with different cylinders. He also provides a model that estimates the probability that a cylinder would land on the lateral surface, depending on the height and diameter of the cylinder.…
Microfabricated cylindrical ion trap
Blain, Matthew G.
2005-03-22
A microscale cylindrical ion trap, having an inner radius of order one micron, can be fabricated using surface micromachining techniques and materials known to the integrated circuits manufacturing and microelectromechanical systems industries. Micromachining methods enable batch fabrication, reduced manufacturing costs, dimensional and positional precision, and monolithic integration of massive arrays of ion traps with microscale ion generation and detection devices. Massive arraying enables the microscale cylindrical ion trap to retain the resolution, sensitivity, and mass range advantages necessary for high chemical selectivity. The microscale CIT has a reduced ion mean free path, allowing operation at higher pressures with less expensive and less bulky vacuum pumping system, and with lower battery power than conventional- and miniature-sized ion traps. The reduced electrode voltage enables integration of the microscale cylindrical ion trap with on-chip integrated circuit-based rf operation and detection electronics (i.e., cell phone electronics). Therefore, the full performance advantages of microscale cylindrical ion traps can be realized in truly field portable, handheld microanalysis systems.
Scattering characteristics of simplified cylindrical invisibility cloaks.
Yan, Min; Ruan, Zhichao; Qiu, Min
2007-12-24
The previously reported simplified cylindrical linear cloak is improved so that the cloak's outer surface is impedance-matched to free space. The scattering characteristics of the improved linear cloak is compared to the previous counterpart as well as the recently proposed simplified quadratic cloak derived from quadratic coordinate transformation. Significant improvement in invisibility performance is noticed for the improved linear cloak with respect to the previously proposed linear one. The improved linear cloak and the simplified quadratic cloak have comparable invisibility performances, except that the latter however has to fulfill a minimum shell thickness requirement (i.e. outer radius must be larger than twice of inner radius). When a thin cloak shell is desired, the improved linear cloak is much more superior than the other two versions of simplified cloaks.
Cylindrical wormholes with positive cosmological constant
NASA Astrophysics Data System (ADS)
Richarte, Martín G.
2013-07-01
We construct cylindrical, traversable wormholes with finite radii by taking into account the cut-and-paste procedure for the case of cosmic string manifolds with a positive cosmological constant. Under reasonable assumptions about the equation of state of the matter located at the shell, we find that the wormhole throat undergoes a monotonous evolution provided it moves at a constant velocity. In order to explore the dynamical nonlinear behavior of the wormhole throat, we consider that the matter of the shell is supported by anisotropic Chaplygin gas, anti-Chaplygin gas, or a mixture of Chaplygin and anti-Chaplygin gases, implying that wormholes could suffer an accelerated expansion or contraction, but that oscillatory behavior seems to be forbidden.
Synthesis of stiffened conical shells.
NASA Technical Reports Server (NTRS)
Thornton, W. A.
1972-01-01
The development of a method to effect the automated minimum weight design of ring and stringer stiffened shells is presented. Membrane theory is used for the shell prebuckling analysis. The buckling analysis is based upon an arbitrary shell of revolution computer program. The structural analysis includes both buckling and yielding modes of failure. The synthesis involves the coupling of an exterior penalty function with a method for the unconstrained minimization of a function comprised of a sum of squares. Results of the application of the method to the design of the Viking Aeroshell cone are presented. The least weight Viking Aeroshell appears to be an all magnesium shell with ring stiffeners of hollow circular cross section. Because the method incorporates a general shell of revolution buckling analysis, it can be readily modified and applied to the design of any axisymmetrically loaded uniformly stiffened shell of revolution for which a membrane prebuckling solution exists.
Core–Shell Plasmonic Nanohelices
2017-01-01
We introduce core–shell plasmonic nanohelices, highly tunable structures that have a different response in the visible for circularly polarized light of opposite handedness. The glass core of the helices is fabricated using electron beam induced deposition and the pure gold shell is subsequently sputter coated. Optical measurements allow us to explore the chiral nature of the nanohelices, where differences in the response to circularly polarized light of opposite handedness result in a dissymmetry factor of 0.86, more than twice of what has been previously reported. Both experiments and subsequent numerical simulations demonstrate the extreme tunability of the core–shell structures, where nanometer changes to the geometry can lead to drastic changes of the optical responses. This tunability, combined with the large differential transmission, make core–shell plasmonic nanohelices a powerful nanophotonic tool for, for example, (bio)sensing applications. PMID:28824931
Simple Analytic Expressions for the Magnetic Field of a Circular Current Loop
NASA Technical Reports Server (NTRS)
Simpson, James C.; Lane, John E.; Immer, Christopher D.; Youngquist, Robert C.; Steinrock, Todd (Technical Monitor)
2001-01-01
Analytic expressions for the magnetic induction and its spatial derivatives for a circular loop carrying a static current are presented in Cartesian, spherical and cylindrical coordinates. The solutions are exact throughout all space outside the conductor.
How does life adapt to a gravitational environment? The outline of the terrestrial gastropod shell.
Okajima, Ryoko; Chiba, Satoshi
2011-12-01
How do several characteristics adapt to gravity while mutually influencing each other? Our study addresses this issue by focusing on the terrestrial gastropod shell. The geometric relationship between the spire index (shell height/diameter) and outline (cylindricality) is theoretically estimated. When the shell grows isometrically, a high-spired shell becomes conical in shape and a low-spired shell becomes cylindrical in shape. A physical model shows that the lowest- and highest-spired shells are the most balanced. In addition, a cone shape is the most balanced for a low-spired shell, and a column shape is the most balanced for a high-spired shell. Spire index and cylindricality measured for freshwater gastropods follow the relationship estimated by the model, whereas those for terrestrial gastropods deviate from this relationship. This translates to a high shell being more cylindrical than a flat shell, except in the case of extremely high or low shells. This suggests that the shape of the most balanced shells (lowest and highest shell heights) is constrained by coiling geometry but that relatively unbalanced shells (intermediate shell heights) do not follow a coiling geometry, as a result of adaptation to enable the snail to carry its shell more effectively.
46 CFR 59.15-10 - Bagged or blistered shell plates.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 46 Shipping 2 2014-10-01 2014-10-01 false Bagged or blistered shell plates. 59.15-10 Section 59.15... shell plates. (a) When the shell plates of cylindrical boilers which are exposed to the radiant heat of... boiler. (b) Where the shell plate is bagged due to overheating, the Officer in Charge, Marine Inspection...
46 CFR 59.15-10 - Bagged or blistered shell plates.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 46 Shipping 2 2012-10-01 2012-10-01 false Bagged or blistered shell plates. 59.15-10 Section 59.15... shell plates. (a) When the shell plates of cylindrical boilers which are exposed to the radiant heat of... boiler. (b) Where the shell plate is bagged due to overheating, the Officer in Charge, Marine Inspection...
46 CFR 59.15-10 - Bagged or blistered shell plates.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 46 Shipping 2 2013-10-01 2013-10-01 false Bagged or blistered shell plates. 59.15-10 Section 59.15... shell plates. (a) When the shell plates of cylindrical boilers which are exposed to the radiant heat of... boiler. (b) Where the shell plate is bagged due to overheating, the Officer in Charge, Marine Inspection...
Nonlinear vibrations of shallow shells with complex boundary: R-functions method and experiments
NASA Astrophysics Data System (ADS)
Kurpa, Lidia; Pilgun, Galina; Amabili, Marco
2007-10-01
Geometrically nonlinear vibrations of shallow circular cylindrical panels with complex shape of the boundary are considered. The R-functions theory and variational methods are used to study the problem. The R-functions method (RFM) allows constructing in analytical form the sequence of basis functions satisfying the given boundary conditions in case of complex shape of the boundary. The problem is reduced to a single second-order differential equation with quadratic and cubic nonlinear terms. The method developed has been initially applied to study free vibrations of shallow circular cylindrical panels with rectangular base for different boundary conditions: (i) clamped edges, (ii) in-plane immovable simply supported edges, (iii) classically simply supported edges, and (iv) in-plane free simply supported edges. Then, the same approach is applied to a shell with complex shape of the boundary. Experiments have been conducted on an aluminum panel with complex shape of the boundary in order to identify the nonlinear response of the fundamental mode; these experimental results have been compared to numerical results.
Mantle flow reversals in cylindrical Earth models
NASA Astrophysics Data System (ADS)
Ghias, Sanaz R.; Jarvis, Gary T.
2007-12-01
We employ a two-dimensional model of mantle convection in a cylindrical shell to study the influence of curvature on the phenomenon of spontaneous flow reversal, which has been found previously only in plane layer models in Cartesian geometry. Our model includes rigidly moving plates, with weak zones at each end, and uniformly distributed internal heat sources. Surface plates in this model are passive in that their lateral velocities reflect the overall buoyancy in the underlying mantle and, at each time step, match the average surface velocity that would occur in the absence of plates. Our principal finding is that flow reversals, similar to those in plane layers, are also found in our cylindrical shell models, thereby attesting to the robustness of this feature. We conduct systematic investigations of the impact on the flow reversal behavior of varying degree of curvature, plate thickness, internal heating rate and aspect ratio of the convection cells. Flow reversals are driven by a build-up of internally heated material adjacent to a major mantle downwelling. When thermal instabilities develop in the upper boundary layer they develop into intermediate sinking plumes which disrupt the build-up of hot material near sinking plumes. Accordingly, parameter values which tend to stabilize the upper thermal boundary layer (low degree of curvature, high plate thickness, small aspect ratio and intermediate internal heating rate) favor regular flow reversals.
Static cylindrically symmetric spacetimes
NASA Astrophysics Data System (ADS)
Fjällborg, Mikael
2007-05-01
We prove the existence of static solutions to the cylindrically symmetric Einstein Vlasov system, and we show that the matter cylinder has finite extension in two of the three spatial dimensions. The same results are also proved for a quite general class of equations of state for perfect fluids coupled to the Einstein equations, extending the class of equations of state considered by Bicak et al (2004 Class. Quantum Grav.21 1583). We also obtain this result for the Vlasov Poisson system.
'Endurance' All Around (cylindrical)
NASA Technical Reports Server (NTRS)
2004-01-01
This 360-degree view of the terrain surrounding NASA's Mars Exploration Rover Opportunity was taken on the rover's 171st sol on Mars (July 17, 2004). It was assembled from images taken by the rover's navigation camera at a position referred to as 'site 33.' Opportunity had driven 11 meters (36 feet) into 'Endurance Crater.' The view is a cylindrical projection with geometrical seam correction.
Hilly Surroundings (cylindrical)
NASA Technical Reports Server (NTRS)
2004-01-01
This 360-degree view of the terrain surrounding NASA's Mars Exploration Rover Spirit was taken on the rover's 189th sol on Mars (July 15, 2004). It was assembled from images taken by the rover's navigation camera at a position referred to as Site 72, which is at the base of the 'West Spur' portion of the 'Columbia Hills.' The view is presented in a cylindrical projection with geometrical seam correction.
Tool for Torquing Circular Electrical-Connector Collars
NASA Technical Reports Server (NTRS)
Gaulke, Kathryn; Werneth, Russell; Grunsfeld, John; O'Neill, Patrick; Snyder, Russ
2006-01-01
An improved tool has been devised for applying torque to lock and unlock knurled collars on circular electrical connectors. The tool was originally designed for, and used by, astronauts working in outer space on the Hubble Space Telescope (HST). The tool is readily adaptable to terrestrial use in installing and removing the same or similar circular electrical connectors as well as a wide variety of other cylindrical objects, the tightening and loosening of which entail considerable amounts of torque.
Ideal cylindrical cloak: perfect but sensitive to tiny perturbations.
Ruan, Zhichao; Yan, Min; Neff, Curtis W; Qiu, Min
2007-09-14
A cylindrical wave expansion method is developed to obtain the scattering field for an ideal two-dimensional cylindrical invisibility cloak. A near-ideal model of the invisibility cloak is set up to solve the boundary problem at the inner boundary of the cloak shell. We confirm that a cloak with the ideal material parameters is a perfect invisibility cloak by systematically studying the change of the scattering coefficients from the near-ideal case to the ideal one. However, because of the slow convergence of the zeroth-order scattering coefficients, a tiny perturbation on the cloak would induce a noticeable field scattering and penetration.
Polar POLICRYPS diffractive structures generate cylindrical vector beams
Alj, Domenico; Caputo, Roberto Umeton, Cesare; Paladugu, Sathyanarayana; Volpe, Giovanni
2015-11-16
Local shaping of the polarization state of a light beam is appealing for a number of applications. This can be achieved by employing devices containing birefringent materials. In this article, we present one such enables converting a uniformly circularly polarized beam into a cylindrical vector beam (CVB). This device has been fabricated by exploiting the POLICRYPS (POlymer-LIquid CRYstals-Polymer-Slices) photocuring technique. It is a liquid-crystal-based optical diffraction grating featuring polar symmetry of the director alignment. We have characterized the resulting CVB profile and polarization for the cases of left and right circularly polarized incoming beams.
The stress distribution in shell bodies and wings as an equilibrium problem
NASA Technical Reports Server (NTRS)
Wagner, H
1937-01-01
This report treats the stress distribution in shell-shaped airplane components (fuselage, wings) as an equilibrium problem; it includes both cylindrical and non-cylindrical shells. In particular, it treats the stress distribution at the point of stress application and at cut-out points.
NASA Astrophysics Data System (ADS)
Bílek, M.; Jungwiert, B.; Ebrová, I.; Bartošková, K.
2015-03-01
Context. Many ellipticals are surrounded by round stellar shells probably stemming from minor mergers. A new method for constraining gravitational potential in elliptical galaxies has recently been suggested. It uses the spectral line profiles of these shells to measure the circular velocity at the edge of the shell and the expansion velocity of the shell itself. MOND is an alternative to the dark matter framework aiming to solve the missing mass problem. Aims: We study how the circular and expansion velocities behave in MOND for large shells. Methods: The asymptotic behavior for infinitely large shells is derived analytically. The applicability of the asymptotic results for finitely sized shells is studied numerically on a grid of galaxies modeled with Sérsic spheres. Results: Circular velocity settles asymptotically at a value determined by the baryonic mass of the galaxy forming the baryonic Tully-Fisher relation known for disk galaxies. Shell expansion velocity also becomes asymptotically constant. The expansion velocities of large shells form a multibranched analogy to the baryonic Tully-Fisher relation, together with the galactic baryonic masses. For many - but not all - shell galaxies, the asymptotic values of these two types of velocities are reached under the effective radius. If MOND is assumed to work in ellipticals, then the shell spectra allow many details of the history to be revealed about the formation of the shell system, including its age. The results pertaining to circular velocities apply to all elliptical galaxies, not only those with shells.
Thermal buckling of laminated composite shells
Thangaratnam, R.K.; Palaninathan, R.; Ramachandran, J. )
1990-05-01
The linear buckling analysis of laminated composite cylindrical and conical shells under thermal load using the finite element method is reported here. Critical temperatures are presented for various cases of cross-ply and angly-ply laminated shells. The effects of radius/thickness ratio, number of layers, ratio of coefficients of thermal expansion, and the angle of fiber orientation have been studied. The results indicate that the buckling behavior of laminated shell under thermal load is different from that of mechanically loaded shell with respect to the angle of fiber orientation. 6 refs.
A cylindrical converging shock tube for shock-interface studies.
Luo, Xisheng; Si, Ting; Yang, Jiming; Zhai, Zhigang
2014-01-01
A shock tube facility for generating a cylindrical converging shock wave is developed in this work. Based on the shock dynamics theory, a specific wall profile is designed for the test section of the shock tube to transfer a planar shock into a cylindrical one. The shock front in the converging part obtained from experiment presents a perfect circular shape, which proves the feasibility and reliability of the method. The time variations of the shock strength obtained from numerical simulation, experiment, and theoretical estimation show the desired converging effect in the shock tube test section. Particular emphasis is then placed on the problem of shock-interface interaction induced by cylindrical converging shock waves. For this purpose, membrane-less gas cylinder is adopted to form the interface between two different fluids while the laser sheet technique to visualize the flow field. The result shows that it is convenient to perform such experiments in this facility.
Structural Concepts Study of Non-circular Fuselage Configurations
NASA Technical Reports Server (NTRS)
Mukhopadhyay, Vivel
1996-01-01
A preliminary study of structural concepts for noncircular fuselage configurations is presented. For an unconventional flying-wing type aircraft, in which the fuselage is inside the wing, multiple fuselage bays with non-circular sections need to be considered. In a conventional circular fuselage section, internal pressure is carried efficiently by a thin skin via hoop tension. If the section is non-circular, internal pressure loads also induce large bending stresses. The structure must also withstand additional bending and compression loads from aerodynamic and gravitational forces. Flat and vaulted shell structural configurations for such an unconventional, non-circular pressurized fuselage of a large flying-wing were studied. A deep honeycomb sandwich-shell and a ribbed double-wall shell construction were considered. Combinations of these structural concepts were analyzed using both analytical and simple finite element models of isolated sections for a comparative conceptual study. Weight, stress, and deflection results were compared to identify a suitable configuration for detailed analyses. The flat sandwich-shell concept was found preferable to the vaulted shell concept due to its superior buckling stiffness. Vaulted double-skin ribbed shell configurations were found to be superior due to their weight savings, load diffusion, and fail-safe features. The vaulted double-skin ribbed shell structure concept was also analyzed for an integrated wing-fuselage finite element model. Additional problem areas such as wing-fuselage junction and pressure-bearing spar were identified.
Sound insulation characteristics of finite length orthotropic shells
NASA Astrophysics Data System (ADS)
Chonan, S.; Koriyama, H.
1988-11-01
An analysis is presented of the acoustic characteristics of orthotropic cylindrical shells excited by axisymmetric plane sound waves traveling within the shells. The shell is exposed in a free field in the range of length, and is otherwise covered with an infinite rigid baffle. The problem is studied on the basis of a thick shell theory in which account is taken of the effects of shear deformation and rotatory inertia. The air outside the shell is described by the Helmholtz linear acoustic equation. The sound transmission loss through the shell wall is obtained and calculated for various values of the physical parameters involved.
NASA Astrophysics Data System (ADS)
Sharma, J. N.; Pathania, Vijayata
2005-03-01
The propagation of thermoelastic waves along circumferential direction in homogeneous, transversely isotropic, cylindrical curved plates has been investigated in the context of theories of thermoelasticity. This type of study is important for ultrasonic non-destructive inspection of large-diameter pipes, which helps in the health monitoring of ailing infrastructure. Longitudinal stress-corrosion cracks are usually temperature dependent and can be detected more efficiently by inducing circumferential waves; hence the study of generalized thermoelastic wave propagation in the circumferential direction in a pipe wall is essential. Mathematical modeling of the problem of obtaining dispersion curves for curved transversely isotropic thermally conducting elastic plates leads to coupled differential equations. The model has been simplified by using the Helmholtz decomposition technique and the resulting equations have been solved by using separation of variable method to obtain the secular equations in isolated mathematical conditions for the plates with stress-free or rigidly fixed, thermally insulated and isothermal boundary surfaces. The closed form solutions are also obtained under different situations and conditions. The longitudinal shear motion and axially symmetric shear vibration modes get decoupled from the rest of the motion and are not affected by thermal variations, whereas for the non-axially symmetric case of plane strain vibrations, these modes remain coupled and are affected by temperature changes. Moreover, these vibration modes are found to be dispersive and dissipative in character. In order to illustrate theoretical development, numerical solutions are obtained and presented graphically for a zinc plate. The obtained results are also compared with those available in the literature in case of waves in cylindrical shell/circular annulus in the absence of thermomechanical coupling and thermal relaxation times.
Cylindrical holographic radar camera
NASA Astrophysics Data System (ADS)
McMakin, Douglas L.; Sheen, David M.; Hall, Thomas E.; Severtsen, Ronald H.
1998-12-01
A novel personnel surveillance system has been developed to rapidly obtain 360 degree, full-body images of humans for the detection and identification of concealed threats. Detectable threats include weapons fabricated with metal, plastic, and ceramic, as well as explosive solids and liquids. This new system uses a cylindrical mechanical scanner to move a seven-foot, 384 element, Ka band (26 - 30 GHz) array circumferentially around a person in four to seven seconds. Low power millimeter-waves, which are nonionizing and not harmful to humans, are employed because they readily penetrate clothing barriers and reflect from concealed threats. The reflected waves provide information that is reconstructed into 3-D cylindrical holographic images with high-speed, digital signal processing (DSP) boards. This system is capable of displaying in an animation format eight, sixteen, thirty-two or sixty-four image frames at various aspect angles around the person under surveillance. This new prototype surveillance system is operational and is presently under laboratory testing and evaluation.
Experimental Simulation of Boiling Phenomena with a Cylindrical Annulus Moderator Cell
Lee, C.H.; Lee, D.J.; Chan, Y.K.; Chang, C.J.
2002-07-01
The improvement and utilization promotion project of the Taiwan Research Reactor (TRR-II) has been carried out at the Institute of Nuclear Energy Research (INER). The Cold Neutron Source (CNS) with a two-phase thermosyphon will be installed in the heavy water reactor. The hydrogen cold loop consists of a cylindrical moderator cell, a single transfer tube, and a condenser. A cylindrical annulus moderator cell consists of the outer shell and the inner shell of which bottom part is open. A series of mockup tests were performed by using the full-scale mock-up test facility and Freon-11 as a working fluid. The test results show that the inner shell contains only vapor and the outer shell contains boiling liquid for simulating the TRR-II CNS in the full power operations. The liquid level in the outer shell is stable without producing a sudden bubbling against the increase of 30% power. (authors)
Buckling of eccentrically stringer-stiffened cylindrical panels under axial compression
NASA Technical Reports Server (NTRS)
Sobel, L. H.; Agarwal, B. L.
1976-01-01
The paper presents numerical results, based on Donnell shell theory, for the axial compressive buckling loads for eccentrically stringer-stiffened circular cylindrical panels, in a study of the effect of boundary conditions and panel width on the buckling load. The two cases of inside and outside stiffeners were considered. The complete cylinder buckling load was reached only for panels under classical simply supported boundary conditions. The prevention of circumferential displacement is found to be the most important in-plane boundary condition from the point of view of increasing the buckling load. Clamping is found more effective in increasing the buckling loads of panels with free circumferential edge displacement than of panels with zero edge displacement. When panel width is equal to or greater than 180 deg, the panel buckling loads are within 10% of the complete cylinder load for all cases except one simply supported panel with outside stringers. Buckling loads were higher for outside stringers, except for very narrow panels that are restrained against circumferential edge displacement. Eccentricity effects are generally similar for clamped and simply supported panels with the same in-plane boundary conditions.
Buckling of cylindrical panels under axial compression
NASA Technical Reports Server (NTRS)
Sobel, L. H.; Weller, T.; Agarwal, B. L.
1976-01-01
This paper investigates the effects of boundary conditions and panel width on the axially compressive buckling behavior of unstiffened, isotropic, circular cylindrical panels. Numerical results are presented for eight different sets of boundary conditions along the straight edges of the panels. For all sets of boundary conditions except one (SS1), the results show that the panel buckling loads monotonically approach the complete cylinder buckling load from above as the panel width is increased. Low buckling loads, sometimes less than half the complete cylinder buckling load, are found for simply supported panels with free in-plane edge displacements (SS1). It is observed that the prevention of circumferential edge displacement is the most important in-plane boundary condition from the point of view of increasing the buckling load; and that the prevention of edge rotation in the circumferential direction also significantly increases the buckling load.
1981-09-01
hardener 738 (IV 11 mnutsfuttured op Fig. 5- Reflection - polariscope arrangement Indi f - 44.4 Iblin. .fi (7.8 AN r.n-fr. 2 aMy 10s1 was given through...special reflection polariscope of the type used by Slot’ and, more recently, by Durelli ei al.’ would appear to be ideal for this problem. With one...uses photoelasticity and requires a large field diffused light polariscope . Several problems of optimization related to the presence of holes in
Chirped microlens arrays for diode laser circularization and beam expansion
NASA Astrophysics Data System (ADS)
Schreiber, Peter; Dannberg, Peter; Hoefer, Bernd; Beckert, Erik
2005-08-01
Single-mode diode lasers are well-established light sources for a huge number of applications but suffer from astigmatism, beam ellipticity and large manufacturing tolerances of beam parameters. To compensate for these shortcomings, various approaches like anamorphic prism pairs and cylindrical telescopes for circularization as well as variable beam expanders based on zoomed telescopes for precise adjustment of output beam parameters have been employed in the past. The presented new approach for both beam circularization and expansion is based on the use of microlens arrays with chirped focal length: Selection of lenslets of crossed cylindrical microlens arrays as part of an anamorphic telescope enables circularization, astigmatism correction and divergence tolerance compensation of diode lasers simultaneously. Another promising application of chirped spherical lens array telescopes is stepwise variable beam expansion for circular laser beams of fiber or solid-state lasers. In this article we describe design and manufacturing of beam shaping systems with chirped microlens arrays fabricated by polymer-on-glass replication of reflow lenses. A miniaturized diode laser module with beam circularization and astigmatism correction assembled on a structured ceramics motherboard and a modulated RGB laser-source for photofinishing applications equipped with both cylindrical and spherical chirped lens arrays demonstrate the feasibility of the proposed system design approach.
Motion of a Cylindrical Dielectric Boundary
Cheng, Li-Tien; Li, Bo; White, Michael; Zhou, Shenggao
2013-01-01
The interplay between geometry and electrostatics contributes significantly to hydrophobic interactions of biomolecules in an aqueous solution. With an implicit solvent, such a system can be described macroscopically by the dielectric boundary that separates the high-dielectric solvent from low-dielectric solutes. This work concerns the motion of a model cylindrical dielectric boundary as the steepest descent of a free-energy functional that consists of both the surface and electrostatic energies. The effective dielectric boundary force is defined and an explicit formula of the force is obtained. It is found that such a force always points from the solvent region to solute region. In the case that the interior of a cylinder is of a lower dielectric, the motion of the dielectric boundary is initially driven dominantly by the surface force but is then driven inward quickly to the cylindrical axis by both the surface and electrostatic forces. In the case that the interior of a cylinder is of a higher dielectric, the competition between the geometrical and electrostatic contributions leads to the existence of equilibrium boundaries that are circular cylinders. Linear stability analysis is presented to show that such an equilibrium is only stable for a perturbation with a wavenumber larger than a critical value. Numerical simulations are reported for both of the cases, confirming the analysis on the role of each component of the driving force. Implications of the mathematical findings to the understanding of charged molecular systems are discussed. PMID:23885130
Cylindrical geometry hall thruster
Raitses, Yevgeny; Fisch, Nathaniel J.
2002-01-01
An apparatus and method for thrusting plasma, utilizing a Hall thruster with a cylindrical geometry, wherein ions are accelerated in substantially the axial direction. The apparatus is suitable for operation at low power. It employs small size thruster components, including a ceramic channel, with the center pole piece of the conventional annular design thruster eliminated or greatly reduced. Efficient operation is accomplished through magnetic fields with a substantial radial component. The propellant gas is ionized at an optimal location in the thruster. A further improvement is accomplished by segmented electrodes, which produce localized voltage drops within the thruster at optimally prescribed locations. The apparatus differs from a conventional Hall thruster, which has an annular geometry, not well suited to scaling to small size, because the small size for an annular design has a great deal of surface area relative to the volume.
Coupling into and scattering from cylindrical structures covered periodically with metallic patches
NASA Technical Reports Server (NTRS)
Cwik, Tom
1990-01-01
Circular cylindrical structures covered periodically with metallic patches are considered. After an analogy to planar periodic surfaces is shown, formulations are presented for calculating induced currents on the curved surface. The equations are solved and results calculated for the specific case of periodic strips on the cylindrical surface. For a cylindrical structure a two-dimensional periodicity exists, as in a planar structure, while a spherical structure allows only a rotational periodicity. When the cylindrical structure is excited by the characteristic harmonic of the system, the spectral response of the transmitted field exhibits resonances that depend on the surface periodicity, as is known for planar structures. Since the cylindrical structure contains finite closed regions, the effects of resonances internal to the structure are seen and give additional information as compared to planar structures.
Cracked shells under skew-symmetric loading
NASA Technical Reports Server (NTRS)
Lelale, F.
1982-01-01
A shell containing a through crack in one of the principal planes of curvature and under general skew-symmetric loading is considered. By employing a Reissner type shell theory which takes into account the effect of transverse shear strains, all boundary conditions on the crack surfaces are satisfied separately. Consequently, unlike those obtained from the classical shell theory, the angular distributions of the stress components around the crack tips are shown to be identical to the distributions obtained from the plane and antiplane elasticity solutions. Extensive results are given for axially and circumferentially cracked cylindrical shells, spherical shells, and toroidal shells under uniform inplane shearing, out of plane shearing, and torsion. The effect of orthotropy on the results is also studied.
Cryogenic line insulation made from prefabricated polyurethane shells
NASA Technical Reports Server (NTRS)
Lerma, G.
1975-01-01
Prefabricated polyurethane foam insulation is inexpensive and easily installed on cryogenic lines. Insulation sections are semicircular half shells. Pair of half shells is placed to surround cryogenic line. Cylindrically-shaped knit sock is pulled over insulation then covered with polyurethane resin to seal system.
Cylindrical quasi-Gaussian beams.
Mitri, F G
2013-11-15
Making use of the complex-source-point method in cylindrical coordinates, an exact solution representing a cylindrical quasi-Gaussian beam of arbitrary waist w(0) satisfying both the Helmholtz and Maxwell's equations is introduced. The Cartesian components of the electromagnetic field are derived stemming from different polarizations of the magnetic and electric vector potentials based on Maxwell's vectorial equations and Lorenz's gauge condition, without any approximations. Computations illustrate the theory for tightly focused and quasi-collimated cylindrical beams. The results are particularly useful in beam-forming design using high-aperture or collimated cylindrical laser beams in imaging microscopy, particle manipulation, optical tweezers, and the study of scattering, radiation forces, and torque on cylindrical structures.
Scattering and radiation from cylindrically conformal antennas
NASA Astrophysics Data System (ADS)
Kempel, Leo Charles
Microstrip patch antennas offer considerable advantages in terms of weight, aerodynamic drag, cost, flexibility, and observability over more conventional protruding antennas. Two hybrid finite element methods are presented and are used to examine the scattering and radiation behavior of cylindrically conformal patches. In conjunction with a new divergence-free cylindrical shell element, the finite element-boundary integral method is shown to have low computational and memory requirements when compared with competing approaches. This method uses an efficient creeping wave series for the computation of the dyadic Green's function and a uniform surface mesh so that a fast Fourier transform may be used to reduce the computational and memory burden of the method. An alternative finite element-absorbing boundary condition approach incorporates a new conformal vector condition which minimizes the computational domain. The latter method is more flexible than the former because it can incorporate surface coatings and protruding antennas. Guidelines are established for minimal ABC displacement from the aperture. These two hybrid finite element methods are used to study the scattering, radiation, and input impedance of typical conformal antenna arrays. In particular, the effect of curvature and cavity size is examined for both discrete and wraparound antenna arrays.
Observation of Compressible Plasma Mix in Cylindrically Convergent Implosions
NASA Astrophysics Data System (ADS)
Barnes, Cris W.; Batha, Steven H.; Lanier, Nicholas E.; Magelssen, Glenn R.; Tubbs, David L.; Dunne, A. M.; Rothman, Steven R.; Youngs, David L.
2000-10-01
An understanding of hydrodynamic mix in convergent geometry will be of key importance in the development of a robust ignition/burn capability on NIF, LMJ and future pulsed power machines. We have made use of the OMEGA laser facility at the University of Rochester to investigate directly the mix evolution in a convergent geometry, compressible plasma regime. The experiments comprise a plastic cylindrical shell imploded by direct laser irradiation. The cylindrical shell surrounds a lower density plastic foam which provides sufficient back pressure to allow the implosion to stagnate at a sufficiently high radius to permit quantitative radiographic diagnosis of the interface evolution near turnaround. The susceptibility to mix of the shell-foam interface is varied by choosing different density material for the inner shell surface (thus varying the Atwood number). This allows the study of shock-induced Richtmyer-Meshkov growth during the coasting phase, and Rayleigh-Taylor growth during the stagnation phase. The experimental results will be described along with calculational predictions using various radiation hydrodynamics codes and turbulent mix models.
Stage Cylindrical Immersive Display
NASA Technical Reports Server (NTRS)
Abramyan, Lucy; Norris, Jeffrey S.; Powell, Mark W.; Mittman, David S.; Shams, Khawaja S.
2011-01-01
Panoramic images with a wide field of view intend to provide a better understanding of an environment by placing objects of the environment on one seamless image. However, understanding the sizes and relative positions of the objects in a panorama is not intuitive and prone to errors because the field of view is unnatural to human perception. Scientists are often faced with the difficult task of interpreting the sizes and relative positions of objects in an environment when viewing an image of the environment on computer monitors or prints. A panorama can display an object that appears to be to the right of the viewer when it is, in fact, behind the viewer. This misinterpretation can be very costly, especially when the environment is remote and/or only accessible by unmanned vehicles. A 270 cylindrical display has been developed that surrounds the viewer with carefully calibrated panoramic imagery that correctly engages their natural kinesthetic senses and provides a more accurate awareness of the environment. The cylindrical immersive display offers a more natural window to the environment than a standard cubic CAVE (Cave Automatic Virtual Environment), and the geometry allows multiple collocated users to simultaneously view data and share important decision-making tasks. A CAVE is an immersive virtual reality environment that allows one or more users to absorb themselves in a virtual environment. A common CAVE setup is a room-sized cube where the cube sides act as projection planes. By nature, all cubic CAVEs face a problem with edge matching at edges and corners of the display. Modern immersive displays have found ways to minimize seams by creating very tight edges, and rely on the user to ignore the seam. One significant deficiency of flat-walled CAVEs is that the sense of orientation and perspective within the scene is broken across adjacent walls. On any single wall, parallel lines properly converge at their vanishing point as they should, and the sense of
The application of a curved, mixed-type shell element.
NASA Technical Reports Server (NTRS)
Visser, W.
1971-01-01
The variational condition given by Herrmann (1967) for finite element bending analyses of plates is extended to general thin shell problems. Emphasis is laid upon shell behavior and, in particular, on boundary layers and inextensional bending. A study of the boundary layer problem on a cylindrical shell compares the refined element and the Herrmann-Campbell (1968) element. Some numerical results on cross-tube and mitred-bend problems are given.
Shearfree cylindrical gravitational collapse
NASA Astrophysics Data System (ADS)
di Prisco, A.; Herrera, L.; MacCallum, M. A. H.; Santos, N. O.
2009-09-01
We consider diagonal cylindrically symmetric metrics, with an interior representing a general nonrotating fluid with anisotropic pressures. An exterior vacuum Einstein-Rosen spacetime is matched to this using Darmois matching conditions. We show that the matching conditions can be explicitly solved for the boundary values of metric components and their derivatives, either for the interior or exterior. Specializing to shearfree interiors, a static exterior can only be matched to a static interior, and the evolution in the nonstatic case is found to be given in general by an elliptic function of time. For a collapsing shearfree isotropic fluid, only a Robertson-Walker dust interior is possible, and we show that all such cases were included in Cocke’s discussion. For these metrics, Nolan and Nolan have shown that the matching breaks down before collapse is complete, and Tod and Mena have shown that the spacetime is not asymptotically flat in the sense of Berger, Chrusciel, and Moncrief. The issues about energy that then arise are revisited, and it is shown that the exterior is not in an intrinsic gravitational or superenergy radiative state at the boundary.
Shearfree cylindrical gravitational collapse
Di Prisco, A.; Herrera, L.; MacCallum, M. A. H.; Santos, N. O.
2009-09-15
We consider diagonal cylindrically symmetric metrics, with an interior representing a general nonrotating fluid with anisotropic pressures. An exterior vacuum Einstein-Rosen spacetime is matched to this using Darmois matching conditions. We show that the matching conditions can be explicitly solved for the boundary values of metric components and their derivatives, either for the interior or exterior. Specializing to shearfree interiors, a static exterior can only be matched to a static interior, and the evolution in the nonstatic case is found to be given in general by an elliptic function of time. For a collapsing shearfree isotropic fluid, only a Robertson-Walker dust interior is possible, and we show that all such cases were included in Cocke's discussion. For these metrics, Nolan and Nolan have shown that the matching breaks down before collapse is complete, and Tod and Mena have shown that the spacetime is not asymptotically flat in the sense of Berger, Chrusciel, and Moncrief. The issues about energy that then arise are revisited, and it is shown that the exterior is not in an intrinsic gravitational or superenergy radiative state at the boundary.
Cylindrically symmetric dust spacetime
NASA Astrophysics Data System (ADS)
Senovilla, José M. M.
2000-07-01
We present an explicit exact solution of Einstein's equations for an inhomogeneous dust universe with cylindrical symmetry. The spacetime is extremely simple but nonetheless it has surprising new features. The universe is `closed' in the sense that the dust expands from a big-bang singularity but recollapses to a big-crunch singularity. In fact, both singularities are connected so that the whole spacetime is `enclosed' within a single singularity of general character. The big-bang is not simultaneous for the dust, and in fact the age of the universe as measured by the dust particles depends on the spatial position, an effect due to the inhomogeneity, and their total lifetime has no non-zero lower limit. Part of the big-crunch singularity is naked. The metric depends on a parameter and contains flat spacetime as a non-singular particular case. For appropriate values of the parameter the spacetime is a small perturbation of Minkowski spacetime. This seems to indicate that flat spacetime may be unstable against some global non-vacuum perturbations.
Vibration of fluid loaded conical shells.
Caresta, Mauro; Kessissoglou, Nicole J
2008-10-01
An analytical model is presented to describe the vibration of a truncated conical shell with fluid loading in the low frequency range. The solution for the dynamic response of the shell is presented in the form of a power series. Fluid loading is taken into account by dividing the shell into narrow strips which are considered to be locally cylindrical. Analytical results are presented for different boundary conditions and have been compared with the computational results from a boundary element model. Limitations of the model to the low frequency range are discussed.
Thin shells joining local cosmic string geometries
NASA Astrophysics Data System (ADS)
Eiroa, Ernesto F.; Rubín de Celis, Emilio; Simeone, Claudio
2016-10-01
In this article we present a theoretical construction of spacetimes with a thin shell that joins two different local cosmic string geometries. We study two types of global manifolds, one representing spacetimes with a thin shell surrounding a cosmic string or an empty region with Minkowski metric, and the other corresponding to wormholes which are not symmetric across the throat located at the shell. We analyze the stability of the static configurations under perturbations preserving the cylindrical symmetry. For both types of geometries we find that the static configurations can be stable for suitable values of the parameters.
Structure-Property Relationships of Steel Cylindrical Shells
2012-03-01
hoop tensile specimens in the pipe’s transverse orienta- tion. The ERDC machine shop prepared the test specimens using a water - jet cutting system...polishing procedure. Abrasive Lubricant Time (min) Step 1 60-grit silicon carbide distilled water until plane Step 2 120-grit silicon carbide...using the procedure outlined in Table 1. Between each polishing step, sonication using distilled water cleaned the specimens. Table 1. Details of
Nearfield Acoustic Radiation from a Point-Excited Cylindrical Shell
1988-05-26
the interest and assistance of Dr. William Von Winkle, Dr. John Kingsbury, Dr. Charles Sherman, Dr. Ronald Radlinski, Larry Freeman, and George Carey is...Fortpflanzungsgesch-windigkeiten von Schwingungen in einem unbegrenzten isotropen kreiscylinder," Z. Math. 81, 324-26. Rayleigh , Lord (J. W. Strutt ) (1887). "On...waves propagating along the surface of an elastic solid," Proc. Math. Soc. London 17, 4. Rayleigh , Lord (J. W. Strutt ) (1945). The Theory of Sound, 2nd
Shape Optimization of Cylindrical Shell for Interior Noise
NASA Technical Reports Server (NTRS)
Robinson, Jay H.
1999-01-01
In this paper an analytic method is used to solve for the cross spectral density of the interior acoustic response of a cylinder with nonuniform thickness subjected to turbulent boundary layer excitation. The cylinder is of honeycomb core construction with the thickness of the core material expressed as a cosine series in the circumferential direction. The coefficients of this series are used as the design variable in the optimization study. The objective function is the space and frequency averaged acoustic response. Results confirm the presence of multiple local minima as previously reported and demonstrate the potential for modest noise reduction.
Electron diffraction from cylindrical nanotubes
Qin, L.C. )
1994-09-01
Electron diffraction intensities from cylindrical objects can be conveniently analyzed using Bessel functions. Analytic formulas and geometry of the diffraction patterns from cylindrical carbon nanotubes are presented in general forms in terms of structural parameters, such as the pitch angle and the radius of a tubule. As an example the Fraunhofer diffraction pattern from a graphitic tubule of structure [18,2] has been simulated to illustrate the characteristics of such diffraction patterns. The validity of the projection approximation is also discussed.
Optimization of Cylindrical Hall Thrusters
Yevgeny Raitses, Artem Smirnov, Erik Granstedt, and Nathaniel J. Fisch
2007-11-27
The cylindrical Hall thruster features high ionization efficiency, quiet operation, and ion acceleration in a large volume-to-surface ratio channel with performance comparable with the state-of-the-art annular Hall thrusters. These characteristics were demonstrated in low and medium power ranges. Optimization of miniaturized cylindrical thrusters led to performance improvements in the 50-200W input power range, including plume narrowing, increased thruster efficiency, reliable discharge initiation, and stable operation.
Optimization of Cylindrical Hall Thrusters
Yevgeny Raitses, Artem Smirnov, Erik Granstedt, and Nathaniel J. Fi
2007-07-24
The cylindrical Hall thruster features high ionization efficiency, quiet operation, and ion acceleration in a large volume-to-surface ratio channel with performance comparable with the state-of-the-art annular Hall thrusters. These characteristics were demonstrated in low and medium power ranges. Optimization of miniaturized cylindrical thrusters led to performance improvements in the 50-200W input power range, including plume narrowing, increased thruster efficiency, reliable discharge initiation, and stable operation. __________________________________________________
[Circular migration in Indonesia].
Mantra, I B
1979-12-01
The author examines circular migration in Indonesia, with primary focus on the 1970s. It is found that circular, or repeated return migration, generally occurs over short distances and for short periods and is more frequent than lifetime migration. The relationships between improvements in the national transport system, access to labor force opportunities in both the formal and informal sectors of the economy, and circular migration are discussed.
Cylindrical millimeter-wave imaging technique and applications
NASA Astrophysics Data System (ADS)
Sheen, David M.; McMakin, Douglas L.; Hall, Thomas E.
2006-05-01
The wideband microwave or millimeter-wave cylindrical imaging technique has been developed at Pacific Northwest National Laboratory (PNNL) for several applications including concealed weapon detection and automated body measurement for apparel fitting. This technique forms a fully-focused, diffraction-limited, three-dimensional image of the person or imaging target by scanning an inward-directed vertical array around the person or imaging target. The array is switched electronically to sequence across the array at high-speed, so that a full 360 degree mechanical scan over the cylindrical aperture can occur in 2-10 seconds. Wideband, coherent reflection data from each antenna position are recorded in a computer and subsequently reconstructed using an FFT-based image reconstruction algorithm developed at PNNL. The cylindrical scanning configuration is designed to optimize the illumination of the target and minimize non-returns due to specular reflection of the illumination away from the array. In this paper, simulated modeling data are used to explore imaging issues that affect the cylindrical imaging technique. Physical optics scattering simulations are used to model realistic returns from curved surfaces to determine the extent to which specular reflection affects the signal return and subsequent image reconstruction from these surfaces. This is a particularly important issue for the body measurement application. Also, an artifact in the imaging technique, referred to as "circular convolution aliasing" is discussed including methods to reduce or eliminate it. Numerous simulated and laboratory measured imaging results are presented.
Cylindrical Millemeter-Wave Imaging Technique and Applications
Sheen, David M.; McMakin, Douglas L.; Hall, Thomas E.
2006-08-01
The wideband microwave or millimeter-wave cylindrical imaging technique has been developed at Pacific Northwest National Laboratory (PNNL) for several applications including concealed weapon detection and automated body measurements for apparel fitting. This technique forms a fully-focused, diffraction-limited, three-dimensional image of the person or imaging target by scanning an inward-directed vertical array around the person or imaging target. The array is switched electronically to sequence across the array at high-speed, so that a full 360 degree mechanical scan over the cylindrical aperture can occur in 2-10 seconds. Wideband, coherent reflection data from each antenna position are recorded in a computer and subsequently reconstructed using an FFT-based image reconstruction algorithm developed at PNNL. The cylindrical scanning configuration is designed to optimize the illumination of the target and minimize non-returns due to specular reflection of the illumination away from the array. In this paper, simulated modeling data is used to explore imaging issues that affect the cylindrical imaging technique. Physical optics scattering simulations are used to model realistic returns from curved surfaces to determine the extent to which specular reflection affects the signal return and subsequent image reconstruction from these surfaces. This is a particularly important issue for the body measurement application. Also, an artifact in the imaging technique, referred to as "circular convolution aliasing" is discussed including methods to reduce or eliminate it. Numerous simulated and laboratory measured imaging results are presented.
NASA Astrophysics Data System (ADS)
Raybould, T. A.; Fedotov, V. A.; Papasimakis, N.; Kuprov, I.; Youngs, I. J.; Chen, W. T.; Tsai, D. P.; Zheludev, N. I.
2016-07-01
We demonstrate that the induced toroidal dipole, represented by currents flowing on the surface of a torus, makes a distinct and indispensable contribution to circular dichroism. We show that toroidal circular dichroism supplements the well-known mechanism involving electric dipole and magnetic dipole transitions. We illustrate this with rigorous analysis of the experimentally measured polarization-sensitive transmission spectra of an artificial metamaterial, constructed from elements of toroidal symmetry. We argue that toroidal circular dichroism will be found in large biomolecules with elements of toroidal symmetry and should be taken into account in the interpretation of circular dichroism spectra of organics.
Kim, Joshua; Ionascu, Dan; Zhang, Tiezhi
2013-01-01
Purpose: To accelerate iterative algebraic reconstruction algorithms using a cylindrical image grid. Methods: Tetrahedron beam computed tomography (TBCT) is designed to overcome the scatter and detector problems of cone beam computed tomography (CBCT). Iterative algebraic reconstruction algorithms have been shown to mitigate approximate reconstruction artifacts that appear at large cone angles, but clinical implementation is limited by their high computational cost. In this study, a cylindrical voxelization method on a cylindrical grid is developed in order to take advantage of the symmetries of the cylindrical geometry. The cylindrical geometry is a natural fit for the circular scanning trajectory employed in volumetric CT methods such as CBCT and TBCT. This method was implemented in combination with the simultaneous algebraic reconstruction technique (SART). Both two- and three-dimensional numerical phantoms as well as a patient CT image were utilized to generate the projection sets used for reconstruction. The reconstructed images were compared to the original phantoms using a set of three figures of merit (FOM). Results: The cylindrical voxelization on a cylindrical reconstruction grid was successfully implemented in combination with the SART reconstruction algorithm. The FOM results showed that the cylindrical reconstructions were able to maintain the accuracy of the Cartesian reconstructions. In three dimensions, the cylindrical method provided better accuracy than the Cartesian methods. At the same time, the cylindrical method was able to provide a speedup factor of approximately 40 while also reducing the system matrix storage size by 2 orders of magnitude. Conclusions: TBCT image reconstruction using a cylindrical image grid was able to provide a significant improvement in the reconstruction time and a more compact system matrix for storage on the hard drive and in memory while maintaining the image quality provided by the Cartesian voxelization on a
Inflation of stressed cylindrical tubes: an experimental study
NASA Astrophysics Data System (ADS)
Guo, Zhiming; Wang, Shibin; Li, Linan; Ji, Hongwei; Wang, Zhiyong; Cai, Songbao
2014-06-01
The inflation of an initially stressed cylindrical shell provides a good illustration of the phenomenon of the initiation and propagation of an instability, which shares the same mathematical and mechanical features with a variety of other strain localization phenomena in engineering structures and materials. The high speed CCD camera and digital image processing system were used to measure the 3D shape of the inflated cylindrical tube. The localized bulge of a cylindrical tube with closed ends forms when the internal pressure reaches a critical value Pcr. As more air is filled into the tube, the pressure drops but the radius at the centre of the bulge will increase until it reaches a maximum value rmax. With continued inflation, the pressure stays at a constant value Pp. The purpose of this study is to investigate the critical and propagation pressures in the tubes and the profile outside when the shells under axial tension and internal pressure were inflating. We focus on the influence of the axial tension on the critical pressure. In this paper the problem is explored through experimental efforts. A series of experiments were conducted on commercially available natural rubber latex tubes involving different geometries and initial axial tensions, which were regarded as isotropic, homogeneous, incompressible and hyper-elastic materials.
Precise DOA Estimation Using SAGE Algorithm with a Cylindrical Array
NASA Astrophysics Data System (ADS)
Takanashi, Masaki; Nishimura, Toshihiko; Ogawa, Yasutaka; Ohgane, Takeo
A uniform circular array (UCA) is a well-known array configuration which can accomplish estimation of 360° field of view with identical accuracy. However, a UCA cannot estimate coherent signals because we cannot apply the SSP owing to the structure of UCA. Although a variety of studies on UCA in coherent multipath environments have been done, it is impossible to estimate the DOA of coherent signals with different incident polar angles. Then, we have proposed Root-MUSIC algorithm with a cylindrical array. However, the estimation performance is degraded when incident signals arrive with close polar angles. To solve this problem, in the letter, we propose to use SAGE algorithm with a cylindrical array. Here, we adopt a CLA Root-MUSIC for the initial estimation and decompose two-dimensional search to double one-dimensional search to reduce the calculation load. The results show that the proposal achieves high resolution with low complexity.
Generalized offset surfaces of cylindrical surfaces
NASA Astrophysics Data System (ADS)
Georgiev, Georgi Hristov
2016-12-01
Cylindrical surfaces play an important role in geometric modeling and architecture. In this paper, we describe a way for constructing a new cylindrical surface from a given cylindrical surface. Our approach is based on the differential geometry of cylindrical surfaces and a generalization of the notion of offset surface. We examine the case of a similarity offset of an arbitrary cylindrical surface which is closely related to direct similarities of Euclidean 3-space. Some illustrative examples are included.
X-ray Spectroscopy of Directly Driven Cylindrical Implosions
NASA Astrophysics Data System (ADS)
Haynes, D.; Hooper, C.; Delamater, N.; Barnes, C.; Oertel, J.; Pollak, G.; Tubbs, D.; Watt, R.; Boehly, T.; Bradley, D.; Jaanimagi, P.; Knauer, J.
1998-11-01
X-ray spectra from a chlorinated polystyrene marker layer in a series of directly driven cylindrical implosions are presented and analyzed. The 4μm thick, 500μm long C_8H_6Cl2 (1.42g/cc) annular spectroscopic tracer layer is centrally located on the interior surface of the 20μm thick, 2250μm long polystyrene (1.044g/cc) 860μ m inner diameter cylindrical shell. The shell is filled with polystyrene foam (60mg/cc).(Barnes, C. W., et al.) 1998, to be published in Rev. Sci. Instrum., Tubbs, D. L., et al. 1998, to be published in Lasers and Particle Beams The implosions are driven by 50 beams of the OMEGA Laser facility. The temperature and density sensitive K-shell Cl spectra are recorded by a time-resolved spectrograph, and compared to calculated spectra in order to infer the evolution of electron temperature and density in the marker layer.(This work was performed under the auspices of the U. S. Department of Energy by the Los Alamos National Laboratory under contract No. W-7405-Eng-36)
2. Northwest circular bastion, seen from edge of southwest circular ...
2. Northwest circular bastion, seen from edge of southwest circular bastion wall. Metal roof beams extend up to form peak. World War II gun installation at right. - Fort Hamilton, Northwest Circular Bastion, Rose Island, Newport, Newport County, RI
Stability analysis of thin-shell wormholes from charged black string
Sharif, M.; Azam, M. E-mail: azammath@gmail.com
2013-04-01
In this paper, we construct thin-shell wormholes from charged black string through cut and paste procedure and investigate its stability. We assume modified generalized Chaplygin gas as a dark energy fluid (exotic matter) present in the thin layer of matter-shell. The stability of these constructed thin-shell wormholes is investigated in the scenario of linear perturbations. We conclude that static stable as well as unstable configurations are possible for cylindrical thin-shell wormholes.
Cylindrical acoustic levitator/concentrator
Kaduchak, Gregory; Sinha, Dipen N.
2002-01-01
A low-power, inexpensive acoustic apparatus for levitation and/or concentration of aerosols and small liquid/solid samples having particulates up to several millimeters in diameter in air or other fluids is described. It is constructed from a commercially available, hollow cylindrical piezoelectric crystal which has been modified to tune the resonance frequency of the breathing mode resonance of the crystal to that of the interior cavity of the cylinder. When the resonance frequency of the interior cylindrical cavity is matched to the breathing mode resonance of the cylindrical piezoelectric transducer, the acoustic efficiency for establishing a standing wave pattern in the cavity is high. The cylinder does not require accurate alignment of a resonant cavity. Water droplets having diameters greater than 1 mm have been levitated against the force of gravity using; less than 1 W of input electrical power. Concentration of aerosol particles in air is also demonstrated.
NASA Astrophysics Data System (ADS)
Marston, Philip L.; Daniel, Timothy D.; Abawi, Ahmad T.; Kirsteins, Ivars
2015-11-01
The modulated radiation pressure (MRP) of ultrasound has been used for decades to selectively excite low frequency modes associated with surface tension of fluid objects in water. Much less is known about the excitation of low frequency modes of less compliant metallic objects. Here we use MRP of focused ultrasound to excite resonant flexural vibrations of a circular metal plate in water. The source transducer was driven with a double-sideband suppressed carrier voltage as in. The response of the target (detected with a hydrophone) was at twice the modulation frequency and proportional to the square of the drive voltage. Since the radiation pressure of focused beams is spatially localized, mode shapes could be identified by scanning the source along the target while measuring the target's response. Additional measurements were done with an open-ended water-filled copper circular cylindrical shell in which resonant frequencies and mode shapes were also identified. These experiments show how focused ultrasound can be used to identify low-frequency modes of elastic objects without direct contact. Supported by ONR.
Circularly polarized Hankel vortices.
Kotlyar, Victor V; Kovalev, Alexey A
2017-04-03
We discuss vector Hankel beams with circular polarization. These beams appear as a generalization of a spherical wave with an embedded optical vortex with topological charge n. Explicit analytical relations to describe all six projections of the E- and H-field are derived. The relations are shown to satisfy Maxwell's equations. Hankel beams with clockwise and anticlockwise circular polarization are shown to have peculiar features while propagating in free space. Relations for the Poynting vector projections and the angular momentum in the far field are also obtained. It is shown that a Hankel beam with clockwise circular polarization has radial divergence (ratio between the radial and longitudinal projections of the Poynting vector) similar to that of the spherical wave, while the beam with the anticlockwise circular polarization has greater radial dependence. At n = 0, the circularly polarized Hankel beam has non-zero spin angular momentum. At n = 1, power flow of the Hankel beam with anticlockwise polarization consists of two parts: right-handed helical flow near the optical axis and left-handed helical flow in periphery. At n ≥2, power flow is directed along the right-handed helix regardless of the direction of the circular polarization. Power flow along the optical axis is the same for the Hankel beams of both circular polarizations, if they have the same topological charge.
Telescoping cylindrical piezoelectric fiber composite actuator assemblies
NASA Technical Reports Server (NTRS)
Allison, Sidney G. (Inventor); Shams, Qamar A. (Inventor); Fox, Robert L. (Inventor); Fox, legal representative, Christopher L. (Inventor); Fox Chattin, legal representative, Melanie L. (Inventor)
2010-01-01
A telescoping actuator assembly includes a plurality of cylindrical actuators in a concentric arrangement. Each cylindrical actuator is at least one piezoelectric fiber composite actuator having a plurality of piezoelectric fibers extending parallel to one another and to the concentric arrangement's longitudinal axis. Each cylindrical actuator is coupled to concentrically-adjacent ones of the cylindrical actuators such that the plurality of cylindrical actuators can experience telescopic movement. An electrical energy source coupled to the cylindrical actuators applies actuation energy thereto to generate the telescopic movement.
Sound Scattering from Submerged Elastic Objects and Shells of General Shape
1993-01-01
carried out using the NOARL T - matrix code [4], another numerical approach is utilized in our analysis of scattering experiments from finite-cylindrical...and also broadside) acoustic resonance scattering from submerged finite-length cylindrical shells and spheroids has been analyzed by a T - matrix code , by
Mikkelsen, Paula M
2002-01-01
In his contributions to the monographic series "Manual of Conchology", Henry Pilsbry reviewed the subgroup Tectibranchiata, comprising those opisthobranch snails that (at least primitively) still possess a shell (Pilsbry, 1894-1896). Exemplified by the Cephalaspidea (bubble shells), others included in this group at Pilsbry's time and since were Anaspidea (sea hares) and the shelled members of Notaspidea (side-gilled slugs) and Sacoglossa (leaf slugs). Pilsbry (and others since his time) considered tectibranchs to be the "root stock" from which more advanced gastropods such as Nudibranchia and Pulmonata were derived. Tectibranch systematics is firmly based on conchology and most species were originally described from empty shells. However, soft-anatomical characters were acknowledged quite early on as equally important in tectibranchs, due to the reduction of their shells and their evolutionary proximity to unshelled gastropods. Today, Tectibranchiata is not recognized as a natural taxon although the word "tectibranch" (like "prosobranch" and "mesogastropod") continues in vernacular use. Shelled opisthobranchs have been redistributed among various taxa, including several new ones--the unresolved basal opisthobranchs (Architectibranchia) and the "lower Heterobranchia", an enigmatic and currently much-studied group of families considered basal to all of Euthyneura (Opisthobranchia and landsnails (Pulmonata)). Despite their polyphyletic status, shelled opisthobranchs remain important subjects in evolutionary studies of gastropods--as the most basal members of nearly every opisthobranch clade and as organisms with mosaic combinations of primitive and derived features within evolutionary "trends" (e.g., loss of the shell, detorsion, concentration of the nervous system, ecological specialization, etc.). Although they play a pivotal role, the shelled opisthobranchs have received minimal attention in more comprehensive gastropod studies, often relegated to token
ERIC Educational Resources Information Center
Gordon, Russell
2008-01-01
Consider a circular segment (the smaller portion of a circle cut off by one of its chords) with chord length c and height h (the greatest distance from a point on the arc of the circle to the chord). Is there a simple formula involving c and h that can be used to closely approximate the area of this circular segment? Ancient Chinese and Egyptian…
ERIC Educational Resources Information Center
Gordon, Russell
2008-01-01
Consider a circular segment (the smaller portion of a circle cut off by one of its chords) with chord length c and height h (the greatest distance from a point on the arc of the circle to the chord). Is there a simple formula involving c and h that can be used to closely approximate the area of this circular segment? Ancient Chinese and Egyptian…
Blast waves from cylindrical charges
NASA Astrophysics Data System (ADS)
Knock, C.; Davies, N.
2013-07-01
Comparisons of explosives are often carried out using TNT equivalency which is based on data for spherical charges, despite the fact that many explosive charges are not spherical in shape, but cylindrical. Previous work has shown that it is possible to predict the over pressure and impulse from the curved surface of cylindrical charges using simple empirical formulae for the case when the length-to-diameter ( L/ D) ratio is greater or equal to 2/1. In this paper, by examining data for all length-to-diameter ratios, it is shown that it is possible to predict the peak over pressure, P, for any length-to-diameter ratio from the curved side of a bare cylindrical charge of explosive using the equation P=K_PM(L/D)^{1/3}/R^3, where M is the mass of explosive, R the distance from the charge and K_P is an explosive-dependent constant. Further out where the cylindrical blast wave `heals' into a spherical one, the more complex equation P=C_1(Z^' ' })^{-3}+C_2(Z^' ' })^{-2}+C_3(Z^' ' })^{-1} gives a better fit to experimental data, where Z^' ' } = M^{1/3}(L/D)^{1/9}/D and C_1, C_2 and C_3 are explosive-dependent constants. The impulse is found to be independent of the L/ D ratio.
Optics Demonstrations Using Cylindrical Lenses
ERIC Educational Resources Information Center
Ivanov, Dragia; Nikolov, Stefan
2015-01-01
In this paper we consider the main properties of cylindrical lenses and propose several demonstrational experiments that can be performed with them. Specifically we use simple glasses full of water to demonstrate some basic geometrical optics principles and phenomena. We also present some less standard experiments that can be performed with such…
Optics Demonstrations Using Cylindrical Lenses
ERIC Educational Resources Information Center
Ivanov, Dragia; Nikolov, Stefan
2015-01-01
In this paper we consider the main properties of cylindrical lenses and propose several demonstrational experiments that can be performed with them. Specifically we use simple glasses full of water to demonstrate some basic geometrical optics principles and phenomena. We also present some less standard experiments that can be performed with such…
Vibrations of moderately thick shallow spherical shells at large amplitudes
NASA Astrophysics Data System (ADS)
Sathyamoorthy, M.
1994-04-01
A shallow shell theory is presented for the geometrically nonlinear analysis of moderately thick isotropic spherical shells. Effects of transverse shear deformation and rotatory inertia are included in the governing equations of motion by means of tracing constants. When these effects are ignored, the governing equations readily reduce to those applicable for thin shallow spherical shells. Solutions to the system of thick shell equations are obtained by means of Galerkin's method and the numerical Runge-Kutta procedure. Numerical results are presented for certain cases of shallow spherical shells considering different geometric shell parameters. Transverse shear and rotatory inertia effects are found to be important in linear as well as nonlinear responses of shallow spherical shells. The nonlinear frequency-amplitude behavior is of the softening type for shallow spherical shells and of the hardening type for circular plates. Frequency ratios are lower at any given amplitude when the effects of transverse shear and rotatory inertia are included in the analysis.
RAGE Simulations of Indirectly Driven Cylindrical Implosions
NASA Astrophysics Data System (ADS)
Scott, John; Beck, J. Bradley
2000-10-01
New physics simulation codes are being developed at Los Alamos National Laboratory as part of ASCI (Accelerated Strategic Computing Initiative). Importance is being placed upon validation of these computational codes with relevant inertial confinement fusion experiments. One of these codes, RAGE [Baltrusaitis, R.M., et al, Phys. Fluids 8, 2471 (1996)], an Eulerian based hydrodynamics code, utilizes adaptive mesh refinement (AMR) to resolve regions of physical interest in the computational domain. A recent addition to RAGE is a multi-group radiation-diffusion transport package. We performed simulations of indirectly-driven cylindrical implosion experiments measuring the effects of the ablative Rayleigh-Taylor and Bell-Plesset instabilities in a convergent geometry [W. W. Hsing and N. M. Hoffman, Phys. Rev. Lett., 78, 3876 (1997)]. In these experiments, the radiation drive contained a distinct M-shell component from the gold hohlraum that preheats the imploding cylinder, a difficult to simulate effect without multi-group radiation transport. Preheat places the target implosion on a higher adiabat reducing convergence and perturbation growth due to the Bell-Plesset effect. We compare the implosion trajectories and perturbation growth from the RAGE code to the experimental data. This work was performed under the auspices of the U. S. Department of Energy by the Los Alamos National Laboratory under contract No. W-7405-Eng-36.
Direct observation of transverse and vortex metastable magnetic domains in cylindrical nanowires
NASA Astrophysics Data System (ADS)
Bran, C.; Fernandez-Roldan, J. A.; Palmero, E. M.; Berganza, E.; Guzman, J.; del Real, R. P.; Asenjo, A.; Fraile Rodríguez, A.; Foerster, M.; Aballe, L.; Chubykalo-Fesenko, O.; Vazquez, M.
2017-09-01
We present experimental evidence of transverse magnetic domains, previously observed only in nanostrips, in CoNi cylindrical nanowires with designed crystal symmetry and tailored magnetic anisotropy. The transverse domains are found together with more conventional vortex domains along the same cylindrical nanowire, denoting a bistable system with similar energies. The surface and the inner magnetization distribution in both types of domains are analyzed by photoemission electron microscopy with x-ray magnetic circular dichroism contrast, and hysteresis loop in individual nanowires are measured by magneto-optical Kerr effect. These experimental data are understood and compared with complementary micromagnetic simulations.
NASA Technical Reports Server (NTRS)
Walowit, Jed A.
1994-01-01
A viewgraph presentation is made showing the capabilities of the computer code SPIRALI. Overall capabilities of SPIRALI include: computes rotor dynamic coefficients, flow, and power loss for cylindrical and face seals; treats turbulent, laminar, Couette, and Poiseuille dominated flows; fluid inertia effects are included; rotor dynamic coefficients in three (face) or four (cylindrical) degrees of freedom; includes effects of spiral grooves; user definable transverse film geometry including circular steps and grooves; independent user definable friction factor models for rotor and stator; and user definable loss coefficients for sudden expansions and contractions.
Circular dichroism in photoelectron images from aligned nitric oxide molecules
Sen, Ananya; Pratt, S. T.; Reid, K. L.
2017-05-03
We have used velocity map photoelectron imaging to study circular dichroism of the photoelectron angular distributions (PADs) of nitric oxide following two-color resonanceenhanced two-photon ionization via selected rotational levels of the A 2Σ+, v' = 0 state. By using a circularly polarized pump beam and a counter-propagating, circularly polarized probe beam, cylindrical symmetry is preserved in the ionization process, and the images can be reconstructed using standard algorithms. The VMI set up enables individual ion rotational states to be resolved with excellent collection efficiency, rendering the measurements considerably simpler to perform than previous measurements conducted with a conventional photoelectron spectrometer.more » The results demonstrate that circular dichroism is observed even when cylindrical symmetry is maintained, and serve as a reminder that dichroism is a general feature of the multiphoton ionization of atoms and molecules. Furthermore, the observed PADs are in good agreement with calculations based on parameters extracted from previous experimental results obtained by using a time-offlight electron spectrometer.« less
Circular dichroism in photoelectron images from aligned nitric oxide molecules.
Sen, Ananya; Pratt, S T; Reid, K L
2017-07-07
We have used velocity map photoelectron imaging to study circular dichroism of the photoelectron angular distributions (PADs) of nitric oxide following two-color resonance-enhanced two-photon ionization via selected rotational levels of the A (2)Σ(+), v(')=0 state. By using a circularly polarized pump beam and a counter-propagating, circularly polarized probe beam, cylindrical symmetry is preserved in the ionization process, and the images can be reconstructed using standard algorithms. The velocity map imaging set up enables individual ion rotational states to be resolved with excellent collection efficiency, rendering the measurements considerably simpler to perform than previous measurements conducted with a conventional photoelectron spectrometer. The results demonstrate that circular dichroism is observed even when cylindrical symmetry is maintained, and serve as a reminder that dichroism is a general feature of the multiphoton ionization of atoms and molecules. The observed PADs are in good agreement with calculations based on parameters extracted from previous experimental results obtained by using a time-of-flight electron spectrometer.
Circular dichroism in photoelectron images from aligned nitric oxide molecules
NASA Astrophysics Data System (ADS)
Sen, Ananya; Pratt, S. T.; Reid, K. L.
2017-07-01
We have used velocity map photoelectron imaging to study circular dichroism of the photoelectron angular distributions (PADs) of nitric oxide following two-color resonance-enhanced two-photon ionization via selected rotational levels of the A 2Σ+, v'=0 state. By using a circularly polarized pump beam and a counter-propagating, circularly polarized probe beam, cylindrical symmetry is preserved in the ionization process, and the images can be reconstructed using standard algorithms. The velocity map imaging set up enables individual ion rotational states to be resolved with excellent collection efficiency, rendering the measurements considerably simpler to perform than previous measurements conducted with a conventional photoelectron spectrometer. The results demonstrate that circular dichroism is observed even when cylindrical symmetry is maintained, and serve as a reminder that dichroism is a general feature of the multiphoton ionization of atoms and molecules. The observed PADs are in good agreement with calculations based on parameters extracted from previous experimental results obtained by using a time-of-flight electron spectrometer.
Fernández-Durán, J J
2007-06-01
Johnson and Wehrly (1978, Journal of the American Statistical Association 73, 602-606) and Wehrly and Johnson (1980, Biometrika 67, 255-256) show one way to construct the joint distribution of a circular and a linear random variable, or the joint distribution of a pair of circular random variables from their marginal distributions and the density of a circular random variable, which in this article is referred to as joining circular density. To construct flexible models, it is necessary that the joining circular density be able to present multimodality and/or skewness in order to model different dependence patterns. Fernández-Durán (2004, Biometrics 60, 499-503) constructed circular distributions based on nonnegative trigonometric sums that can present multimodality and/or skewness. Furthermore, they can be conveniently used as a model for circular-linear or circular-circular joint distributions. In the current work, joint distributions for circular-linear and circular-circular data constructed from circular distributions based on nonnegative trigonometric sums are presented and applied to two data sets, one for circular-linear data related to the air pollution patterns in Mexico City and the other for circular-circular data related to the pair of dihedral angles between consecutive amino acids in a protein.
On the elastic stability of shells
NASA Technical Reports Server (NTRS)
Horton, W. H.
1976-01-01
A synopsis of a series of investigations into the instability of axially compressed cylindrical shells is given. The objective of the research, which was made with models, was to devise a technique of nondestructive evaluation. The results show that, with models at any rate, success was achieved. Probing methods which can be used to determine the locations of weakness and the pertinent instability load levels were devised. The research on large scale shells was undertaken to determine the critical loads under as uniform a circumferential distribution of axial compressive force as possible. It is clear from the results presented that this objective was met.
Brau, Charles A.; Kurnit, Norman A.; Cooper, Richard K.
1984-01-01
A high efficiency, free electron laser utilizing a circular relativistic electron beam accelerator and a circular whispering mode optical waveguide for guiding optical energy in a circular path in the circular relativistic electron beam accelerator such that the circular relativistic electron beam and the optical energy are spatially contiguous in a resonant condition for free electron laser operation. Both a betatron and synchrotron are disclosed for use in the present invention. A free electron laser wiggler is disposed around the circular relativistic electron beam accelerator for generating a periodic magnetic field to transform energy from the circular relativistic electron beam to optical energy.
Compact waveguide circular polarizer
Tantawi, Sami G.
2016-08-16
A multi-port waveguide is provided having a rectangular waveguide that includes a Y-shape structure with first top arm having a first rectangular waveguide port, a second top arm with second rectangular waveguide port, and a base arm with a third rectangular waveguide port for supporting a TE.sub.10 mode and a TE.sub.20 mode, where the end of the third rectangular waveguide port includes rounded edges that are parallel to a z-axis of the waveguide, a circular waveguide having a circular waveguide port for supporting a left hand and a right hand circular polarization TE.sub.11 mode and is coupled to a base arm broad wall, and a matching feature disposed on the base arm broad wall opposite of the circular waveguide for terminating the third rectangular waveguide port, where the first rectangular waveguide port, the second rectangular waveguide port and the circular waveguide port are capable of supporting 4-modes of operation.
Implosion of Cylindrical Cavities via Short Duration Impulsive Loading
NASA Astrophysics Data System (ADS)
Huneault, Justin; Higgins, Andrew
2014-11-01
An apparatus has been developed to study the collapse of a cylindrical cavity in gelatin subjected to a symmetric impact-driven impulsive loading. A gas-driven annular projectile is accelerated to approximately 50 m/s, at which point it impacts a gelatin casting confined by curved steel surfaces that allow a transition from an annular geometry to a cylindrically imploding motion. The implosion is visualized by a high-speed camera through a window which forms the top confining wall of the implosion cavity. The initial size of the cavity is such that the gelatin wall is two to five times thicker than the impacting projectile. Thus, during impact the compression wave which travels towards the cavity is closely followed by a rarefaction resulting from the free surface reflection of the compression wave in the projectile. As the compression wave in the gelatin reaches the inner surface, it will also reflect as a rarefaction wave. The interaction between the rarefaction waves from the gelatin and projectile free surfaces leads to large tensile stresses resulting in the spallation of a relatively thin shell. The study focuses on the effect of impact parameters on the thickness and uniformity of the imploding shell formed by the cavitation in the imploding gelatin cylinder.
Improved cylindrical mirror energy analyzer
NASA Astrophysics Data System (ADS)
Baranova, L. A.
2017-03-01
A study has been carried out of the electron-optical properties of improved design of the cylindrical mirror energy analyzer. Both external and internal electrodes of the analyzer are divided into three isolated parts, whereby the potentials on the individual parts can be regulated independently from each other. In symmetric operating mode at identical potentials on the side parts of the electrodes, a significant increase has been obtained in resolving power and light-gathering power of the analyzer compared to the standard design of the cylindrical mirror. In asymmetric operating mode, which is implemented in a linear potential distribution on the external electrode, the conditions have been found under which the linear dispersion of the analyzer increases several times.
76 FR 62148 - Title VI; Proposed Circular, Environmental Justice; Proposed Circular
Federal Register 2010, 2011, 2012, 2013, 2014
2011-10-06
... Federal Transit Administration Title VI; Proposed Circular, Environmental Justice; Proposed Circular...; Proposed Circular'' and ``Environmental Justice; Proposed Circular.'' FOR FURTHER INFORMATION CONTACT: For... Circular'' (76 FR 60593) and ``Environmental Justice; Proposed Circular'' (76 FR 60590). Corrections The...
Bremsstrahlung from cylindrical beta sources.
NASA Technical Reports Server (NTRS)
Harris, D. W.; Silverman, J.
1972-01-01
Refined experimental measurements of the bremsstrahlung number and energy fluxes from thick cylindrical sources of several nuclides are presented, dose rates calculated from experimental energy fluxes are compared with theoretical results based on Wyard's thick-target approximation, and experiments are correlated with both thick- and thin-target bremsstrahlung theory to obtain accurate values of bremsstrahlung yields. The data presented should prove useful for the design of radioisotope power supplies, particularly those used in spacecraft and in biological applications.
Solutions of the cylindrical nonlinear Maxwell equations.
Xiong, Hao; Si, Liu-Gang; Ding, Chunling; Lü, Xin-You; Yang, Xiaoxue; Wu, Ying
2012-01-01
Cylindrical nonlinear optics is a burgeoning research area which describes cylindrical electromagnetic wave propagation in nonlinear media. Finding new exact solutions for different types of nonlinearity and inhomogeneity to describe cylindrical electromagnetic wave propagation is of great interest and meaningful for theory and application. This paper gives exact solutions for the cylindrical nonlinear Maxwell equations and presents an interesting connection between the exact solutions for different cylindrical nonlinear Maxwell equations. We also provide some examples and discussion to show the application of the results we obtained. Our results provide the basis for solving complex systems of nonlinearity and inhomogeneity with simple systems.
ERIC Educational Resources Information Center
Atkinson, Bill
1982-01-01
The author critiques the program design and educational aspects of the Shell Games, a program developed by Apple Computer, Inc., which can be used by the teacher to design objective tests for adaptation to specific assessment needs. (For related articles, see EC 142 959-962.) (Author)
ERIC Educational Resources Information Center
Atkinson, Bill
1982-01-01
The author critiques the program design and educational aspects of the Shell Games, a program developed by Apple Computer, Inc., which can be used by the teacher to design objective tests for adaptation to specific assessment needs. (For related articles, see EC 142 959-962.) (Author)
Gao, Nan; Zhang, Yuchao; Xie, Changqing
2011-11-01
We introduce circular Fibonacci gratings (CFGs) that combine the concept of circular gratings and Fibonacci structures. Theoretical analysis shows that the diffraction pattern of CFGs is composed of fractal distributions of impulse rings. Numerical simulations are performed with two-dimensional fast Fourier transform to reveal the fractal behavior of the diffraction rings. Experimental results are also presented and agree well with the numerical results. The fractal nature of the diffraction field should be of great theoretical interest, and shows potential to be further developed into practical applications, such as in laser measurement with wideband illumination.
NASA Technical Reports Server (NTRS)
Nielsen, Jack N
1955-01-01
A theoretical method is presented for calculating the flow field about wing-body combinations employing bodies deviating only slightly in shape from a circular cylinder. The method is applied to the calculation of the pressure field acting between a circular cylindrical body and a rectangular wing. The case of zero body angle of attack and variable wing incidence is considered as well as the case of zero wing incidence and variable body angle of attack. An experiment was performed especially for the purpose of checking the calculative examples.
Acoustic radiation from a shell with internal structures
NASA Technical Reports Server (NTRS)
El-Raheb, M.; Wagner, P.
1989-01-01
A method is developed to compute frequency response and acoustic radiation of a complex shell. The axisymmetric geometry of the shell includes cylindrical, conical, and spherical segments stiffened by discrete rings and bulkheads. The shell is coupled to internal masses and elastic frames. Shell segments are treated by transfer matrices. Rings, bulkheads, frames, and concentrated masses are treated by impedances at junctions of segments. The shell is coupled to an external acoustic fluid treated by Green's function and curved surface elements. A major issue facing the method's treatment of the fluid would be lack of existence or uniqueness encountered in the uncoupled, external acoustic problem at characteristic wavenumbers. By using a simple spherical shell, without internal structures, this potential hindrance is shown not to arise. A fuller application of the method awaits subsequent results.
Shell Buckling Design Criteria Based on Manufacturing Imperfection Signatures
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Nemeth, Michael P.; Starnes, James H., Jr.
2004-01-01
An analysis-based approach .for developing shell-buckling design criteria for laminated-composite cylindrical shells that accurately accounts for the effects of initial geometric imperfections is presented. With this approach, measured initial geometric imperfection data from six graphite-epoxy shells are used to determine a manufacturing-process-specific imperfection signature for these shells. This imperfection signature is then used as input into nonlinear finite-element analyses. The imperfection signature represents a "first-approximation" mean imperfection shape that is suitable for developing preliminary-design data. Comparisons of test data and analytical results obtained by using several different imperfection shapes are presented for selected shells. Overall, the results indicate that the analysis-based approach presented for developing reliable preliminary-design criteria has the potential to provide improved, less conservative buckling-load estimates, and to reduce the weight and cost of developing buckling-resistant shell structures.
Cracked shells under skew-symmetric loading. [Reissner theory
NASA Technical Reports Server (NTRS)
Delale, F.
1981-01-01
The general problem of a shell containing a through crack in one of the principal planes of curvature and under general skew-symmetric loading is considered. By employing a Reissner type shell theory which takes into account the effect of transverse shear strains, all boundary conditions on the crack surfaces are satisfied separately. Consequently, unlike those obtained from the classical shell theory, the angular distributions of the stress components around the crack tips are shown to be identical to the distributions obtained from the plane and anti-plane elasticity solutions. Results are given for axially and circumferentially cracked cylindrical shells, spherical shells, and toroidal shells under uniform in-plane shearing, out of plane shearing, and torsion. The problem is formulated for specially orthostropic materials, therefore, the effect of orthotropy on the results is also studied.
Acoustic radiation from a shell with internal structures
NASA Technical Reports Server (NTRS)
El-Raheb, M.; Wagner, P.
1989-01-01
A method is developed to compute frequency response and acoustic radiation of a complex shell. The axisymmetric geometry of the shell includes cylindrical, conical, and spherical segments stiffened by discrete rings and bulkheads. The shell is coupled to internal masses and elastic frames. Shell segments are treated by transfer matrices. Rings, bulkheads, frames, and concentrated masses are treated by impedances at junctions of segments. The shell is coupled to an external acoustic fluid treated by Green's function and curved surface elements. A major issue facing the method's treatment of the fluid would be lack of existence or uniqueness encountered in the uncoupled, external acoustic problem at characteristic wavenumbers. By using a simple spherical shell, without internal structures, this potential hindrance is shown not to arise. A fuller application of the method awaits subsequent results.