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.
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.
Load Tests on a Stiffened Circular Cylindrical Shell
NASA Technical Reports Server (NTRS)
Schapitz, E; Krumling, G
1938-01-01
The present report describes tests in which the stress distribution may be determined in a stiffened circular cylindrical shell loaded longitudinally at four symmetrically situated points. As being of particular importance are the cases investigated of groups of bending and arching or convexing forces, respectively. From the stress measurements on the longitudinal stiffeners, the shear stresses and the bulkhead ring stresses in the skin could be evaluated. These measurements showed that the "simple shear field" used in theoretical computations in which all normal stresses in the skin are neglected, must be extended by the addition of the transverse or circumferential stresses if the bulkhead rings are not riveted to the skin.
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.
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
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.
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.
A parametric study on inelastic buckling in steel cylindrical shells with circular cutouts
NASA Astrophysics Data System (ADS)
Miladi, S.; Razzaghi, M. S.
2014-03-01
Thin-walled cylindrical shells are important components of many industrial complexes. Most of these components have circular cutouts in manholes and pipe-to-shell junctions. Performance of cylindrical shells due to the extreme loading conditions shows that buckling is the major failure mode in such components. This study aims to indicate the effect of circular cutouts on buckling capacity of cylindrical shells due to pure axial compression. To this end, cylindrical shells of different geometric specifications and various arrangements and sizes of cutouts were considered. Numerical nonlinear analyses were conducted using ANSYS software. Result of this study revealed that cutouts can play a noticeable role in creating stress concentration and affect destructively the stability of structures. It is shown that there is a noticeable difference between the effects on cutouts in buckling of thinner shells and thicker ones. Cutouts reduce the local buckling capacity of shell about 10-15 % in the cylindrical shells, with the diameter to thickness ratio of less than 1,000. Meanwhile in shells with diameter to thickness, more than 1,000 such cutouts reduce the shell capacity about 30-35 %.
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.
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
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.
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.
Nonlinear dynamics of harmonically excited circular cylindrical shells containing fluid flow
NASA Astrophysics Data System (ADS)
Karagiozis, K.; Amabili, M.; Païdoussis, M. P.
2010-08-01
In the present study, the geometrically nonlinear vibrations of circular cylindrical shells, subjected to internal fluid flow and to a radial harmonic excitation in the spectral neighbourhood of one of the lowest frequency modes, are investigated for different flow velocities. The shell is modelled by Donnell's nonlinear shell theory, retaining in-plane inertia and geometric imperfections; the fluid is modelled as a potential flow with the addition of unsteady viscous terms obtained by using the time-averaged Navier-Stokes equations. A harmonic concentrated force is applied at mid-length of the shell, acting in the radial direction. The shell is considered to be immersed in an external confined quiescent liquid and to contain a fluid flow, in order to reproduce conditions in previous water-tunnel experiments. For the same reason, complex boundary conditions are applied at the shell ends simulating conditions intermediate between clamped and simply supported ends. Numerical results obtained by using pseudo-arclength continuation methods and bifurcation analysis show the nonlinear response at different flow velocities for (i) a fixed excitation amplitude and variable excitation frequency, and (ii) fixed excitation frequency by varying the excitation amplitude. Bifurcation diagrams of Poincaré maps obtained from direct time integration are presented, as well as the maximum Lyapunov exponent, in order to classify the system dynamics. In particular, periodic, quasi-periodic, sub-harmonic and chaotic responses have been detected. The full spectrum of the Lyapunov exponents and the Lyapunov dimension have been calculated for the chaotic response; they reveal the occurrence of large-dimension hyperchaos.
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)
Khalifa, Ahmed Mousa
2011-11-01
The combination of Flügge's shell theory, the transfer matrix approach and the Romberg integration method are used to investigate the free vibration behaviour of stepped orthotropic cylindrical shells. The hoop step on the shell surface is described by a reduced thickness over part of its circumference. Modal displacements of the shell can be described by trigonometric functions and Fourier's approach is used to separate the variables. The vibration equations of the shell are reduced to eight first-order differential equations in the circumferential coordinate, and by using the transfer matrix of the shell, these equations can be written in a matrix differential equation. The transfer matrix is derived from the non-linear differential equations of the cylindrical shells by introducing the trigonometric functions in the longitudinal direction and applying the numerical integration in the circumferential direction. The proposed model is used to get the vibration frequencies and the corresponding mode shapes for symmetrical and antisymmetrical type-modes. Computed results indicate the sensitivity of the frequency parameters and the bending deformations to the geometry of stepped shell, and also to the axial and circumferential rigidities of the shell.
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.
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 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.
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)
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)
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.
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.
Vibration of perforated cylindrical shells
NASA Astrophysics Data System (ADS)
Cousseau, Peter L.
For a credible design of an inertial confinement fusion (ICF) target chamber, the vibration characteristics of the chamber must be completely understood. Target chambers are usually cylindrical or spherical in shape and contain hundreds of perforations (called ports) to allow access to the inside of the chamber. The fusion reaction within the chamber creates a uniform impulsive loading, which the chamber walls must be designed to contain. Also prior to an implosion, a delicate alignment process of the drivers and diagnostics takes place. The vibration of the chamber from rotating machinery, e.g., vacuum pumps, and ambient sources must be completely understood and accounted for during these alignment procedures. This dissertation examines the vibration characteristics of perforated cylindrical shells. Because the target chambers' thickness-to-radius ratio is small, such chambers can be modeled as thin shells. Included in the text is a literature review of perforated plates and shells and examples of the use of perforated structures in constructed and proposed ICF target chambers. The natural frequencies and corresponding mode shapes of perforated and unperforated cylindrical shells are studied analytically, numerically (via finite elements) and experimentally. Conclusions and comparisons between the different solution methods are made for both the perforated and unperforated cases. In addition, the dynamic response of perforated cylindrical shells to an axisymmetric impulsive loading has been identified. A demonstration showing how the convolution integral can be used to determine the response of a cylinder to a non-impulsive loading is presented.
NASA Astrophysics Data System (ADS)
Castillo, Henry A., Jr.
1992-06-01
The objective of this research is to create a flexible code which is to be used in the investigation of optimum (minimum weight) shell designs. A shell analysis/design program, DAPS3, and a general purpose numerical optimization program, ADS, are incorporated into a single code, THESIS. This code provides the user great flexibility in changing the design variables and constraints which model the optimization problem. The optimum designs produced by this code are compared to DAPS3 optimum designs in order to identify any improvements made by the numerical optimization technique.
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.
Sound transmission into a laminated composite cylindrical shell
NASA Technical Reports Server (NTRS)
Koval, L. R.
1980-01-01
In the context of the transmission of airborne noise into an aircraft fuselage, a mathematical model is presented for the transmission of an oblique plane sound wave into a laminated composite circular cylindrical shell. Numerical results are obtained for geometry typical of a narrow-bodied jet transport. Results indicate that from the viewpoint of noise attenuation on laminated composite shell does not appear to offer any significant advantage over an aluminum shell. However, the transmission loss of a laminated composite shell is sensitive to the orientation of the fibers and this suggests the possibility of using a laminated composite shell to tailor the noise attenuation characteristics to meet a specific need.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Mercan, Kadir; Demir, Çiğdem; 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.
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.
Buckling analysis of cylindrical shells with cracks
Limam, A.; Jullien, J.F.; Ouayou, B.S.
1995-12-31
In many areas of aeronautical nuclear and civil engineering practice, large thin-walled structural panels are increasingly becoming characteristic architectural features. Indeed, nuclear reactor vessels and cryogenic tanks of a launcher, for instance, are made up of several thin-walled panels welded together. Instability and buckling phenomenon present over-riding constraints on the design process. In addition, the presence of joints which are very often the origin of surface fissures poses increasing dangers on the overall stability of these structures. This research deals with the analysis of the effects of cracks on the behavior of cylindrical shells subject to external pressure. The study was divided into two major parts. In the first part, experiments were carried out with shells without cracks, in order to obtain reference data. A numerical study of various models explains the experimental results and shows the combined effect of the geometric imperfections and boundary conditions on the critical load. The second part focused on several experimental tests and numerical simulations on shells with in- depth fissures as a function of their population, orientation, length and position with respect to the welds or joints. The agreement between numerical and experimental results confirms the new possibility to design with the aid of the finite element program under the condition that the calculations are carried out by means of an appropriate numerical method.
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.
Plasmon modes of circular cylindrical double-layer graphene.
Zhao, Tao; Hu, Min; Zhong, Renbin; Chen, Xiaoxing; Zhang, Ping; Gong, Sen; Zhang, Chao; Liu, Shenggang
2016-09-01
In this paper, a theoretical investigation on plasmon modes in a circular cylindrical double-layer graphene structure is presented. Due to the interlayer electromagnetic interaction, there exist two branches of plasmon modes, the optical plasmon mode and the acoustic plasmon mode. The characteristics of these two modes, such as mode pattern, effective mode index and propagation loss, are analyzed. The modal behaviors can be effectively tuned by changing the distance between two graphene layers, the chemical potential of graphene and the permittivity of interlayer dielectric. Importantly, the breakup of tradeoff between mode confinement and propagation loss is discovered in the distance-dependent modal behavior, which originates from the unique dispersion properties of a double-layer graphene system. As a consequence, both strong mode confinement and longer propagation length can be achieved. Our results may provide good opportunities for developing applications based on graphene plasmonics in circular cylindrical structure. PMID:27607651
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.
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.
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.
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.
Nagal, K.; Yamaguchi, T.
1995-11-01
This paper presents numerical solutions for the chaotic oscillations of a shallow cylindrical shell. The shell having a circular cylindrical surface and a rectangular boundary is excited by periodic acceleration laterally. The Donnell equations modified with the transverse inertia force are used. The basic equation is reduced to the nonlinear differential equation of a multiple-degree-of-freedom system by the Galerkin procedure. The fundamental characteristics are found for the shell of a square boundary and of all boundaries simply supported. The time progresses of the chaotic responses are investigated by the numerical integration by the Runge-Kutta-Gill method. The chaotic response is identified by the Lyapunov exponent and the Poincare projection onto the phase space. The Lyapunov dimension is examined by changing the assumed modes of vibration.
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.
Flow-induced vibration of circular cylindrical structures
NASA Astrophysics Data System (ADS)
Chen, Shoei-Sheng
The vibrational response of circular cylinder (CC) structures subjected to flow is characterized analytically, summarizing the results of recent theoretical and experimental investigations. Topics addressed include a single CC in quiescent fluid, multiple CCs in quiescent fluid, CC shells containing fluid, pipes conveying fluid, and CCs in axial flow. Consideration is given to cross-flow configurations involving a single CC, an array of CCs, and two CCs; the fluid-elastic instability of a group of CCs in cross flow; and design techniques. Diagrams and graphs are provided, and the vibration of damped linear systems, the general fluid equations, and characteristic equations and adjoint eigenfunctions are treated in appendices.
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.
Evolution of bulk strain solitons in cylindrical inhomogeneous shells
NASA Astrophysics Data System (ADS)
Shvartz, A.; Samsonov, A.; Dreiden, G.; Semenova, I.
2015-10-01
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.
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.
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. PMID:26627797
Nonlinear vibrations and imperfection sensitivity of a cylindrical shell containing axial fluid flow
NASA Astrophysics Data System (ADS)
del Prado, Z.; Gonçalves, P. B.; Païdoussis, M. P.
2009-10-01
The high imperfection sensitivity of cylindrical shells under static compressive axial loads is a well-known phenomenon in structural stability. On the other hand, less is known of the influence of imperfections on the nonlinear vibrations of these shells under harmonic axial loads. The aim of this work is to study the simultaneous influence of geometric imperfections and an axial fluid flow on the nonlinear vibrations and instabilities of simply supported circular cylindrical shells under axial load. The fluid is assumed to be non-viscous and incompressible and the flow to be isentropic and irrotational. The behavior of the thin-walled shell is modeled by Donnell's nonlinear shallow-shell equations. It is subjected to a static uniform compressive axial pre-load plus a harmonic axial load. A low-dimensional modal expansion, which satisfies the relevant boundary and continuity conditions, and takes into account all relevant nonlinear modal interactions observed in the past in the nonlinear vibrations of cylindrical shells with and without flow is used together with the Galerkin method to derive a set of eight coupled nonlinear ordinary differential equations of motion which are, in turn, solved by the Runge-Kutta method. The shell is considered to be initially at rest, in a position corresponding to a pre-buckling configuration. Then, a harmonic excitation is applied and conditions for parametric instability and dynamic snap-through are sought. The results clarify the marked influence of geometric imperfections and fluid flow on the dynamic stability boundaries, bifurcations and basins of attraction.
2DEG on a cylindrical shell with a screw dislocation
NASA Astrophysics Data System (ADS)
Filgueiras, Cleverson; Silva, Edilberto O.
2015-09-01
A two dimensional electron gas on a cylindrical surface with a screw dislocation is considered. More precisely, we investigate how both the geometry and the deformed potential due to a lattice distortion affect the Landau levels of such system. The case showing the deformed potential can be thought in the context of 3D common semiconductors where the electrons are confined on a cylindrical shell. We will show that important quantitative differences exist due to this lattice distortion. For instance, the effective cyclotron frequency is diminished by the deformed potential, which in turn enhances the Hall conductivity.
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.
Non-linear dynamic analysis of anisotropic cylindrical shells
Lakis, A.A.; Selmane, A.; Toledano, A.
1996-12-01
A theory to predict the influence of geometric non-linearities on the natural frequencies of an empty anisotropic cylindrical shell is presented in this paper. It is a hybrid of finite element and classical thin shell theories. Sanders-Koiter non-linear and strain-displacement relations are used. Displacement functions are evaluated using linearized equations of motion. Modal coefficients are then obtained for these displacement functions. Expressions for the mass, linear and non-linear stiffness matrices are derived through the finite element method. The uncoupled equations are solved with the help of elliptic functions. The period and frequency variations are first determined as a function of shell amplitudes and then compared with the results in the literature.
NASA Astrophysics Data System (ADS)
Amabili, M.
2014-03-01
Bich and Xuan Nguyen [1] studied nonlinear free and forced vibrations of FG shells under pre-load compression at constant temperature. Based on Donnell's shell theory and neglecting in-plane inertia, they employed a single-mode Galerkin approximation to discretize the transverse displacement. An averaging method was used to obtain the backbone curves while a Runge-Kutta scheme was utilized to obtain the frequency-response curves.
The Destructive High Pressure Tests of Cylindrical Shells
Yasumi Kitajima; Satoru Shibata
2002-07-01
We conducted the limit state tests of cylindrical shells to establish criteria for the occurrence of steel wall/liner tearing in the reactor containment vessels (such as Steel Containment Vessels (SCV), Prestressed Concrete Containment Vessels (PCCV) and Reinforced Concrete Containment Vessels (RCCV)) under the limit state pressure. In the tests, precisely manufactured cylindrical shell vessels (about 800 mm in height and 300 mm in diameter) were pressurized to the failure using water. We also conducted the finite element analyses. The conclusions are as follows: 1. We obtained good agreement (within 2-3%) between the tests and the analyses in structural behavior such as internal pressure loading vs. displacement and strain to the failure. However, in the case of the test piece which included weld line on the cylindrical wall, the difference between the tests and the analyses was larger (about 1.5 times) than the rest. 2. The localized strains began to increase when radial strains in general structure reached 5-10%. We are intended to apply these results to the finite element analyses and the integrity evaluation of containment vessels (SCV, PCCV and RCCV). (authors)
Explosion-Induced Implosions of Cylindrical Shell Structures
NASA Astrophysics Data System (ADS)
Ikeda, C. M.; Duncan, J. H.
2010-11-01
An experimental study of the explosion-induced implosion of cylindrical shell structures in a high-pressure water environment was performed. The shell structures are filled with air at atmospheric pressure and are placed in a large water-filled pressure vessel. The vessel is then pressurized to various levels P∞=αPc, where Pc is the natural implosion pressure of the model and α is a factor that ranges from 0.1 to 0.9. An explosive is then set off at various standoff distances, d, from the model center line, where d varies from R to 10R and R is the maximum radius of the explosion bubble. High-speed photography (27,000 fps) was used to observe the explosion and resulting shell structure implosion. High-frequency underwater blast sensors recorded dynamic pressure waves at 6 positions. The cylindrical models were made from aluminum (diameter D = 39.1 mm, wall thickness t = 0.89 mm, length L = 240 mm) and brass (D = 16.7 mm, t = 0.36 mm, L=152 mm) tubes. The pressure records are interpreted in light of the high-speed movies. It is found that the implosion is induced by two mechanisms: the shockwave generated by the explosion and the jet formed during the explosion-bubble collapse. Whether an implosion is caused by the shockwave or the jet depends on the maximum bubble diameter and the standoff distance.
An Experimental Investigation of the Implosion of Cylindrical Shell Structures
NASA Astrophysics Data System (ADS)
Ikeda, C. M.; Wilkerling, J.; Duncan, J. H.
2009-11-01
An experimental study of the physics of the implosion of cylindrical shell structures in a high-pressure water environment was performed. The shell structures are filled with air at atmospheric pressure and the implosions occur when the water pressure is raised above the shell buckling stability limit. High-speed photography (27,000 fps) was used to observe and measure the motion of the structure during its implosion. High-frequency underwater blast sensors recorded dynamic pressure waves at 13 positions in the tank. The cylindrical models are made from various aluminum alloys (diameter D = 39.1 mm, wall thickness t = 0.89 mm) and brass (D = 16.7 to 25.4 mm, t = 0.33 to 0.36 mm). The ends of the tubes were sealed with Aluminum caps. The pressure records are interpreted in light of the high-speed movies. Cylinder length-to-diameter (L/D) ratios between 6 and 10 were examined; in this range the cylinders implode in a mode 2 cross-sectional shape at pressures between 6.9 and 28.7 bar. It is found that the pressure versus time records from sensors placed at the same dimensionless radial position (r/D) from the cylinder surface scale well with time and pressure scales from cavitation bubble collapse theory.
A cylindrical shell with an arbitrarily oriented crack
NASA Technical Reports Server (NTRS)
Yahsi, O. S.; Erdogan, F.
1983-01-01
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 to 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. Previously annunced in STAR as N83-16783
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.
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.
Flow-induced vibration of circular cylindrical structures
Chen, S.S.
1985-06-01
This report summarizes the flow-induced vibration of circular cylinders in quiescent fluid, axial flow, and crossflow, and applications of the analytical methods and experimental data in design evaluation of various system components consisting of circular cylinders. 219 figs., 30 tabs. (JDB)
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.
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.
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.
A note on the interference of two collinear cracks in a cylindrical shell
NASA Technical Reports Server (NTRS)
Erdogan, F.; Ratwani, M.
1973-01-01
A stress analysis of a pressurized shallow cylindrical shell containing two collinear axial cracks of equal length was conducted. The mathematical relationships for conducting the stress analysis are developed. Graphs are presented to show the stress intensity factor ratio in the cylindrical shell and the bending components of the stress intensity factor ratio.
Flow-induced vibration of circular cylindrical structures
Chen, S.S.
1987-01-01
This book presents the flow-induced vibration of circular cylinders in quiescent fluid, axial flow, and crossflow, and applications of the analytical methods and experimental data in design evaluation of various system components consisting of circular cylinders. The information is organized into five general topical areas: Introduction: Chapter 1 presents an overview of flow-induced vibration of circular cylinders. It includes examples of flow-induced vibration, various fluid force components, and nondimensional parameters as well as different excitation mechanisms. The general principles are applicable under different flow conditions. Quiescent Fluid: Fluid inertia and fluid damping are discussed in Chapters 2, 3 and 4. Various flow theories are applied in different situations. Axial Flow: Axial flow can cause subcritical vibration and instability. Chapter 5 summarizes the results for internal flow, while Chapter 6 considers external flow. Both theoretical results and experimental data are examined. Crossflow: Different excitation mechanisms can be dominant in different conditions for crossflow. Those include turbulent buffeting, acoustic resonance, vortex excitation, and dynamic instability. Design Considerations: Applications of the general methods of analysis in the design evaluation of system components are described and various techniques to avoid detrimental vibration are presented.
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.
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.
Efficient method for analyzing multiple circular cylindrical nanoparticles on a substrate
NASA Astrophysics Data System (ADS)
Lu, Xun; Lu, Ya Yan
2016-05-01
Due to the existing nanofabrication techniques, many metallic or dielectric nanoparticles are cylindrical objects with top and bottom surfaces parallel to a substrate and side boundaries perpendicular to the substrate. In this paper, we develop a relatively simple and efficient semi-analytic method for analyzing the scattering of light by a set of circular cylindrical objects (of finite height) on a layered background. The method relies on expanding the field in one-dimensional modes in layered regions where the material properties change with one spatial variable only, to establish a linear system on the boundaries separating the layered regions. Although the ‘expansion coefficients’ are two-dimensional (2D) functions, they satisfy scalar 2D Helmholtz equations which have analytic solutions due to the special geometry. The method is used to analyze dielectric and metallic circular cylindrical nanoparticles on a substrate or in free space.
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.
Buckling of Cracked Laminated Composite Cylindrical Shells Subjected to Combined Loading
NASA Astrophysics Data System (ADS)
Allahbakhsh, Hamidreza; Shariati, Mahmoud
2013-10-01
A series of finite element analysis on the cracked composite cylindrical shells under combined loading is carried out to study the effect of loading condition, crack size and orientation on the buckling behavior of laminated composite cylindrical shells. The interaction buckling curves of cracked laminated composite cylinders subject to different combinations of axial compression, bending, internal pressure and external pressure are obtained, using the finite element method. Results show that the internal pressure increases the critical buckling load of the CFRP cylindrical shells and bending and external pressure decrease it. Numerical analysis show that axial crack has the most detrimental effect on the buckling load of a cylindrical shell and results show that for lower values of the axial compressive load and higher values of the external pressure, the buckling is usually in the global mode and for higher values of axial compressive load and lower levels of external pressure the buckling mode is mostly in the local mode.
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
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. PMID:26074457
The vector potential of a circular cylindrical antenna in terms of a toroidal harmonic expansion
NASA Astrophysics Data System (ADS)
Selvaggi, Jerry; Salon, Sheppard; Chari, M. V. K.
2008-08-01
A toroidal harmonic expansion is developed which is used to represent the vector potential due to a circular cylindrical antenna with a rectangular cross section at any arbitrary point in space. The singular part of the antenna kernel is represented by an associated toroidal harmonic expansion and the analytic part of the kernel is represented by a binomial expansion. A simple example is given to illustrate the application of the toroidal expansion.
NASA Technical Reports Server (NTRS)
Koval, L. R.
1980-01-01
In the context of the transmission of airborne noise into an aircraft fuselage, a mathematical model is presented for the transmission of an oblique plane sound wave into a finite cylindrical shell stiffened by stringers and ring frames. The rings and stringers are modeled as discrete structural elements. The numerical case studied was typical of a narrow-bodied jet transport fuselage. The numerical results show that the ring-frequency dip in the transmission loss curve that is present for a monocoque shell is still present in the case of a stiffened shell. The ring frequency effect is a result of the cylindrical geometry of the shell. Below the ring frequency, stiffening does not appear to have any significant effect on transmission loss, but above the ring frequency, stiffeners can enhance the transmission loss of a cylindrical shell.
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.
NASA Astrophysics Data System (ADS)
Torki, Mohammad Ebrahim; Kazemi, Mohammad Taghi; Mahmoudkhani, Saied
2012-12-01
The effect of length and thickness on dynamic stability analysis of cantilever cylindrical shells under follower forces is addressed. Beck's, Leipholz's, and Hauger's problems were solved for cylindrical shells with different length-to-radius and thicknesses-to-radius ratios using the Galerkin method. First-order shear theory was used, and rotary inertias were considered in deriving the differential equations. Critical circumferential and longitudinal mode numbers and loads were evaluated for each case. Diagrams containing nondimensional load parameters vs. length and thickness parameters were plotted for each problem. For some shells with small length-to-radius ratios, flutter occurred in high longitudinal mode numbers where the first-order shear theory may not suffice to accurately evaluate the deformations. However, for long and moderately thick shells, there are ranges in which the shell can be analyzed using the simplified equivalent beam model.
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
The implosion of cylindrical shell structures in a high-pressure water environment.
Ikeda, C M; Wilkerling, J; Duncan, J H
2013-12-01
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, P c, 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/D 0, 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 P c and the time scale [Formula: see text] (where R i 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/D 0, 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, P c V , 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 [Formula: see text], but that the shape and amplitudes of the pressure records are strongly affected by the mode number. PMID:24353473
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.
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.
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.
A Circular-cylindrical Flux-rope Analytical Model for Magnetic Clouds
NASA Astrophysics Data System (ADS)
Nieves-Chinchilla, T.; Linton, M. G.; Hidalgo, M. A.; Vourlidas, A.; Savani, N. P.; Szabo, A.; Farrugia, C.; Yu, W.
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). Our model extends the circular-cylindrical concept of Hidalgo et al. 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 field and plasma in situ observations and with a new parameter (EPP, the Electron Pitch angle distribution Parameter) which quantifies the bidirectionally of the plasma 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. An extension of our current modeling framework to account for such non-circular CMEs will be presented in a forthcoming publication.
NASA Astrophysics Data System (ADS)
Paranin, Vyacheslav D.; Karpeev, Sergey V.; Kazanskiy, Nikolay L.; Krasnov, Andrey P.
2016-03-01
The optical system for converting laser beams with circular polarization to cylindrical vector beams on the basis of anisotropic crystals has been developed. The experimental research of beam formation quality has been carried out on the both polarization and structural characteristics. The research showed differences in the formation of the azimuthal and radial polarizations for Gaussian modes and Bessel beams. The boundaries of changes of the optical system parameters to form different types of polarizations with different amplitude and phase distributions have been identified.
Ray-based modeling of reverberation in subsurface circular cylindrical void
NASA Astrophysics Data System (ADS)
Chen, Ping; Xia, Dan; Chen, Boyuan; Li, Lin; Li, Xiuzhong; Dong, Tian-lin
2011-03-01
Ray representation of electromagnetic resonance (reverberation) mode in subsurface circular cylindrical dielectric resonator (including void) is proposed. The modal ray path must be regular polygon or polystar. Travel time formulas for fundamental resonance multiples and the detecting conditions for non-exact-backscattering rays are derived. Simulation of time-distance curves of a modal hollow concrete block is generally concurred to the measured ground penetrating radar signal pattern. The proposed modeling method can be generalized to other resonant cavities with different profiles and provide a sound base for further applications of other more complicated geophysics science and engineering fields, particularly in ray-based tomography.
Swimming at low Reynolds number of a cylindrical body in a circular tube
NASA Astrophysics Data System (ADS)
Felderhof, B. U.
2010-11-01
Swimming at low Reynolds number of a cylindrical body due to wavelike surface displacement is studied for the situation where the fluid is confined to a circular tube. The body has infinite length and swims in the direction of the tube axis. The swimming speed and dissipation are calculated to second order in the surface displacement for four different strokes. Both speed and dissipation are affected significantly by the confinement. For a helical stroke the body achieves both a translational and a rotational swimming velocity.
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.
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.
NASA Astrophysics Data System (ADS)
Kapuria, S.; Kumari, P.; Nath, J. K.
2009-07-01
An exact two-dimensional (2D) piezoelasticity solution is presented for free vibration and steady-state forced response of simply supported piezoelectric angle-ply laminated circular cylindrical panels in cylindrical bending under harmonic electromechanical load, with and without damping. The piezoelectric layers are polarized along radial direction to induce extension actuation/sensing mechanism. The variables are expanded layerwise in Fourier series to satisfy the boundary conditions at the simply supported ends. The governing equations get reduced to ordinary differential equations in thickness direction with variable coefficients and these are solved by the modified Frobenius method. The unknown coefficients of the solution are obtained using the transfer matrix method. Results for the natural frequency and its variation with ply angle and for steady-state response due to harmonic electromechanical excitation are presented for single layer piezoelectric panel, and hybrid multilayered inhomogeneous test, composite and sandwich panels. The numerical results presented in tabular form would serve as useful benchmark for assessing one-dimensional (1D) panel theories for free vibration and harmonic response of hybrid cylindrical panels.
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.
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.
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.
Equations of nonlinear dynamics of elastic shells in cylindrical Eulerian coordinates
NASA Astrophysics Data System (ADS)
Zubov, L. M.
2016-05-01
The equations of dynamics of elastic shells subjected to large deformations are formulated. The Eulerian coordinates on a circular cylinder and time are accepted as independent variables, and one of the unknown functions is the distance from a point of the shell surface to the cylinder axis. The equations of dynamics of nonlinearly elastic shells in the Eulerian coordinates are convenient for exact formulation of the problem on the interaction of strongly deformable shells with moving fluids and gases. The equations obtained can be used for dynamic calculations of fluids and gases flowings in pipelines, blood vessels, hoses, and other nonlinearly deformable thin-walled tubular elements of constructions.
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.
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.
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.
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.
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.
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Kim, Young-Wann
2015-12-01
The free vibration characteristics of fluid-filled functionally graded cylindrical shells buried partially in elastic foundations are investigated by an analytical method. The elastic foundation of partial axial and angular dimensions is represented by the Pasternak model. The motion of the shells is represented by the first-order shear deformation theory to account for rotary inertia and transverse shear strains. The functionally graded cylindrical shells are composed of stainless steel and silicon nitride. Material properties vary continuously through the thickness according to a power law distribution in terms of the volume fraction of the constituents. The governing equation is obtained using the Rayleigh-Ritz method and a variation approach. The fluid is described by the classical potential flow theory. Numerical examples are presented and compared with existing available results to validate the present method.
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.
NASA Astrophysics Data System (ADS)
Zhou, Jie; Bhaskar, Atul; Zhang, Xin
2015-11-01
This paper investigates sound transmission through double-walled cylindrical shell lined with poroelastic material in the core, excited by pressure fluctuations due to the exterior turbulent boundary layer (TBL). Biot's model is used to describe the sound wave propagating in the porous material. Three types of constructions, bonded-bonded, bonded-unbonded and unbonded-unbonded, are considered in this study. The power spectral density (PSD) of the inner shell kinetic energy is predicted for two turbulent boundary layer models, different air gap depths and three types of polyimide foams, respectively. The peaks of the inner shell kinetic energy due to shell resonance, hydrodynamic coincidence and acoustic coincidence are discussed. The results show that if the frequency band over the ring frequency is of interest, an air gap, even if very thin, should exist between the two elastic shells for better sound insulation. And if small density foam has a high flow resistance, a superior sound insulation can still be maintained.
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. PMID:27409933
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
Scattering of cylindrical electric field waves from an elliptical dielectric cylindrical shell
NASA Astrophysics Data System (ADS)
Urbanik, E. A.
1982-12-01
This thesis examines the scattering of cylindrical waves by large dielectric scatterers of elliptic cross section. The solution method was the method of moments using a Galerkin approach. Sinusoidal basis and testing functions were used resulting in a higher convergence rate. The higher rate of convergence made it possible for the program to run on the Aeronautical Systems Division's CYBER computers without any special storage methods. This report includes discussion on moment methods, solution of integral equations, and the relationship between the electric field and the source region or self cell singularity. Since the program produced unacceptable run times, no results are contained herein. The importance of this work is the evaluation of the practicality of moment methods using standard techniques. The long run times for a mid-sized scatterer demonstrate the impracticality of moment methods for dielectrics using standard techniques.
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.
Effectiveness of the magnetostatic shielding by the cylindrical shells
NASA Astrophysics Data System (ADS)
Grabchikov, S. S.; Trukhanov, A. V.; Trukhanov, S. V.; Kazakevich, I. S.; Solobay, A. A.; Erofeenko, V. T.; Vasilenkov, N. A.; Volkova, O. S.; Shakin, A.
2016-01-01
The experimental research of the magnetostatic shielding effectiveness and the analytical calculations of the average magnetic permeability of single-layer cylindrical sample of the shields based on electrolytically deposited Ni80Fe20 alloy are carried out. The locations of maxima on the Ef(H) and μ(H) curves do not match each other, which is difficult to interpret in terms of the shunting model. The results are explained by the non-linear distribution of the magnetic permeability through the thickness of the shield. It has been shown that in the magnetic fields range from 100 A/m up to 2700 A/m, the shields based on the Ni80Fe20 alloy are preferred over ones based on the 84KHSR amorphous ribbon. It is concluded that at the selection of shield materials it should take into account not only the main magnetic characteristics - μ; Hs; Hc but also Hmax parameter, which is important to evaluate the effectiveness of magnetic shielding.
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.
Modal analysis of thin cylindrical shells with cardboard liners and estimation of loss factors
NASA Astrophysics Data System (ADS)
Koruk, Hasan; Dreyer, Jason T.; Singh, Rajendra
2014-04-01
Cardboard liners are often installed within automotive drive shafts to reduce radiated noise over a certain frequency range. However, the precise mechanisms that yield noise attenuation are not well understood. To overcome this void, a thin shell (under free boundaries) with different cardboard liner thicknesses is examined using analytical, computational and experimental methods. First, an experimental procedure is introduced to determine the modal behavior of a cylindrical shell with a cardboard liner. Then, acoustic and vibration frequency response functions are measured in acoustic free field, and natural frequencies and the loss factors of structures are determined. The adverse effects caused by closely spaced modes during the identification of modal loss factors are minimized, and variations in measured natural frequencies and loss factors are explored. Material properties of a cardboard liner are also determined using an elastic plate treated with a thin liner. Finally, the natural frequencies and modal loss factors of a cylindrical shell with cardboard liners are estimated using analytical and computational methods, and the sources of damping mechanisms are identified. The proposed procedure can be effectively used to model a damped cylindrical shell (with a cardboard liner) to predict its vibro-acoustic response.
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.
Elastic-plastic fracture of cylindrical shells containing a part-through circumferential crack
Ezzat, H.; Erdogan, F.
1982-11-01
The problem of fatigue crack propagation and ductile fracture of a cylindrical shell containing a macroscopic circumferential flaw is considered. The main interest in the study is in applications to line pipes and other cylindrical containers under secondary axial stresses in addition to the primary stresses coming from the internal pressure. The stress intensity factor for the part-through crack used in analyzing and correlating the fatigue crack propagation rate is obtained by using a line spring model in conjunction with Reissner's shell theory. To analyze the ductile fracture instability and to correlate the experimental and theoretical results, the crack mouth opening displacement is used as the parameter. The limited data on fatigue crack propagation give the expected result, namely that the crack propagation rate in pipes may be predicted from the fatigue results performed on simpler geometries provided the stress intensity factors in pipes are calculated with sufficient accuracy. 14 references.
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.
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 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.
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.
España, Aubrey L; Williams, Kevin L; Plotnick, Daniel S; Marston, Philip L
2014-07-01
Understanding the physics governing the interaction of sound with targets in an underwater environment is essential to improving existing target detection and classification algorithms. To illustrate techniques for identifying the key physics, an examination is made of the acoustic scattering from a water-filled cylindrical shell. Experiments were conducted that measured the acoustic scattering from a water-filled cylindrical shell in the free field, as well as proud on a sand-water interface. Two modeling techniques are employed to examine these acoustic scattering measurements. The first is a hybrid 2-D/3-D finite element (FE) model, whereby the scattering in close proximity to the target is handled via a 2-D axisymmetric FE model, and the subsequent 3-D propagation to the far field is determined via a Helmholtz integral. This model is characterized by the decomposition of the fluid pressure and its derivative in a series of azimuthal Fourier modes. The second is an analytical solution for an infinitely long cylindrical shell, coupled with a simple approximation that converts the results to an analogous finite length form function. Examining these model results on a mode-by-mode basis offers easy visualization of the mode dynamics and helps distinguish the different physics driving the target response. PMID:24993199
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.
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 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
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.
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.
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).
Sound scattering by free surface piercing and fluid-loaded cylindrical shells.
Avital, Eldad J; Miloh, Touvia
2011-07-28
A vertical flexible, thin, cylindrical shell is considered to be clamped to a rigid base in shallow water and piercing its surface. The shell is composed of an isotropic and homogeneous material and may be empty inside or filled with compressible fluid. Linear acoustics and structural dynamics are used to model sound scattering caused by an external incident sound wave. A solution is derived using a Fourier transform in the tangential and vertical directions. A collocation technique coupled with an orthogonalization procedure is used to account for the edge conditions of the shell. It is shown that zero sound scattering, indicating acoustic invisibility, is theoretically attainable and can be achieved when a continuous distribution of an oscillating pressure load is applied on the shell's wall. Similarly, zero sound transmission into the shell's inner fluid can also be considered. The possibility of using a pre-determined discrete distribution of the applied pressure load is also discussed. The derived equations are numerically solved to examine sound scattering by a thin aluminium shell in shallow water. PMID:21690137
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
Dranchenko, B.N.; Portnov, B.B.; Seleznev, A.V.; Danilova, T.N.; Komarova, S.N.; Ponomareva, V.K.
1994-06-01
Cylindrical shells with regular perforation are widely used in power generating equipment and in particular in collectors 1 of the circuit of steam generators of power generating installations with water-water reactors (WWPR) The state of stress of collectors is determined by a broad spectrum of technological and operational loads, it is therefore difficult to analyze it theoretically. The aim of the present work is the experimental investigation of stresses in the cylindrical shells of collectors subjected to internal pressure, the generalization and systematization of empirical data in the form of engineering formulas and nomographs. The investigations were carried out with photoelastic three-dimensional models with the use of {open_quotes}freezing{close_quotes}. The basic characteristics of the state of stress of perforated shells (in particular those used in calculations of the strength and life of collectors) are the values of the stress intensity factor K and of the stress intensification factor {gamma}{sub {bar {sigma}}}{sub me} of the mean integral stress level in the neck between neighboring holes. The presented data make it possible to establish quantitatively the regularities of change of K and {gamma}{sub {bar {sigma}}}{sub me} in dependence on the geometry of the perforated shells. These data were systematized according to a special program of multifactor regression analysis. It follows from the presented formulas and nomographs in particular that in the ranges of the geometry of the perforated shells K may change from 2.5 to 4.0, and {gamma}{sub {bar {sigma}}}{sub me} from 1.1 to 2.3. Therefore varied geometric parameters have a substantial effect on the load intensity of perforated shells, and that once again confirms how topical it is to obtain new experimental data, to generalize and systematize them.
NASA Astrophysics Data System (ADS)
Kapuria, S.; Kumar, Amit
2010-04-01
The work presents an analytical three-dimensional solution for simply supported angle-ply piezoelectric (hybrid) laminated cylindrical shells in cylindrical bending with interlaminar bonding imperfections, in an electro-thermomechanical loading environment. The jumps in displacements, electric potential and temperature at the imperfect interfaces are modeled using linear spring-layer model. The solution includes the case when, besides at inner and outer surfaces, electric potentials are prescribed at layer interfaces also for effective actuation/sensing. The entities for each layer are expanded in Fourier series in circumferential coordinate to satisfy the boundary conditions at the simply supported ends. The resulting ordinary differential equations in thickness coordinate with variable coefficients are solved by the modified Frobenius method. Numerical results are presented for hybrid composite and sandwich shells with varying imperfection compliance. The effect of location of imperfect interface on the response is studied for cross-ply panels while the effect of ply angle on the sensitivity towards imperfection is studied for angle-ply panels. The effect of weak bonding at actuator/sensor interface on the actuation/sensing authority is investigated. The presented results would also help assessing 2D shell theories that incorporate interlaminar bonding imperfections.
Vibration characteristics of thin rotating cylindrical shells with various boundary conditions
NASA Astrophysics Data System (ADS)
Sun, Shupeng; Chu, Shiming; Cao, Dengqing
2012-08-01
An analysis is presented for the vibration characteristics of thin rotating cylindrical shells with various boundary conditions by use of Fourier series expansion method. Based on Sanders' shell equations, the governing equations of motion which take into account the effects of centrifugal and Coriolis forces as well as the initial hoop tension due to rotating are derived. The displacement field is expressed as a product of Fourier series expressions which represents the axial modal displacements and trigonometric functions which represents the circumferential modal displacements. Stokes' transformation is employed to derive the derivatives of the Fourier series expressions. Then, through the process of formula derivation, an explicit expression of the exact frequency equation can be obtained for a thin rotating cylinder with classical boundary conditions of any type. Once the frequency equation has been determined, the frequencies are calculated numerically. To validate the present analysis, comparisons between the results of the present method and previous studies are performed and very good agreement is achieved. Finally, the method is applied to investigate the vibration characteristics of thin rotating cylindrical shells under various boundaries, and the results are presented.
NASA Astrophysics Data System (ADS)
Wang, Bin; Nie, Guo-Hua
2015-10-01
A theoretical model is proposed in this paper to predict the bi-stable states of initially stressed cylindrical shell structures attached by surface anisotropic piezoelectric layers. The condition for existence of bi-stability of the shell structural system is presented and analytical expressions for corresponding rolled-up radii of the stable shell are given based on the principle of minimum strain energy. The resulting solution indicates that the shell system may have two stable configurations besides its initial state under a combined action of the actuating electric field and initial stresses characterized by the bending moment. If the piezoelectric layer materials act as only sensor materials without the actuating electric field, initial stresses may produce the bi-stable states, but one corresponding to its initial state. For the shell without initial stresses, the magnitude in the actuating electric field determines the number of the stable states, one or two stable configurations besides the initial state. The theoretical prediction for the bi-stable states is verified by finite element method (FEM) simulation by using the ABAQUS code.
NASA Astrophysics Data System (ADS)
Torki, Mohammad Ebrahim; Kazemi, Mohammad Taghi; Reddy, Junuthula N.; Haddadpoud, Hassan; Mahmoudkhani, Saeid
2014-02-01
In this paper, flutter of functionally graded material (FGM) cylindrical shells under distributed axial follower forces is addressed. The first-order shear deformation theory is used to model the shell, and the material properties are assumed to be graded in the thickness direction according to a power law distribution using the properties of two base material phases. The solution is obtained by using the extended Galerkin's method, which accounts for the natural boundary conditions that are not satisfied by the assumed displacement functions. The effect of changing the concentrated (Beck's) follower force into the uniform (Leipholz's) and linear (Hauger's) distributed follower loads on the critical circumferential mode number and the minimum flutter load is investigated. As expected, the flutter load increases as the follower force changes from the so-called Beck's load into the so-called Leipholz's and Hauger's loadings. The increased flutter load was calculated for homogeneous shell with different mechanical properties, and it was found that the difference in elasticity moduli bears the most significant effect on the flutter load increase in short, thick shells. Also, for an FGM shell, the increase in the flutter load was calculated directly, and it was found that it can be derived from the simple power law when the corresponding increase for the two base phases are known.
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, R.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{sup 4} s{sup {minus}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{degree} 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
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.
On sound transmission into a thin cylindrical shell under 'flight conditions'
NASA Technical Reports Server (NTRS)
Koval, L. R.
1975-01-01
A mathematical model for sound transmission into a thin cylindrical shell is used to study sound transmission under flight conditions, i.e., under conditions of external air flow past a pressurized cylinder at flight altitude. Numerical results for different incidence angles are presented for a typical narrow-bodied jet in cruising flight at 10,660 m with interior pressure at 2440 m. A comparison is made between no-flow sound transmission at standard conditions on the ground to sound transmission under flight conditions. It is shown that at M = 0, the cylinder transmission loss (TL) has dips at the cylinder ring frequency (fR) and the critical frequency (fc) for a flat panel of same material and thickness as shell. Between fR and fc, cylinder TL follows a mass-law behavior. Flow provides a modest increase in TL in the mass-law region, and strongly interacts with the cylinder resonances below fR.
Ray and wave scattering in smoothly curved thin shell cylindrical ridges
NASA Astrophysics Data System (ADS)
Søndergaard, Niels; Chappell, David J.
2016-09-01
We propose wave and ray approaches for modelling mid- and high-frequency structural vibrations through smoothed joints on thin shell cylindrical ridges. The models both emerge from a simplified classical shell theory setting. The ray model is analysed via an appropriate phase-plane analysis, from which the fixed points can be interpreted in terms of the reflection and transmission properties. The corresponding full wave scattering model is studied using the finite difference method to investigate the scattering properties of an incident plane wave. Through both models we uncover the scattering properties of smoothed joints in the interesting mid-frequency region close to the ring frequency, where there is a qualitative change in the dynamics from anisotropic to simple geodesic propagation.
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)
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_{± }).
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.
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.
1985-01-01
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.
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). PMID:11885684
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. PMID:19586650
NASA Astrophysics Data System (ADS)
Rajabi, Majid
2016-05-01
The method of wave function expansion is adopted to study the three dimensional scattering of a plane progressive harmonic acoustic wave incident upon an arbitrarily thick-walled helically filament-wound composite cylindrical shell submerged in and filled with compressible ideal fluids. An approximate laminate model in the context of the so-called state-space formulation is employed for the construction of T-matrix solution to solve for the unknown modal scattering coefficients. Considering the nonaxisymmetric wave propagation phenomenon in anisotropic cylindrical components and following the resonance scattering theory which determines the resonance and background scattering fields, the stimulated resonance frequencies of the shell are isolated and classified due to their fundamental mode of excitation, overtone and style of propagation along the cylindrical axis (i.e., clockwise or anticlockwise propagation around the shell) and are identified as the helically circumnavigating waves.
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.
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)
Guggenberger, W.
2006-05-01
In this paper the elastic stability and imperfection sensitivity of axially loaded cylindrical shells on narrow discrete supports is explored. This is done by parametric geometrically nonlinear finite element analyses of the perfect and imperfect cylinders up to the critical load maxima. In addition, classical buckling eigenvalues are computed for reference purposes. The obtained numerical results are plotted in a systematic unified way and related curve-fit expressions are developed for the critical load maxima in dependency of the geometrical parameters of the problem. The support width, the shell slenderness and the type of local support, i.e. flexible versus rigid local support conditions, are varied. The present basic investigation is restricted to shells with linear-elastic material behaviour. The study of the buckling behaviour for narrow local supports, including the limiting case of point supports is of special concern. Strictly speaking, point supports exist only in the mathematical limit, since the stress singularities which occur in this case are mere artefacts and have no direct physical significance. But it turns out that the local buckling behaviour, like shape and evolution of buckles, magnitude of buckling loads etc. tends to an invariant typical limiting scenario, which is surprising but understandable at the same time. This typical local mono-modal buckling scenario, which is also investigated and presented in this paper, may be viewed as the counterpart to the well-known multi-modal characteristic global buckling scenario which occurs under uniform axial compression.
Flow-induced vibrations of an elastic cylindrical shell conveying a compressible fluid
NASA Astrophysics Data System (ADS)
Sorokin, S. V.; Terentiev, A. V.
2006-10-01
The paper addresses the effects of generation and transmission of the vibro-acoustic energy in an elastic cylindrical shell filled with water. The energy input is produced by velocity and pressure pulsations due to the presence of an obstacle in a flowing fluid. It is assumed that there is no back-reaction of the vibro-acoustic response on the driving turbulent field. The concept of modal Green's functions and modal boundary integral equations is introduced and the role of elastic deformations of a tube is highlighted in view of the energy re-distribution between the structural and the acoustical transmission paths. Another important aspect of the problem of 'flow-induced sound generation', which is addressed in this paper, is the treatment of a CFD pressure output for the modelling of vibro-acoustic field generation. For an elastic shell in heavy fluid loading conditions, it is indicated that only the pressure distribution at the surface of a shell provided by a CFD solver is requested in order to adequately predict its coupled vibro-acoustic response. The 'inner' and 'outer' acousto-elastic domains are introduced and the low-order system of linear algebraic equations is set up, which is constituted by modal boundary equations and continuity conditions. Several 'generic' excitation cases are studied and the results of analysis are explained.
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.
Model-based failure detection for cylindrical shells from noisy vibration measurements.
Candy, J V; Fisher, K A; Guidry, B L; Chambers, D H
2014-12-01
Model-based processing is a theoretically sound methodology to address difficult objectives in complex physical problems involving multi-channel sensor measurement systems. It involves the incorporation of analytical models of both physical phenomenology (complex vibrating structures, noisy operating environment, etc.) and the measurement processes (sensor networks and including noise) into the processor to extract the desired information. In this paper, a model-based methodology is developed to accomplish the task of online failure monitoring of a vibrating cylindrical shell externally excited by controlled excitations. A model-based processor is formulated to monitor system performance and detect potential failure conditions. The objective of this paper is to develop a real-time, model-based monitoring scheme for online diagnostics in a representative structural vibrational system based on controlled experimental data. PMID:25480059
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.
Active Control of Coupled Wave Propagation in Fluid-Filled Elastic Cylindrical Shells.
NASA Astrophysics Data System (ADS)
Brevart, Bertrand Jean
The vibrational energy propagating in straight fluid-filled elastic pipes is carried by the structure as well as by the internal fluid. This study demonstrates that, whether the propagating energy is predominantly conveyed in the shell or in the fluid, large attenuations of the total power flow may be achieved by using an active control approach. As the shell and fluid motions are fully coupled, the implementation of intrusive sources/sensors in the acoustic field can be also avoided. The approach is based on using radial control forces applied to the outer shell wall and error sensors observing the structural motion. The cylindrical shell is assumed to be infinite, in vacuo or filled with water. The first disturbance source investigated is a propagating free wave of circumferential order n = 0 or n = 1. The control forces are appropriate harmonic line forces radially applied to the structure. The radial displacement of the shell wall at discrete locations downstream of the control forces is minimized using linear quadratic optimal control theory. The attenuation of the total power flow in the system after control is used to study the impact of the fluid on the performance of the control approach. Results for the shell in vacuo are presented for comparison. Considering the breathing mode (n = 0), the fluid decreases the control performance when the disturbance is a structural-type incident wave. Significant reductions of the transmitted power flow can be achieved when the disturbance is a fluid-type of wave. Regarding the beam mode (n = 1), the fluid increases the control performance below the first acoustic cut-off frequency and decreases it above this frequency. The analytical study is then extended to the active control of the pipe vibrations induced by more realistic disturbances such as a point force or an internal monopole source. The point force disturbance addresses the problem of mechanical excitation whereas the internal monopole source directs the
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.
Semi-analytic computation of the driven fields in right circular cylindrical microwave applicators
Nelson, E.M.; Kares, R.J.; Stringfield, R.M.
1995-05-01
A semi-analytic technique for computing the driven fields in a pillbox microwave applicator composed of concentric right circular cylinders (e.g., load, tube and air regions) is described. The fields are driven by idealized apertures on the cavity wall. A modal expansion of the driven fields provides insight about thermal energy deposition in the load.
Design guide for calculating fluid damping for circular cylindrical structures. [LMFBR
Chen, S.S.
1983-06-01
Fluid damping plays an important role for structures submerged in fluid, subjected to flow, or conveying fluid. This design guide presents a summary of calculational procedures and design data for fluid damping for circular cylinders vibrating in quiescent fluid, crossflow, and parallel flow.
NASA Technical Reports Server (NTRS)
Starnes, James H.; Rose, Cheryl A.
1998-01-01
The results of an analytical study of the nonlinear response of a thin unstiffened aluminum cylindrical shell with a longitudinal crack are presented. The shell is analyzed with a nonlinear shell analysis code that maintains the shell in a nonlinear equilibrium state while the crack is grown. The analysis accurately accounts for global and local structural response phenomena. Results are presented for internal pressure, axial compression, and combined internal pressure and axial compression loads. The effects of varying crack length on the nonlinear response of the shell subjected to internal pressure are described. The effects of varying crack length on the prebuckling, buckling and postbuckling responses of the shell subjected to axial compression, and subjected to combined internal pressure and axial compression are also described. The results indicate that the nonlinear interaction between the in-plane stress resultants and the out-of-plane displacements near a crack can significantly affect the structural response of the shell. The results also indicate that crack growth instabilities and shell buckling instabilities can both affect the response of the shell as the crack length is increased.
NASA Astrophysics Data System (ADS)
Rajabi, Majid; Behzad, Mehdi
2014-10-01
A body insonified by a constant (time-varying) intensity sound field is known to experience a steady (oscillatory) force that is called the steady-state (dynamic) acoustic radiation force. Using the classical resonance scattering theorem (RST) which suggests the scattered field as a superposition of a resonance field and a background (non-resonance) component, we show that the radiation force acting on a cylindrical shell may be synthesized as a composition of three components: background part, resonance part and their interaction. The background component reveals the pure geometrical reflection effects and illustrates a regular behavior with respect to frequency, while the others demonstrate a singular behavior near the resonance frequencies. The results illustrate that the resonance effects associated to partial waves can be isolated by the subtraction of the background component from the total (steady-state or dynamic) radiation force function (i.e., residue component). In the case of steady-state radiation force, the components are exerted on the body as static forces. For the case of oscillatory amplitude excitation, the components are exerted at the modulation frequency with frequency-dependant phase shifts. The results demonstrate the dominant contribution of the non-resonance component of dynamic radiation force at high frequencies with respect to the residue component, which offers the potential application of ultrasound stimulated vibro-acoustic spectroscopy technique in low frequency resonance spectroscopy purposes. Furthermore, the proposed formulation may be useful essentially due to its intrinsic value in physical acoustics. In addition, it may unveil the contribution of resonance modes in the dynamic radiation force experienced by the cylindrical objects and its underlying physics.
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.
NASA Astrophysics Data System (ADS)
Bakulin, V. N.; Volkov, E. N.; Nedbai, A. Ya.
2016-06-01
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)
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.
Chaotic Energy Exchange Through Auto-Parametric Resonance in Cylindrical Shells
NASA Astrophysics Data System (ADS)
POPOV, A. A.; THOMPSON, J. M. T.; MCROBIE, F. A.
2001-11-01
Internal auto-parametric instabilities in the free non-linear vibrations of a cylindrical shell are studied numerically, focusing on two modes (a concertina mode and a chequerboard mode) whose non-linear interaction breaks the in-out symmetry of the linear vibration theory. The two-mode interaction leads to preferred vibration patterns with larger deflection inwards than outwards, and at internal resonance, significant energy transfer occurs between the modes. This has regular and chaotic features. Here, direct numerical integration is employed to examine chaotic motions. Using a set of 2-D Poincaré sections, each valid for a fixed level of the Hamiltonian, H, the instability under increasing H appears, as a supercritical period-doubling pitchfork bifurcation. Chaotic motions near a homoclinic separatrix appear immediately after the bifurcation, giving an irregular exchange of energy. This chaos occurs at arbitrarily low amplitude as perfect tuning is approached. The instability manifests itself as repeating excursions around the separatrix, and a number of practical predictions can be made. These include the magnitude of the excursion, the time taken to reach this magnitude and the degree of chaos and unpredictability in the outcome. The effect of small damping is to pull the motion away from what was the chaotic separatrix, giving a response that resembles, for a while, the lower-energy quasi-periodic orbits of the underlying Hamiltonian system.
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.
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.
Zamani Nejad, Mohammad; Jabbari, Mehdi; Ghannad, Mehdi
2014-01-01
Using disk form multilayers, a semi-analytical solution has been derived for determination of displacements and stresses in a rotating cylindrical shell with variable thickness under uniform pressure. The thick cylinder is divided into disk form layers form with their thickness corresponding to the thickness of the cylinder. Due to the existence of shear stress in the thick cylindrical shell with variable thickness, the equations governing disk layers are obtained based on first-order shear deformation theory (FSDT). These equations are in the form of a set of general differential equations. Given that the cylinder is divided into n disks, n sets of differential equations are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. A numerical solution using finite element method (FEM) is also presented and good agreement was found. PMID:24719582
NASA Astrophysics Data System (ADS)
Daneshfar, Nader; Moradbeigi, Nasrin
2015-12-01
This article considers the problem of finding the electrostatic potential that is given in terms of a scalar function called Green function in dielectric cylindrical nanoparticles with core-shell structure using the image charge method. By using this method that allows us to solve differential form of electric potential problem by the Green function, we investigate the distribution of the electric field in the configuration of a cylindrical nanoparticle surrounded by a continuum dielectric medium. By utilizing this well-known method, we obtain exact analytical formulas for the electrostatic potential and the electric field inside the shell, core and surrounding space of nanoparticle that can be applied to analysis of electromagnetic problems, electrostatic interactions in biomolecular simulations and also computer simulations of condensed-matter media.
NASA Astrophysics Data System (ADS)
Liu, Hongmin; Chen, Suwen; Peng, Yan; Sun, Jianliang
2015-01-01
As the traditional forging process has many problems such as low efficiency, high consumption of material and energy, large cylindrical shell rolling is introduced. Large cylindrical shell rolling is a typical rotary forming technology, and the upper and lower rolls have different radii and speeds. To quickly predict the three-dimensional stresses and eliminate fishtail defect, an improved strip layer method is developed, in which the asymmetry of the upper and lower rolls, non-uniform deformation and stress, as well as the asymmetrical spread on the end surface are considered. The deformation zone is divided into a certain number of layers and strips along the thickness and width, respectively. The transverse displacement model is constructed by polynomial function, in order to increase the computation speed greatly. From the metal plastic mechanics principle, the three-dimensional stress models are established. The genetic algorithm is used for optimization calculation in an industrial experiment example. The results show that the rolling pressure, the normal stresses, the upper and lower friction stress distributions are not similar with those of a general plate rolling. There are two relative maximum values in rolling pressure distribution. The upper and lower longitudinal friction stresses change direction nearby the upper and lower neutral points, respectively. The fishtail profile of spread on the end surface is predicted satisfactorily. The reduction could be helpful to eliminate fishtail defect. The large cylindrical shell rolling example illustrates the calculation results acquired rapidly are good agreements with the finite element simulation and experimental values of previous study. A highly effective and reliable three-dimensional simulation method is proposed for large cylindrical shell rolling and other asymmetrical rolling.
NASA Astrophysics Data System (ADS)
Sun, Dongming; Wang, Sheng; Sakurai, Junpei; Choi, Kee-Bong; Shimokohbe, Akira; Hata, Seiichi
2010-04-01
A piezoelectric linear ultrasonic motor is proposed, with a cylindrical stator and slider structure. The length and diameter of the motor are about 10 and 1.5 mm, respectively. The stator consists of two piezoelectric ceramic (PZT) tubes connected by a thin film metallic glass (TFMG) pipe. The stator is designed based on theoretical analyses and finite element method (FEM) simulation. The traveling wave propagation is obtained in the FEM simulation under the proper geometrical sizes, suitable boundary conditions and driving voltage signals. The trajectories of particles on the TFMG pipe are elliptical motion. In the experiment, a 25 µm thick TFMG pipe is fabricated using the rotating magnetron sputtering technique and the vibration characteristics of the stator are measured by a laser Doppler vibrometer (LDV) system. Bidirectional motion of the slider is observed around 600 kHz, the maximum velocity is near to 40 mm s - 1 at 50 Vp-p for the loose slider and the maximum output force is 6 mN at 70 Vp-p for the tight slider.
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 Technical Reports Server (NTRS)
Delale, F.; Erdogan, F.
1982-01-01
The line-spring model developed by Rice and Levy (1972) is used to obtain an approximate solution for a cylindrical shell containing a part-through surface crack. A Reissner type theory is used to account for the effects of the transverse shear deformations, and the stress intensity factor at the deepest penetration point of the crack is 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, and qualitatively the line-spring model gives the expected results in comparison with elasticity solutions.
NASA Astrophysics Data System (ADS)
Ng, Kam Wing
A theoretical and experimental study was conducted to investigate the flow-induced noise and vibration caused by confined jet flows in a cylindrical duct. Unrestricted pipe flow and flows restricted by various orifices were tested for a wide range of velocities to simulate the flow in piping systems. Wall pressure data showed that the noise levels vary with the pipe's axial location and the peak noise is located at the vicinity of the end of the jet potential core. A non-dimensional wall pressure spectrum was established for the various confined jets by the Strouhal relationship, where the length scale is the jet hydraulic diameter. This jet pressure spectrum agrees with the wall pressure spectrum of a turbulent boundary layer above a rigid plane. Correlations of wall pressure fluctuations and pipe wall acceleration signals showed that jet flows generate more deterministic features than pipe flow. The coherence functions of the wall pressure and pipe wall acceleration signals are relatively high near the exit of the jet. The high coherence is probably due to the large-scale coherent structures. An analytical model was developed to study the effect of the turbulent jet flow field on the wall pressure and vibratory motion of the duct wall. Based on flow field measurements, the blocked surface pressure was calculated using Lighthill's method, and then used to drive the fluid -filled shell. The wall pressure and pipe wall acceleration were determined by solving the coupled fluid solid interaction problem. The wall pressure was obtained by summing the blocked surface pressure and the pressure due to the wall vibration. An amplitude modulated convecting wave field was used to simulate the moving acoustic sources of the jet. The random nature of the turbulent jet was incorporated into the analytical model. Specifically, the acoustic pressure was assumed to result from hydrodynamic pressure fluctuations which are uncorrelated in the radial direction, but are correlated in
NASA Astrophysics Data System (ADS)
Kivity, Y.; Florie, C.; Lenselink, H.
1993-02-01
This paper considers the plastic deformation of a thin cylindrical shell subjected to an internal explosion. It is assumed that the explosive charge is placed on the axis of symmetry of the shell so that an axisymmetric blast wave is produced. The shell response is calculated assuming an elastic-perfectly plastic material. The plastic response is evaluated for two types of loads. In the first type, the blast is assumed to have an ideal shock front with a discontinuous jump to the peak pressure. In the second type of loading, the shock front has a finite rise-time. This type of loading was introduced to study the effect of finite width shock fronts. Such finite width shock fronts are typical of hydrocode calculations when simulating problems involving blast waves and their interactions with adjacent structures. It is found that for equal impulse loads, the numerical rise-time reduces the shell plastic response significantly. Numerical calculations with a three-dimensional hydrocode are presented to illustrate the analytical results. A generalization of the analysis is given which may be used to determine the required mesh resolution of a hydrocode calculation in order to obtain a prescribed accuracy in the shell response.
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.
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 Astrophysics Data System (ADS)
Wang, Qingshan; Shi, Dongyan; Pang, Fuzhen; Liang, Qian
2016-04-01
A Fourier-Ritz method for predicting the free vibration of composite laminated circular panels and shells of revolution subjected to various combinations of classical and non-classical boundary conditions is presented in this paper. A modified Fourier series approach in conjunction with a Ritz technique is employed to derive the formulation based on the first-order shear deformation theory. The general boundary condition can be achieved by the boundary spring technique in which three types of liner and two types of rotation springs along the edges of the composite laminated circular panels and shells of revolution are set to imitate the boundary force. Besides, the complete shells of revolution can be achieved by using the coupling spring technique to imitate the kinematic compatibility and physical compatibility conditions of composite laminated circular panels at the common meridian with θ = 0 and 2π. The comparisons established in a sufficiently conclusive manner show that the present formulation is capable of yielding highly accurate solutions with little computational effort. The influence of boundary and coupling restraint parameters, circumference angles, stiffness ratios, numbers of layer and fiber orientations on the vibration behavior of the composite laminated circular panels and shells of revolution are also discussed.
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.
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
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.
2015-12-15
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)].
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)].
NASA Astrophysics Data System (ADS)
Gleiser, Reinaldo J.; Barraco, Daniel E.
2014-03-01
In this paper we study the evolution of the ‘Momentarily Static and Radiation Free’ (MSRF) initial data for the Apostolatos-Thorne cylindrical shell model. After briefly reviewing the equations of motion, the definition of the MSRF initial data and of its relation to the static solution that corresponds to the given conserved intrinsic parameters of the shell, we show that for MSRF data the initial acceleration of the shell is always directed towards the static radius. We analyse in detail the relation between the parameters characterizing the configuration corresponding to the initial data and those for the assumed final static configuration, and show that, once the appropriate properties of the solutions of the cylindrical wave equation are taken into account, there is a priori no conflict for any choice of initial MSRF data, in contrast with some recent results of Nakao, Ida and Kurita. To obtain a more detailed description of the evolution we consider the case where the problem can be analysed in the linear approximation, and show that the evolution is stable in all cases. The possible form of the approach to the final static configuration is also analysed. We find that this approach is very slow, with an inverse logarithmic dependence on time at fixed radius. Given the absence of analytic solutions for the problem, we introduce a numerical computation procedure that allows us to visualize the explicit form of the evolution of the shell and the gravitational field up to large times. The results are in agreement with the qualitative behaviour conjectured by Apostolatos and Thorne, with an initial damped oscillatory stage, but we find that these oscillations are not about the final static radius but rather about a position that approaches slowly that of the static final state, as indicated by our analysis. We also include one appendix, where we review some properties of the solutions of the cylindrical wave equation, and prove the existence of solutions with
NASA Astrophysics Data System (ADS)
Tornabene, Francesco; Viola, Erasmo; Inman, Daniel J.
2009-12-01
This paper focuses on the dynamic behavior of functionally graded conical, cylindrical shells and annular plates. The last two structures are obtained as special cases of the conical shell formulation. The first-order shear deformation theory (FSDT) is used to analyze the above moderately thick structural elements. The treatment is developed within the theory of linear elasticity, when materials are assumed to be isotropic and inhomogeneous through the thickness direction. The two-constituent functionally graded shell consists of ceramic and metal that are graded through the thickness, from one surface of the shell to the other. Two different power-law distributions are considered for the ceramic volume fraction. The homogeneous isotropic material is inferred as a special case of functionally graded materials (FGM). The governing equations of motion, expressed as functions of five kinematic parameters, are discretized by means of the generalized differential quadrature (GDQ) method. The discretization of the system leads to a standard linear eigenvalue problem, where two independent variables are involved without using the Fourier modal expansion methodology. For the homogeneous isotropic special case, numerical solutions are compared with the ones obtained using commercial programs such as Abaqus, Ansys, Nastran, Straus, Pro/Mechanica. Very good agreement is observed. Furthermore, the convergence rate of natural frequencies is shown to be very fast and the stability of the numerical methodology is very good. Different typologies of non-uniform grid point distributions are considered. Finally, for the functionally graded material case numerical results illustrate the influence of the power-law exponent and of the power-law distribution choice on the mechanical behavior of shell structures.
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)
Corrado, Charles N., Jr.
The measurements and analyses were conducted over a mid-frequency range of 2 < ka < 12 corresponding to about 1/2 to 3 times the ring frequency of the empty shell. The measurements were all conducted with the use of wide-band pulses yielding good time resolution of propagating waves. Various time and frequency domain representations of the scattered field are presented to illustrate the evolution of observed backscattering processes. Although the field measured at all aspect angles is reviewed, emphasis is placed on interpretation of the backscatter observed over a range within 30 degrees of beam aspect where phase matched (coincident) excitation of membrane waves occurs. Coincident shear wave radiation is the dominant source of backscatter generated by the empty shell at oblique angles of incidence within 30^circ of beam aspect. Peak levels of backscatter are generally found at combinations of aspect angle and frequency where coincidence and peak levels of length-scale modulation coexist. Coincident back radiation of shear waves remains evident in the backscatter of the ring stiffened shell, but the backscatter is smeared in time and frequency because the rings directly scatter energy to the acoustic medium, as well as from one membrane wave type to another, and to subsonic flexural waves. The decay rate of the empty shell backscatter exceeds that of the ring stiffened shell by a factor of 2-3 because the rings scatter energy to poorly radiating waves. Although details of the backscatter produced by the empty and ring stiffened shells differ, peak levels of target strength consistently fall within a range of -20 to -15 dB re 1 m. The internal loading further impairs coincident radiation but increases the target strength by about 2 dB for ka > 5.5. The damping provided by the resilient mounts increases backscatter decay rates by roughly 1.2 to 1.4 relative to those of the ring stiffened shell. Bistatic measurements of the internally loaded shell also demonstrate
Non-linear vibrations of laminated cylindrical shallow shells under thermomechanical loading
NASA Astrophysics Data System (ADS)
Ribeiro, P.; Jansen, E.
2008-08-01
The geometrically non-linear vibrations of linear elastic composite laminated shallow shells under the simultaneous action of thermal fields and mechanical excitations are analysed. For this purpose, a model based on a very efficient p-version first-order shear deformation finite element, with hierarchical basis functions, is employed. The equations of motion are solved in the time domain by a Newmark implicit time integration method. The model and code developed are partially validated by comparison with published data. Parametric studies are carried out in order to study the influence of temperature change, initial curvature, panel thickness and fibre orientation on the shells' dynamics.
NASA Astrophysics Data System (ADS)
Ebaid, A.
2008-08-01
In this Letter, we considered a numerical treatment for the solution of the hydromagnetic peristaltic flow of a bio-fluid with variable viscosity in a circular cylindrical tube using Adomian decomposition method and a modified form of this method. The axial velocity is obtained in a closed form. Comparison is made between the results obtained by only three terms of Adomian series with those obtained previously by perturbation technique. It is observed that only few terms of the series expansion are required to obtain the numerical solution with good accuracy.
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 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.
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.
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.
NASA Technical Reports Server (NTRS)
Yahsi, O. S.; Erdogan, F.
1985-01-01
In this paper a cylindrical shell having a very stiff end plate or a flange is considered. It is assumed that near the end the cylinder contains an axial flow which may be modeled as a part-through surface crack or through crack. The primary objective is to study the effect of the end constraining on the stress intensity factor which is the main fracture mechanics parameter. 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 I 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 equation of the shell problem has the same generalized Cauchy kernel as the corresponding plane stress elasticity problem. Even though the problem is formulated for a general surface crack profile and arbitrary crack surface tractions, the numerical results are obtained only for a semielliptic part-through axial crack located at the inside or outside surface of the cylinder and for internal pressure acting on the cylinder. The stress intensity factors are calculated and presented for a relatively wide range of dimensionless length parameters of the problem.
NASA Astrophysics Data System (ADS)
Britt, Vicki Owen
A preliminary design tool for metallic stiffened fuselage cylindrical panels subjected to longitudinal compression has been developed and validated by comparison to test results. Several methodologies for stiffened panel buckling and failure predictions were examined and evaluated. An appropriate level of analysis fidelity was determined for different failure modes and design details. Results from panel tests conducted to verify analytical methods used to design the Gulfstream V aircraft were presented. The panels were representative of four general skin/stringer configurations on the aircraft. Finite Element analyses and standard analytical methods were used to predict panel failure loads. The accuracy of the finite element analysis predictions was dependent upon the level of detail included in the model. The inclusion of such details as fasteners had a significant effect on the predicted failure load. The omission of such complexities from the finite element model led to unconservative failure predictions. Standard analytical methods were found to be more efficient than finite element methods and produced conservative panel failure loads. Improvements for a preliminary design tool were identified to reduce conservatism in failure predictions and thereby reduce structural weight.
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.
Series solution for a cylindrical composite shell subject to axisymmetric loadings
NASA Astrophysics Data System (ADS)
Lindstrom, D. W.
1990-07-01
Elasticity equations were solved to an arbitrary degree of precision for a thick-walled orthotropic cylinder subject to axisymmetric loading. The theory is directly applicable to a layered composite material where each layer is orthotropic in character. The solution proceeds by representing the deformations of the cylinder wall as a power series in a nondimensional radial parameter. By introducing a generalized stress resultant and a generalized stiffness for the material, a series of coupled second order differential equations in the coefficients of the deformation series results. These were solved using a generalized eigenvalue technique for an infinitely long cylinder, a simply held cylinder, and a rigidly clamped cylinder. The solution was shown to reduce to standard shell solutions for thin cylinders. A thick-walled filament wound test specimen is also described that when fabricated and pressurized would experimentally verify the refined theory developed.
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.
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.
NASA Astrophysics Data System (ADS)
Pollock, Justin G.; Iyer, Ashwin K.; Pratap, Dheeraj; Anantha Ramakrishna, S.
2016-02-01
This paper investigates a class of circular waveguiding structures containing anisotropic metamaterials and explores their potential benefits in applications from RF to optical frequencies. The introduction of anisotropy in these waveguides is shown to provide substantial control of the dispersion and field distributions of several supported modes. For exotic material parameters such as permittivity and permeability that are typically associated with metamaterials, intriguing propagation phenomena such as backward-wave behavior, frequency-reduced modes, monomodal propagation, and field confinement are observed and provide enabling functionalities for a wide range of RF/microwave and optical applications.
NASA Astrophysics Data System (ADS)
Schmidt, J. M.; Cairns, Iver H.; Xie, Hong; St. Cyr, O. C.; Gopalswamy, N.
2016-03-01
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)
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.
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)
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 Astrophysics Data System (ADS)
Isaev, S. A.; Guvernyuk, S. V.; Zubin, M. A.; Baranov, P. A.; Ermakov, A. M.
2015-01-01
Comparative analysis of the results of solution of the steady-state Reynolds equations closed with the use of the shear-stress transfer model for the air fl ow in a divergent channel with suction of the air from the surface of the cylindrical central body positioned in the circular vortex cavity built in the lower wall of the channel with the corresponding experimental data has been performed.
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
Technology Transfer Automated Retrieval System (TEKTRAN)
. This paper describes a method to determine the moisture content of in-shell peanuts with a parallel-plate electrode system fitted inside a cylinder by using impedance measurements made on the system. Two parallel-plate electrodes were mounted inside a cylinder, made of acrylic material, and the s...
Effect of heating rate on the stress-strain state in a cylindrical shell with a stiffener ring
Sorokina, I.V.; Babanskii, V.G.; Rachkov, V.I.
1988-05-01
The effect of the heating rate on the stress-strain state of chemical production systems during start-up was examined in a quasistatic formulation of the thermoelasticity problem. The temperature fields were determined for a thin-walled shell with a stiffener ring by solving the nonstationary problem of heat conductivity. The calculations incorporate heat balance equations using the thermal conductivity and specific heat of the shell and ring materials. Thermoelastic stresses were determined for the calculated temperature field as a function of time. Results show that the heating rate has a strong effect on the stress-strain state of the thin-wall structures in the zone of the edge effect and that a linear increase in heating rate increases thermal stresses almost proportionally. The method was designed for optimizing the time required for startup and shutdown of chemical plant equipment and maximizing plant efficiency.
Response of moderately thick laminated cross-ply composite shells subjected to random excitation
NASA Technical Reports Server (NTRS)
Elishakoff, Isaak; Cederbaum, Gabriel; Librescu, Liviu
1989-01-01
This study deals with the dynamic response of transverse shear deformable laminated shells subjected to random excitation. The analysis encompasses the following problems: (1) the dynamic response of circular cylindrical shells of finite length excited by an axisymmetric uniform ring loading, stationary in time, and (2) the response of spherical and cylindrical panels subjected to stationary random loadings with uniform spatial distribution. The associated equations governing the structural theory of shells are derived upon discarding the classical Love-Kirchhoff (L-K) assumptions. In this sense, the theory is formulated in the framework of the first-order transverse shear deformation theory (FSDT).
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).
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.
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.
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.
Free Vibration Analysis of Cylindrical Tanks Partially Filled with Liquid
NASA Astrophysics Data System (ADS)
Gonçalves, P. B.; Ramos, N. R. S. S.
1996-08-01
A simple but effective modal solution based on the underlying ideas of the hierarchical finite element method is presented for evaluating the free vibration characteristics of vertical, thin, circular, cylindrical shells, partially or completely filled with liquid and subjected to any variationally consistent set of boundary conditions on the lower and upper boundaries. Effects of static liquid pressure, in-plane inertias and liquid free surface motions are taken into account. The solution of the shell problem is obtained through a procedure in which Sander's shell equations are transformed into a new system of first order ordinary differential equations which are solved by the Galerkin error-minimization procedure. The system variables are those quantities which appear in the boundary conditions on a rotationally symmetric edge of a cylindrical shell. The liquid is taken as non-viscous and incompressible, and the coupling between the deformable shell and this medium is taken into account. The solution for the liquid velocity potential is assumed as a sum of two sets of linear combinations of suitable harmonic functions which satisfy Laplace equation and the relevant boundary conditions. This procedure leads to a determinantal equation for the determination of the shell and liquid natural frequencies and the associated mode shapes. Application of the method to a few selected cases and comparisons of the numerical results with those obtained by other theories and from experiments are found to be good and demonstrate the effectiveness and accuracy of the present methodology.
NASA Astrophysics Data System (ADS)
Zhou, Jie; Bhaskar, Atul; Zhang, Xin
2014-03-01
Sound transmission through a system of double shells, lined with poroelastic material in the presence of external mean flow, is studied. The porous material is modeled as an equivalent fluid because shear wave contributions are known to be insignificant. This is achieved by accounting for the energetically most dominant wave types in the calculations. The transmission characteristics of the sandwich construction are presented for different incidence angles and Mach numbers over a wide frequency range. It is noted that the transmission loss exhibits three dips on the frequency axis as opposed to flat panels where there are only two such frequencies—results are discussed in the light of these observations. Flow is shown to decrease the transmission loss below the ring frequency, but increase this above the ring frequency due to the negative stiffness and the damping effect added by the flow. In the absence of external mean flow, porous material provides superior insulation for most part of the frequency band of interest. However, in the presence of external flow, this is true only below the ring frequency—above this frequency, the presence of air gap in sandwich constructions is the dominant factor that determines the acoustic performance. In the absence of external flow, an air gap always improves sound insulation.
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.
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.
NASA Astrophysics Data System (ADS)
Abrosimov, N. A.; Novosel'tseva, N. A.
2015-11-01
A method for identification of material parameters of the constitutive relations of elastoplastic and viscoelastic deformation of isotropic and composite materials is developed. The method is based on minimizing the functional of the residue of results of numerical and experimental analysis of unsteady deformation of structural elements made of examined materials. The method is tested, and prospects of its application for determining material parameters of viscoelastic and elastoplastic models of nonlinear deformation of cylindrical metal-plastic shells under explosive loading are demonstrated.
Mobility Power Flow (MPF) approach applied to a fluid-loaded shell with a plate bulkhead
NASA Astrophysics Data System (ADS)
McCain, Thomas Scott; Cuschieri, Joseph M.
Cylindrical shells, immersed in heavy fluids, coupled to plate-like bulkheads are commonly encountered in engineered structures. Often the performance of such systems is dependent upon the vibrational characteristics of the system as a whole or parts thereof. In distributed systems such as these, characterization of vibrational energy transmission between substructures, in addition to the vibrational response, is required for complete understanding of the vibrational characteristics of the system. In this paper, the vibrational characteristics of an infinite, thin cylindrical shell, immersed in an unbounded heavy fluid, coupled internally to a damped, circular plate is considered.
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
Circularly-Polarized Microstrip Antenna
NASA Technical Reports Server (NTRS)
Stanton, P. H.
1985-01-01
Microstrip construction compact for mobile applications. Circularly polarized microstrip antenna made of concentric cylindrical layers of conductive and dielectric materials. Coaxial cable feedlines connected to horizontal and vertical subelements from inside. Vertical subelement acts as ground for horizontal subelement.
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.
NASA Astrophysics Data System (ADS)
Serebryannikov, A. E.; Ozbay, Ekmel
2009-11-01
We demonstrate that a circular dielectric cylinder can be nearly invisible at multiple frequencies when being coated with a ring shell, which is made of an isotropic material simultaneously showing large positive or large negative values of permittivity and permeability. The suggested cloaking mechanism is based on the use of radial resonances, which are similar to those in conventional Fabry-Perot resonators. It can be used for cylindrical objects for a wide range of variation of the diameter-to-wavelength ratio, which includes the values corresponding to subwavelength to resonant-sized objects. The presence of frequency dispersion of the shell material positively affects the possibility of multifrequency operation.
NASA Astrophysics Data System (ADS)
Yilmaz, Mehmet F.; Safronova, Alla S.; Kantsyrev, Victor L.; Esaulov, Andrey A.; Williamson, Kenneth M.; Shrestha, Ishor K.; Weller, Michael E.; Osborne, Glenn C.; Shlyaptseva, Veronica V.
2012-03-01
Radiative emission from alloyed Al single, double and compact cylindrical wire arrays have been studied using the 1 MA Zebra UNR generator. Single planar wire arrays using ten wires and double planar wire arrays and compact cylindrical wire arrays (CCWA) that both had sixteen wires were utilized. The wire composition is Al-5056 (95% of Al and 5% of Mg). We have observed that implosion of these alloyed Al wire loads generated optically thick Al plasmas that can be diagnosed using K-shell Mg lines. In particular, among the considered loads, the K-shell lines of Al from implosions of the double planar wire arrays have the highest optical depth for He-like Al resonance transitions, which occurred near the stagnation phase. X-ray time-gated and time-integrated spectra and pinhole images as well as photoconductive detectors signals were analyzed to provide information on the plasma parameters; electron temperatures and densities, implosion dynamics features and power and yields of the X-ray radiation. Previously developed non-LTE models were applied to model axially-resolved time-integrated, as well as time-gated spatially-integrated, K-shell spectra from Al and Mg. The derived time-dependent electron temperature, density and axial opacity were studied and compared. In addition, the wire ablation dynamics model (WADM) was used to calculate the kinetic energy of the plasma, which with the aid of a Local Thermal Equilibrium (LTE) magneto-hydrodynamics (MHD) simulation, allowed to estimate the precursor and stagnated z-pinch plasma electron temperatures from implosions of wire array loads.
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.
Batdorf parameter for the spherical shells tectonics
NASA Astrophysics Data System (ADS)
Kikuchi, Kazuhei; Nagahama, Hiroyuki
2015-04-01
The buckling phenomena of the subducting lithosphere due to the sphericity of the earth has been studied as spherical shell tectonics which happen the megaquake along the boundary of subducting lithosphere. The earthquake scale is decided by slab length or arc length. However, a relationship between slab length and the normalized hydrostatic pressure along the bottom circumferential edge of a hemispherical shell has not been clear yet. So, by using the data set of the geometrical parameters for subducting lithosphere andBuckingham's Pi-theorem, we found out a new linear relationship between Batdorf parameter Z = L2(l - v2)0.5/(Rh) for the measurement of the slab length L and the normalized hydrostatic pressure along the bottom circumferential edge of a hemispherical shell Q = qRL2/(π2D), where D = Eh3/[12(1 - v2)] with E = modulus of elasticity of lithosphere, R is Earth radius, q is the hydrostatic pressure along the bottom circumferential edge of a hemispherical shell, and h is the thickness of subducting lithosphere. In the engineering sciences, a similar relationship between Batdorf parameter for the panel length and normalized hydrostatic pressure was proposed for the buckling of partially liquid-filled circular cylindrical shells under hydrostatic pressure. Moreover, by previous researches, the slab length is approximately proportional to the arc length or the lithosphere thickness related to lithosphere age. Therefore, the Batdorf parameter for subducting lithosphere is an important parameter for the spherical shells tectonics.
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 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.