Nonlinear Response of a Cylindrical Shell to an Impulsive Pressure

1969 ◽  
Vol 36 (2) ◽  
pp. 277-284 ◽  
Author(s):  
E. G. Lovell ◽  
I. K. McIvor
Keyword(s):  
Cylindrical Shell ◽  
Nonlinear Response ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Fundamental Difference ◽  
Large Displacements ◽  
Flexural Response ◽  
Modal Coupling ◽  
Impulsive Pressure

When a circular cylindrical shell (plane strain) is subjected to a uniform radial impulse, the resulting circular mode may be unstable. In such a case flexural motion is excited, resulting in rather large displacements and stress. A previous nonlinear analysis [1]1 used a linear inextensionality constraint and displacement representation for the flexural response. A formulation employing a nonlinear inextensionality constraint is presented in this paper, and a comparison is made with the earlier work. The most significant result is a fundamental difference between the equations of motion; in this analysis the nonlinear modal coupling is primarily inertial. The condition for stability of the circular mode is unaffected, but substantial differences may occur in the long-term (nonlinear) response.

Approximate Formulas for Cylindrical Shell Free Vibration Based on Vlasov’s and Enhanced Vlasov’s Semi-Momentless Theory

2018 ◽  
Author(s):  
Igor Orynyak ◽  
Yaroslav Dubyk
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Middle Surface ◽  
Axial Direction ◽  
Mode Shapes ◽  
Natural Mode ◽  
Transverse Deflection ◽  
Approximate Formulas

Simple approximate formulas for the natural frequencies of circular cylindrical shells are presented for modes in which transverse deflection dominates. Based on the Donnell-Mushtari thin shell theory the equations of motion of the circular cylindrical shell are introduced, using Vlasov assumptions and Fourier series for the circumferential direction, an exact solution in the axial direction is obtained. To improve the results assumptions of Vlasov’s semimomentless theory are enhanced, i.e. we have used only the hypothesis of middle surface inextensibility to obtain a solution in axial direction. Nonlinear characteristic equations and natural mode shapes, are derived for all type of boundary conditions. Good agreement with experimental data and FEM is shown and advantage over the existing formulas for a variety of boundary conditions is presented.

Nonlinear Response of an Elastic Cylindrical Shell to a Transient Acoustic Wave

1981 ◽  
Vol 48 (1) ◽  
pp. 15-24 ◽  
Author(s):  
T. L. Geers ◽  
C.-L. Yen
Keyword(s):  
Cylindrical Shell ◽  
Acoustic Wave ◽  
Nonlinear Response ◽  
Circular Cylindrical Shell ◽  
Elastic Cylindrical Shell ◽  
Fluid Medium ◽  
Energy Functionals ◽  
Potential Formulation ◽  
Rigorous Treatment ◽  
Residual Potential

Governing equations are developed for the nonlinear response of an infinite, elastic, circular cylindrical shell submerged in an infinite fluid medium and excited by a transverse, transient acoustic wave. These equations derive from circumferential Fourier-series decomposition of the field quantities appearing in appropriate energy functionals, and from application of the “residual potential formulation” for rigorous treatment of the fluid-structure interaction. Extensive numerical results are presented that provide understanding of the phenomenology involved.

Internal Resonance and Nonlinear Vibrations of Eccentric Rotating Composite Laminated Circular Cylindrical Shell

2019 ◽  
Author(s):  
Tao Liu ◽  
Wei Zhang ◽  
Yan Zheng ◽  
Yufei Zhang
Keyword(s):  
Cylindrical Shell ◽  
Differential Equations ◽  
Internal Resonance ◽  
Nonlinear Vibrations ◽  
Multiple Scales ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equations ◽  
Shear Deformation Theory ◽  
Internal Resonances

Abstract This paper is focused on the internal resonances and nonlinear vibrations of an eccentric rotating composite laminated circular cylindrical shell subjected to the lateral excitation and the parametric excitation. Based on Love thin shear deformation theory, the nonlinear partial differential equations of motion for the eccentric rotating composite laminated circular cylindrical shell are established by Hamilton’s principle, which are derived into a set of coupled nonlinear ordinary differential equations by the Galerkin discretization. The excitation conditions of the internal resonance is found through the Campbell diagram, and the effects of eccentricity ratio and geometric papameters on the internal resonance of the eccentric rotating system are studied. Then, the method of multiple scales is employed to obtain the four-dimensional nonlinear averaged equations in the case of 1:2 internal resonance and principal parametric resonance-1/2 subharmonic resonance. Finally, we study the nonlinear vibrations of the eccentric rotating composite laminated circular cylindrical shell systems.

Dynamic Response Analysis and Comparative Study of Circular Cylindrical Shell Subjected to Radial Impact

2007 ◽  
Vol 51 (02) ◽  
pp. 94-103
Author(s):  
Li Xuebin
Keyword(s):  
Cylindrical Shell ◽  
Dynamic Response ◽  
Normal Mode ◽  
Shell Theory ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Response Analysis ◽  
Mode Theory ◽  
Normal Mode Theory ◽  
Exact Derivation

Following Flu¨ gge's exact derivation for the buckling of cylindrical shells, the equations of motion for dynamic loading of a circular cylindrical shell under external hydrostatic pressure have been formulated. The normal mode theory is used to provide transient dynamic response for the equations of motion. The responses of displacements, strain, and stress are obtained for the area of impact, while those outside the area of impact are also calculated. The accuracy of normal mode theory and Timoshenko shell theory are examined in this paper.

Vibration analysis of a thin eccentric rotating circular cylindrical shell

2018 ◽  
Vol 233 (5) ◽  
pp. 1588-1600 ◽  
Author(s):  
Zhihua Wu ◽  
Guo Yao ◽  
Yimin Zhang
Keyword(s):  
Cylindrical Shell ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Initial Stresses ◽  
Eccentric Rotation ◽  
Element Analysis ◽  
Coriolis Forces ◽  
Rotating Speed ◽  
Irregular Frequency ◽  
Thin Shell Theory

In this study, the vibration characteristics of a thin eccentric rotating circular cylindrical shell with simply supported boundary conditions are studied. Energy formulations based on Flügge’s thin shell theory, Hamilton’s principle, and the method of linear approximation are applied to derive the governing equations of motion. In addition to the effects of centrifugal and Coriolis forces, the effect of nonuniform initial stresses resulting from eccentric rotation are taken into account. The natural frequencies of the shell with respect to rotating speed and eccentricity are obtained using Galerkin’s method. To validate the present analysis, comparisons are carried out with the results in published literatures and finite element analysis, and good agreements are obtained. The effect of the eccentricity on the natural frequency of the eccentric rotating cylindrical shell is investigated. Some further numerical results are given to illustrate the irregular frequency mutation behaviors resulting from the eccentricity. The effects of the eccentricity on the critical speed and flutter speed of the eccentric rotating circular cylindrical shell are also investigated.

Inelastic Response of an Infinite Cylindrical Shell to Transient Acoustic Waves

1989 ◽  
Vol 56 (4) ◽  
pp. 900-909 ◽  
Author(s):  
Thomas L. Geers ◽  
Chi-Lin Yen
Keyword(s):  
Cylindrical Shell ◽  
Acoustic Waves ◽  
Nonlinear Response ◽  
Circular Cylindrical Shell ◽  
Pressure Profile ◽  
Response Analysis ◽  
Fluid Medium ◽  
Convolution Integrals ◽  
Infinite Cylindrical Shell ◽  
Incident Waves

The geometrically and constitutively nonlinear response of an infinite, circular, cylindrical shell submerged in an infinite fluid medium to a transverse, transient acoustic wave is analyzed. Circumferential Fourier series solutions are obtained through the numerical integration of coupled ordinary differential equations and convolution integrals. Numerical results are presented in the form of response histories, response snapshots, and iso-damage curves for incident waves of rectangular pressure profile. Response solutions obtained with the first-order doubly asymptotic approximation are compared with their “exact” counterparts. It is found that doubly asymptotic approximations are unsuitable for two-dimensional, shock-response analysis of yielding submerged structures.

Dynamic Stability of an Isotropic Metal Foam Cylindrical Shell Subjected to External Pressure and Axial Compression

2011 ◽  
Vol 78 (4) ◽  
Author(s):  
Tomasz Belica ◽  
Marek Malinowski ◽  
Krzysztof Magnucki
Keyword(s):  
Cylindrical Shell ◽  
Dynamic Stability ◽  
Metal Foam ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Element Model ◽  
External Pressure ◽  
Combined Loads ◽  
Nonlinear Approach ◽  
Isotropic Metal

This paper presents a nonlinear approach with regard to the dynamic stability of an isotropic metal foam circular cylindrical shell subjected to combined loads. The mechanical properties of metal foam vary in the thickness direction. Combinations of external pressure and axial load are taken into account. A nonlinear hypothesis of deformation of a plane cross section is formulated. The system of partial differential equations of motion for a shell is derived on the basis of Hamilton’s principle. The system of equations is analytically solved by Galerkin’s method. Numerical investigations of dynamic stability for the family of cylindrical shells with regard to analytical solution are carried out. Moreover, finite element model analysis is presented, and the results of the numerical calculations are shown in figures.

Large Amplitude Forced Vibrations of Simply Supported Thin Cylindrical Shells

1973 ◽  
Vol 40 (2) ◽  
pp. 471-477 ◽  
Author(s):  
J. H. Ginsberg
Keyword(s):  
Nonlinear Response ◽  
Nonlinear Boundary ◽  
Circular Cylindrical Shell ◽  
Perturbation Technique ◽  
Equations Of Motion ◽  
Harmonic Excitation ◽  
Inertia Effects ◽  
Modal Expansion ◽  
Wide Range ◽  
Nonlinear Equations Of Motion

The response of a thin circular cylindrical shell to resonant harmonic excitation is examined by a modal expansion approach. The nonlinear strain-displacement relations lead to a nonlinear boundary condition, as well as nonlinear equations of motion. The solution, which retains tangential inertia effects, is obtained by a perturbation technique that yields a consistent first approximation of the nonlinear response. The results are applicable for a wide range of parameters and to cases of excitation near any of the three lowest natural frequencies corresponding to given axial and circumferential wavelengths. For situations where shallow shell theory is valid, the results of previous studies, which were based upon such a theory, are in close agreement.

SUPERSONIC FLUTTER CONTROL OF AN ELECTRORHEOLOGICAL FLUID-BASED SMART CIRCULAR CYLINDRICAL SHELL

2014 ◽  
Vol 14 (02) ◽  
pp. 1350064 ◽  
Author(s):  
SEYYED M. HASHEMINEJAD ◽  
M. AGHAYI MOTAALEGHI
Keyword(s):  
Cylindrical Shell ◽  
Gas Flow ◽  
Sliding Mode ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Electrorheological Fluid ◽  
Open Loop ◽  
Point Load ◽  
Integration Algorithm ◽  
Line Load

In this paper, active flutter suppression of a simply supported circular sandwich cylindrical shell with a tunable electrorheological fluid (ERF) core, under axial supersonic gas flow, is studied. The structural analysis is based on the classical thin shell theory, the ERF core is modeled as a first-order Kelvin–Voigt material, and the Krumhaar's modified supersonic piston theory is utilized to model the aerodynamic loading. Hamilton's principle is used to formulate the dynamic equations of motion together with the relevant boundary conditions. The generalized Fourier expansions in the circumferential and axial directions in conjunction with the classical Galerkin method are employed to set up the governing equations in the state-space domain. The critical free stream static pressures at which unstable oscillations arise are calculated for selected applied electric field strengths and cylinder length ratios. The Runge–Kutta time integration algorithm is used to determine the open-loop aeroelastic response of the system in two basic loading configurations, namely, a concentrated impulse point load and a sonic boom line load. Subsequently, a sliding mode control (SMC) strategy is adopted to actively suppress the closed loop system dynamic response in supersonic flight condition. Simulation results demonstrate performance and effectiveness of the adopted ERF-based SMC scheme. Limiting cases are considered and good agreements with the data available in the literature are obtained.

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