Effect of Boundary Conditions on Nonlinear Vibration and Flutter of Laminated Cylindrical Shells

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
E. L. Jansen
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Vibration ◽  
Cylindrical Shells ◽  
Perturbation Expansion ◽  
Present Theory ◽  
Dependent Variables ◽  
Lamination Theory ◽  
Initial Geometric Imperfections ◽  
Nonlinear Static ◽  
Laminated Cylindrical Shells

A nonlinear vibration analysis of laminated cylindrical shells is presented in which the effect of the specified boundary conditions at the shell edges, including nonlinear fundamental state deformations, can be accurately taken into account. The method is based on a perturbation expansion for both the frequency parameter and the dependent variables. The present theory includes the effects of finite vibration amplitudes, initial geometric imperfections, and a nonlinear static deformation. Nonlinear Donnell-type equations formulated in terms of the radial displacement W and an Airy stress function F are used, and classical lamination theory is employed. Furthermore, an extension of the theory is presented to analyze linearized flutter in supersonic flow, based on piston theory. The effect of different types of boundary conditions on the nonlinear vibration and linearized flutter behavior of cylindrical shells is illustrated for several characteristic cases.

The Effect of Boundary Conditions on Nonlinear Vibration and Flutter of Laminated Cylindrical Shells

2004 ◽  
Author(s):  
E. L. Jansen
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Vibration ◽  
Cylindrical Shells ◽  
Perturbation Expansion ◽  
Present Theory ◽  
Dependent Variables ◽  
Different Types ◽  
Lamination Theory ◽  
Initial Geometric Imperfections ◽  
Nonlinear Static

A nonlinear vibration analysis of cylindrical shells is presented, in which the specified boundary conditions at the shell edges can be satisfied rigorously. The method is based on a perturbation expansion for both the frequency parameter and the dependent variables. The present theory includes the effects of finite vibration amplitudes, initial geometric imperfections and a nonlinear static deformation. Nonlinear Donnell-type equations formulated in terms of the radial displacement W and an Airy stress function F are used, and classical lamination theory is employed. Further, an extension of the theory is presented to analyze linearized flutter in supersonic flow, based on piston theory. The effect of different types of boundary conditions on the nonlinear vibration and linearized flutter behavior of cylindrical shells is illustrated for several characteristic cases.

scholarly journals Research on nonlinear vibration control of laminated cylindrical shells with discontinuous piezoelectric layer

2021 ◽  
Author(s):  
Chaofeng Li ◽  
Peiyong Li ◽  
Xueyang Miao
Keyword(s):  
Cylindrical Shell ◽  
Vibration Control ◽  
Nonlinear Vibration ◽  
Piezoelectric Layer ◽  
Cylindrical Shells ◽  
Harmonic Balance Method ◽  
Amplitude Response ◽  
Nonlinear Vibration Control ◽  
Laminated Cylindrical Shell ◽  
Laminated Cylindrical Shells

Abstract In this paper, the nonlinear vibration control of the piezoelectric laminated cylindrical shell with point supported elastic boundary condition is analyzed, in which the geometric nonlinearity is considered by the first-order shear nonlinear shell theory. In the model, different boundary conditions are simulated by introducing a series of artificial springs. The elastic-electrically coupled differential equations of piezoelectric laminated cylindrical shells are obtained based on the Chebyshev polynomials and Lagrange equation, and decoupled by using the negative velocity feedback adjustment. Later, the Incremental Harmonic Balance Method (IHBM) is deduced, and the frequency-amplitude response of the piezoelectric laminated cylindrical shell is obtained by IHBM. Finally, the influence of the constant gain, size and position of the piezoelectric layer on frequency-amplitude response are investigated. The results show that the position, size and constant gain of the piezoelectric layer have a significant influence on its nonlinear vibration control.

POSTBUCKLING OF SHEAR-DEFORMABLE ANISOTROPIC LAMINATED CYLINDRICAL SHELLS UNDER AXIAL COMPRESSION

2008 ◽  
Vol 08 (03) ◽  
pp. 389-414 ◽  
Author(s):  
ZHI-MIN LI ◽  
HUI-SHEN SHEN
Keyword(s):  
Cylindrical Shell ◽  
Axial Compression ◽  
Perturbation Technique ◽  
Cylindrical Shells ◽  
Anisotropic Shell ◽  
Equilibrium Path ◽  
Singular Perturbation Technique ◽  
Initial Geometric Imperfections ◽  
Shear Deformable ◽  
Laminated Cylindrical Shells

A postbuckling analysis is presented for a shear-deformable anisotropic laminated cylindrical shell of finite length subjected to axial compression. The material of each layer of the shell is assumed to be linearly elastic, anisotropic and fiber-reinforced. The governing equations are based on a higher order shear-deformable shell theory with the von Kármán–Donnell type of kinematic nonlinearity and including the extension/twist, extension/flexural and flexural/twist couplings. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, moderately thick, anisotropic laminated cylindrical shells with different values of shell parameters and stacking sequence. The results confirm that there exists a compressive stress along with an associate shear stress and twisting when the anisotropic shell is subjected to axial compression. The postbuckling equilibrium path is unstable for the moderately thick cylindrical shell under axial compression and the shell structure is imperfection-sensitive.

A Method for Obtaining Stresses and Displacements in Thick Cylindrical Shells Under Arbitrary Boundary Conditions

1973 ◽  
Vol 40 (1) ◽  
pp. 221-226 ◽  
Author(s):  
E. B. Golub ◽  
F. Romano
Keyword(s):  
Stress State ◽  
Variational Principle ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Cylindrical Shells ◽  
Present Theory ◽  
Bending Stress ◽  
Arbitrary Boundary ◽  
Elasticity Solutions ◽  
Circular Cylindrical Shells

This paper presents a means for obtaining both the stress and displacement states which appear in thick, circular, cylindrical shells under arbitrary load and boundary conditions. The governing differential equations and the associated boundary conditions are obtained by utilizing Reissner’s variational principle [6], the assumed form of the stress state containing, in addition to terms corresponding to conventional membrane and bending stress resultants, supplementary sets of self-equilibrating stress resultants. Comparison of results obtained from known elasticity solutions shows that the present theory accurately yields solutions for shells with radius-thickness ratios of the order of 3.0. Numerically computed here, for comparison purposes, is the axisymmetric, periodically spaced, band load problem of Klosner and Levine.

Sign in / Sign up

Export Citation Format

Share Document