Effect of initial camber on natural nonlinear vibrations of cylindrical shells

1982 ◽  
Vol 18 (1) ◽  
pp. 34-39 ◽  
Author(s):  
V. D. Kubenko ◽  
P. S. Koval'chuk ◽  
T. S. Krasnopol'skaya
Keyword(s):  
Nonlinear Vibrations ◽  
Cylindrical Shells ◽  
Initial Camber

A Multi-Mode Approach for the Nonlinear Vibrations of Circular Cylindrical Shells

2001 ◽  
Author(s):  
Francesco Pellicano ◽  
Marco Amabili ◽  
Michael P. Païdoussis
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Vibrations ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Nonlinear Behavior ◽  
Symbolic Manipulation ◽  
Comparison Functions ◽  
Circular Cylindrical Shells ◽  
Multi Mode

Abstract The nonlinear vibrations of simply supported, circular cylindrical shells, having geometric nonlinearities is analyzed. Donnell’s nonlinear shallow-shell theory is used, and the partial differential equations are spatially discretized by means of the Galerkin procedure, using a large number of degrees of freedom. A symbolic manipulation code is developed for the discretization, allowing an unlimited number of modes. In the displacement expansion particular care is given to the comparison functions in order to reduce as much as possible the dimension of the dynamical system, without losing accuracy. Both driven and companion modes are included, allowing for traveling-wave response of the shell. The fundamental role of the axisymmetric modes, which are included in the expansion, is confirmed and a convergence analysis is performed. The effect of the geometric shell characteristics, radius, length and thickness, on the nonlinear behavior is analyzed.

scholarly journals Nonlinear Vibrations of Functionally Graded Cylindrical Shells: Effect of the Geometry

2012 ◽  
Author(s):  
Matteo Strozzi ◽  
Francesco Pellicano ◽  
Antonio Zippo
Keyword(s):  
Differential Equations ◽  
Nonlinear Vibrations ◽  
Cylindrical Shells ◽  
Nonlinear Partial Differential Equations ◽  
Linear Analysis ◽  
Finite Amplitude ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Lagrange Equations ◽  
Displacement Fields

In this paper, the effect of the geometry on the nonlinear vibrations of functionally graded (FGM) cylindrical shells is analyzed. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The shell deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported boundary conditions are considered. The displacement fields are expanded by means of a double mixed series based on harmonic functions for the circumferential variable and Chebyshev polynomials for the longitudinal variable. In the linear analysis, after spatial discretization, mass and stiff matrices are computed, natural frequencies and mode shapes of the shell are obtained. In the nonlinear analysis, the three displacement fields are re-expanded by using approximate eigenfunctions obtained by the linear analysis; specific modes are selected. The Lagrange equations reduce nonlinear partial differential equations to a set of ordinary differential equations. Numerical analyses are carried out in order to characterize the nonlinear response of the shell. A convergence analysis is carried out to determine the correct number of the modes to be used. The analysis is focused on determining the nonlinear character of the response as the geometry of the shell varies.

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