A Single and Double Mode Approach to Chaotic Vibrations of a Cylindrical Shell with Large Deflection

Liming Dai,Qiang Han,Mingzhe Dong

doi:10.1155/2004/486249

Liming Dai, Qiang Han + Show 1 more

Open Access

https://doi.org/10.1155/2004/486249

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Abstract

The chaotic vibrations of a cylindrical shell of large deflection subjected to two-dimensional exertions are studied in the present research. The dynamic nonlinear governing equations of the cylindrical shell are derived on the basis of single and double mode models established. Two different types of nonlinear dynamic equations are obtained with varying dimensions and loading parameters. The criteria for chaos are determined via Melnikov function for the single mode model. The chaotic motion of the cylindrical shell is investigated and the comparison between the single and double mode models is carried out. Results of the research show that the single mode method usually used may lead to incorrect conclusions under certain conditions. Double mode or higher order mode methods should be used in these cases.

Highlights

In recent years, chaos in nonlinear dynamic systems has aroused more and more interest in the field of theoretical and experimental mechanics
The periodic and chaotic behavior of a viscoelastic nonlinear bar subjected to harmonic excitations was investigated by Suire et al [5] on the based of a dynamics model established with implementation of Galerkin principle
The characteristics of the nonlinear transverse vibration of an elastic cylindrical shell with large deflection and under uniform harmonic excitations are investigated in the present research based on the single and double mode models

Summary

Introduction

Chaos in nonlinear dynamic systems has aroused more and more interest in the field of theoretical and experimental mechanics. The forced response of a nearly square plate, the nonlinear dynamics of a shallow arch, and the chaotic motion of a circular plate and a cylindrical shell are a few typical studies in mechanical and structural systems found in the research [7,8,9]. L. Dai et al / A single and double mode approach to chaotic vibrations of a cylindrical shell with large deflection. This article significantly contributes to the chaotic response of an elastic beam subjected to a periodic excitation with nonlinear boundary conditions and provided the criterion for chaos on the basis of a single mode model. The criteria for chaos of the cylindrical shell will be developed and the chaotic behavior of the transverse vibration of the shell will be investigated through a numerical analysis by the P-T method [10]. Results generated by single and double mode models will be compared and the differences of the two models will be identified and analyzed

Governing equations

Melnikov function for the single mode motion

Numerical simulations

Concluding remarks