Dynamical Analysis of Axially Moving Plate by Finite Difference Method

Abstract

The complex natural frequencies for linear free vibrations and bifurcation and chaos for forced nonlinear vibration of axially moving viscoelastic plate are investigated in this paper. The governing partial differential equation of out-of-plane motion of the plate is derived by Newton's second law. The finite difference method in spatial field is applied to the differential equation to study the instability due to flutter and divergence. The finite difference method in both spatial and temporal field is used in the analysis of a nonlinear partial differential equation to detect bifurcations and chaos of a nonlinear forced vibration of the system. Numerical results show that, with the increasing axially moving speed, the increasing excitation amplitude, and the decreasing viscosity coefficient, the equilibrium loses its stability and bifurcates into periodic motion, and then the periodic motion becomes chaotic motion by period-doubling bifurcation. © 2011 Springer Science+Business Media B.V.

Department(s)

Mechanical and Aerospace Engineering

Keywords and Phrases

Axially Moving Plate; Bifurcation; Chaos; Finite Difference Method; Instability

International Standard Serial Number (ISSN)

0924-090X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2012 Springer Verlag, All rights reserved.

Publication Date

01 Jan 2012

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