Open Access
Translator Disclaimer
2014 Stability and Bifurcation for a Simply Supported Functionally Graded Material Plate with One-to-One Internal Resonance
Dongmei Zhang, Fangqi Chen
J. Appl. Math. 2014: 1-11 (2014). DOI: 10.1155/2014/414903

Abstract

Stability and bifurcation behaviors for a model of simply supported functionally graded materials rectangular plate subjected to the transversal and in-plane excitations are studied by means of combination of analytical and numerical methods. The resonant case considered here is 1 : 1 internal resonances and primary parametric resonance. Two types of degenerated equilibrium points are studied in detail, which are characterized by a double zero and two negative eigenvalues, and a double zero and a pair of pure imaginary eigenvalues. For each case, the stability regions of the initial equilibrium solution and the critical bifurcation curves are obtained in terms of the system parameters which may lead to Hopf bifurcation and 2D torus. With both analytical and numerical methods, bifurcation behaviors on damping parameters and detuning parameters are studied, respectively. A time integration scheme is used to find the numerical solutions for these bifurcation cases, and numerical results agree with the analytic predictions.

Citation

Download Citation

Dongmei Zhang. Fangqi Chen. "Stability and Bifurcation for a Simply Supported Functionally Graded Material Plate with One-to-One Internal Resonance." J. Appl. Math. 2014 1 - 11, 2014. https://doi.org/10.1155/2014/414903

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07131583
Digital Object Identifier: 10.1155/2014/414903

Rights: Copyright © 2014 Hindawi

JOURNAL ARTICLE
11 PAGES


SHARE
Vol.2014 • 2014
Back to Top