Stability and Bifurcation for a Simply Supported Functionally Graded Material Plate with One-to-One Internal ResonanceReport as inadecuate




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Journal of Applied MathematicsVolume 2014 2014, Article ID 414903, 11 pages

Research Article

Department of Mechanics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

School of Science, Linyi University, Shandong 276005, China

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received 2 January 2014; Accepted 22 April 2014; Published 26 May 2014

Academic Editor: Xiao-Qiao He

Copyright © 2014 Dongmei Zhang and Fangqi Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.





Author: Dongmei Zhang and Fangqi Chen

Source: https://www.hindawi.com/



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