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Global bifurcations of symmetric cross‐ply composite laminated plates with 1:2 internal resonance
Author(s) -
Zhang Li,
Chen Fangqi
Publication year - 2018
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201600049
Subject(s) - homoclinic orbit , chaotic , nonlinear system , composite number , bifurcation , phase space , resonance (particle physics) , mathematics , mathematical analysis , classical mechanics , physics , computer science , algorithm , quantum mechanics , artificial intelligence , particle physics , thermodynamics
This paper investigates the global bifurcations and chaotic dynamics for nonlinear oscillations of symmetric cross‐ply composite laminated plates in case of 1:2 internal resonance. The higher‐dimensional Melnikov method and its extensions developed by Kova c ˘ i c ˘ and Wiggins is employed to analyze the global bifurcations for composite laminated plates. The explicitly sufficient conditions of the existence of Silnikov‐type homoclinic orbits in perturbed phase space are gained, which may lead to chaotic motions for composite laminated plates. Finally, numerical results obtained by fourth‐order Runge‐Kutta method also indicate that there exist the jumping phenomena and chaotic responses for the nonlinear composite laminated plates, which agree with theoretic predictions.