Symplectic analysis for wave propagation in one-dimensional nonlinear periodic structures

Xiu Hui Hou, Zi Chen Deng, Jia Xi Zhou

科研成果: 期刊稿件文章同行评审

10 引用 (Scopus)

摘要

The wave propagation problem in the nonlinear periodic mass-spring structure chain is analyzed using the symplectic mathematical method. The energy method is used to construct the dynamic equation, and the nonlinear dynamic equation is linearized using the small parameter perturbation method. Eigen-solutions of the symplectic matrix are used to analyze the wave propagation problem in nonlinear periodic lattices. Nonlinearity in the mass-spring chain, arising from the nonlinear spring stiffness effect, has profound effects on the overall transmission of the chain. The wave propagation characteristics are altered due to nonlinearity, and related to the incident wave intensity, which is a genuine nonlinear effect not present in the corresponding linear model. Numerical results show how the increase of nonlinearity or incident wave amplitude leads to closing of transmitting gaps. Comparison with the normal recursive approach shows effectiveness and superiority of the symplectic method for the wave propagation problem in nonlinear periodic structures.

源语言英语
页(从-至)1371-1382
页数12
期刊Applied Mathematics and Mechanics (English Edition)
31
11
DOI
出版状态已出版 - 11月 2010

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