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

作　　者：侯秀慧 邓子辰 周加喜 

机构地区：[1]Department of Engineering Mechanics,Northwestern Polytechnical University [2]State Key Laboratory of Structural Analysis for Industrial Equipment,Dalian University of Technology [3]College of Mechanical and Vehicle Engineering,Hunan University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2010年第11期1371-1382,共12页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Nos. 10972182,10772147,and 10632030);the National Basic Research Program of China (No. 2006CB 601202);the National 111 Project of China (No. B07050);the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment (No. GZ0802);the Doctoral Foundation of Northwestern Polytechnical University (No. CX200908);the China Postdoctoral Science Foundation (No. 20090450170);the Northwestern Polytechnical University Foundation for Fundamental Research (No. JC200938)

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.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.

关 键 词：symplectic mathematical method nonlinear periodic structure elastic wave propagation 

分 类 号：O347.4[理学—固体力学]