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 d...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.展开更多
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)+4 种基金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)
文摘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.
