TY - JOUR
T1 - Symplectic analysis for wave propagation in one-dimensional nonlinear periodic structures
AU - Hou, Xiu Hui
AU - Deng, Zi Chen
AU - Zhou, Jia Xi
PY - 2010/11
Y1 - 2010/11
N2 - 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.
AB - 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.
KW - elastic wave propagation
KW - nonlinear periodic structure
KW - symplectic mathematical method
UR - http://www.scopus.com/inward/record.url?scp=78650120444&partnerID=8YFLogxK
U2 - 10.1007/s10483-010-1369-7
DO - 10.1007/s10483-010-1369-7
M3 - 文章
AN - SCOPUS:78650120444
SN - 0253-4827
VL - 31
SP - 1371
EP - 1382
JO - Applied Mathematics and Mechanics (English Edition)
JF - Applied Mathematics and Mechanics (English Edition)
IS - 11
ER -