Symplectic method on calculation of band gap of one-dimensional phononic crystals
LIU Tie-quan1; DENG Zi-chen1,2; ZHOU Jia-xi1
1.School of Mechanics and Civil&Architecture,Northwestern Polythechnical University,Xi'an 710129, China;2.State Key Laboratory of Structural Analysis for Industrial Equipment,Dalian University of Technology,Dalian 116024, China
Abstract：Abstract: The unit cell of the one-dimensional phononic crystal is reduced to a spring-mass structure with limited number of degrees. The lattice vibrations are investigated under the dual variable system, and the dispersion relation is obtained by the symplectic mathematical method. Furthermore, the eigenfrequency is given by using the Wittrick-Williams algorithm, thus the band gap is obtained. Comparing the results calculated by the present method with the traditional lump-mass method, it is obvious that there is a good agreement. However, the former is capable of improving the calculation accuracy and computational efficiency, and more importantly, having better convergence.
刘铁权;邓子辰;周加喜. 基于辛数学方法的一维声子晶体禁带计算[J]. , 2010, 29(12): 102-105.
LIU Tie-quan;DENG Zi-chen;ZHOU Jia-xi. Symplectic method on calculation of band gap of one-dimensional phononic crystals . , 2010, 29(12): 102-105.
2010, Vol. 29 
