Analysis on band gap properties of periodic structures of bar system using the spectral element method

Abstract

In this paper, the band gap properties of the periodic structures of bar system, which include the rod-joint, truss, and frame structures, are studied using spectral element method (SEM). The spectral equations of the rod, beam, and joint elements are established and the spectral equations of the whole structures are further assembled. The frequency responses of the whole structures are calculated and the results are compared with those calculated by the finite element method (FEM). It can be observed that the SEM is more accurate in high frequency ranges. The band gap properties of the three types of periodic structures are studied, respectively. Furthermore, the effects of structural length, unit cell number, structural configurations, load conditions, and structural damping on the band gap properties are investigated.

Acknowledgments

The authors wish to express gratitude for the support provided by the National Natural Science Foundation of China under Grant Nos. 11172084, 11002045, 10672017 and 50935002 for this research work.