Band gap characteristics of flexural wave of two-dimensional periodic frame structure composed of locally resonant composite beam

In this paper, single material beams as the basic structural members in the traditional periodic frame structure were extended to the ones of multi-material composite beam with locally resonant (LR) unit. Based on the spectral element method and the topological characteristics of structure, an assembly method of the stiffness matrix for virtual full component model is presented. This method can be applied not only to the periodic structures, but also to the aperiodic structures, because the whole stiffness matrix of the structure is assembled by its topological information. The effects of the rest design parameters on the band gap behavior of two-dimension (2D) periodic frame structure were studied when the lattice constant was fixed. The results show that the Bragg band gaps can be adjusted by changing the lengths of structural members and the length ratio of the subunit A to the structural members. The results also show that the LR band gaps can be adjusted by adding LR units with different parameters into different members. The results in this work enrich and expand the modulatory pathway of the band gaps of periodic frame structure, and provide a modified approach to the design and correction of the passive vibration suppression system. (C) 2019 Elsevier Ltd. All rights reserved.