Multi-frequency and low frequency bandgap characteristics of concentric ring cement-based locally resonant phononic crystal

The elastic wave bandgap (BG) properties of locally resonant phononic crystal (LRPC) make it has great potential in the research and development of damping composite material and the application of vibration control engineering. However, the number of BG of the traditional LRPC is only one, the BG frequency range is too concentrated, and the multi-frequency BGs is not opened, so the application in practical engineering is limited. In response to the above issues, this paper designs a concentric ring cement-based locally resonant phononic crystal (CRCBLRPC) composite material, and studies and analyzes its BG characteristics. Firstly, the improved plane wave expansion method (IPWEM) and finite element method (FEM) are used to calculate the band structure of the CRCBLRPC. Secondly, the transfer function and BG mechanism of CRCBLRPC are calculated using FEM. Then, the factors affecting the BG of CRCBLRPC are analyzed. Finally, an equivalent model of spring-mass system is proposed to theoretically estimate the BG range of CRCBLRPC. The results show that the CRCBLRPC opens multi-frequency and low frequency BGs within the 200 Hz frequency band, and the number of BGs is more than that of the traditional LRPC. Within the BG frequency range, the CRCBLRPC has a good inhibition effect on vibration. Among them, the density of the scatterer and the elastic modulus of the coating layer are the main factors affecting the BG of the CRCBLRPC. The established spring-mass system equivalent model can accurately calculate the BG range of the CRCBLRPC. The research content and related conclusions of this paper provide new perspectives and insights for the study and design of LRPC composite materials with multi-frequency and low frequency BGs, and can also provide new ideas and methods for solving low frequency vibration in practical engineering.