Optimal bandgaps of a spiral structure based on locally resonant phononic crystals

Abstract

A spiral locally resonant phononic crystal (LRPC) with the optimal bandgaps (BGs) between 20 and 250 Hz is proposed. The single factor analysis of three key geometric parameters (the thickness of spiral elastic beams, the side length of square scatterers and the spirals’ turns) are performed to obtain corresponding influences on BGs, two-factor (the thickness of spiral elastic beams and the side length of the square scatterer) and seven-level experiment under the four fixed spirals’ turns are designed to obtain optimal BGs with better low-frequency broadband properties. According to numerical experiments, BG data of present spiral LRPCs can be calculated by finite element method (FEM). Relationships (i.e., the relationship between the starting frequency of the first BG and the two factors, the relationship between the bandwidth of the first BG and the two factors, and the relationship between the bandwidth of the second BG and the two factors) are further obtained using the response surface methodology (RSM). The optimal BGs with better properties are finally calculated using the interior point method.