Optimal locally resonant bandgaps in a windmill-like phononic crystal structure

Abstract

In this paper, a windmill-like phononic crystal (PC) structure with optimal locally resonant bandgaps (LRBGs) is proposed. By analyzing the variation trend of BGs, three geometric parameters (the side length and height of cuboid scatterer, and the width of elastic beams) are found to be key factors for the determination of BGs. Using response surface methodology (RSM), 3-factor and 7-level experiment are designed to obtain experimental data with the help of finite element simulations. Three relationships (fitting equations) between the three factors and the second BGs terminating frequency, the first BGs bandwidth, and the second BGs bandwidth, are further obtained by fitting the simulation data. Based on the three fitting equations, the optimal LRBGs are finally obtained using a simple optimization method. The proposed windmill-like structure PC is demonstrated to possess an optimal range of BG.