Optimization scheme of geometric parameters for a 2D locally resonant phononic crystal structure

A ring locally resonant phononic crystal with an effective optimization scheme is proposed. In order to obtain low-frequency broadband properties, three loops of 2-factor (the two key geometric parameters, i.e., the thickness of elastic beam and the radius of scatterer) and 7-level numerical experiments are designed to perform the response surface methodology (RSM) analysis. The low-frequency band gaps (BGs) of the present structures are calculated using finite element method to obtain enough simulation data for RSM analysis. After calculations, the two relationships can be obtained, i.e., the relationship of the starting frequency of the first BG and the two factors; and the relationship of the total bandwidth of the first two BGs and the two factors. Aiming at the lower starting frequency of the first BG and the wider total bandwidth of the first two BGs, the two key geometric parameters are optimized using interior point method.