Design parameter analysis and optimization of bandgap characteristics of locally resonant phononic crystals based on response surface methodology

The bandgap characteristics of locally resonant phononic crystals (LRPC) are a comprehensive manifestation of the design parameters (including structural and material parameters). In order to investigate the composite influence mechanism of the design parameters on the bandgap characteristics of LRPC, the response surface methodology (RSM) is performed to collectively analyze and multi-objectively optimize the bandgap characteristics (starting bandgap frequency, cutoff bandgap frequency, and bandgap width) of LRPC to achieve an effective coverage of the target frequency range. Firstly, the bandgap characteristics of the LRPC are comprehensively analyzed by the finite element method (FEM), and the key design parameters sensitive to the bandgap are identified. Then, with the help of Box-Behnken design technique in RSM, the response surface regression models adapted to the structural and material parameters that can be used to describe the bandgap characteristics of the LRPC are established, and the effects of the interactions between the design parameters on the bandgap characteristics of the LRPC are highlighted and recognized. Finally, the LRPC bandgap characteristics are synthetically optimized by the multi-objective simultaneous nonlinear optimization technique, and the design parameters that satisfy the target frequency range are obtained. The results demonstrated that the structural parameters (lattice constant, scatterer radius and coating radius) and material parameters (scatterer density, elastic modulus and Poisson's ratio of the coating, and matrix density) are the key design parameters affecting the bandgap characteristics of LRPC. The optimal structural parameters and optimal material parameters that can be used to effectively cover the target frequency range are obtained through the optimized design, respectively. The established response surface regression model features good accuracy and predictability, which provides an effective means for the efficient design of the bandgap characteristics of LRPC.