Abstract
This paper investigates the band gap (BG) characteristic of a two-dimensional square spiral locally resonant phononic crystal, and a BG optimization scheme is proposed. First, the influence of three structural parameters (the side length of scatterer, the thickness of elastic beams and the number of square rings) on BGs are studied. Meanwhile, the BG formation mechanism is analyzed by studying the displacement fields of the eigenmodes at the BG boundaries. Second, a 7-level numerical experiment of 3-parameter is designed. The finite element method is employed to analysis the start frequency of the first BG and the total width of the first two BGs, which are expressed as regression equations through response surface method. Finally, the optimal structural parameters with low-frequency broadband characteristic are calculated by interior point method. The numerical results are in good agreement with the calculation results, which show the effectiveness of the optimization scheme.
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