Optimal geometric parameters for a double panel structure with low frequency forbidden characteristics

Abstract

In this paper, a locally resonant phononic crystal (LRPC) double panel structure with optimal geometric parameters is investigated. The present LRPC structure can open band gaps (BGs) with low frequency forbidden characteristics. The effects of several parameters such as the thickness of steel and aluminum plates, the width of elastic beams, the side length and height of cuboid scatterer onto BGs are analyzed. The thickness of the steel and aluminum plates as well as the width of elastic beams is identified to be the most influential factors on BGs. Seventy-seven experimental runs based on the three-factor and seven-level experimental design are performed to complete response surface analysis, three functional relationships are obtained between the three-factor and the terminating frequency of the second BG, the bandwidth of the first BG, and the bandwidth of the second BG. Additionally, the interior point method is also applied to optimize the closed-form expressions of functional relationships to obtain the optimal LRPC double panel structure with the low-frequency forbidden properties from 90 Hz to 250 Hz.