Optimization for a Locally Resonant Phononic Crystal of Square Spiral With Circle Inside

Hang Xiang,Jiawei Xiang,Xingfu Ma

doi:10.1109/access.2019.2946085

Abstract

This paper presents an optimization scheme to better design phononic crystals. A locally resonant phononic crystal (LRPC) structure called square spiral with circle inside is employed to verify the performance of the present scheme. Four geometric parameters, i.e., the side length of square scatterer, the length of each elastic beam, the thickness of elastic beams, and the radii of inner circles, are considered to obtain the corresponding influences on band gaps (BGs) using finite element method (FEM). According to the significant influences of the late two key parameters, a 2-factor (the radii of inner circles, and the thickness of elastic beams) and 7-level experiment is designed to obtain optimal BGs with better low-frequency broadband properties. By 29 times calculations using FEM for the different combination of levels, three relationships between the 2-factor and the first BG’s starting frequency, the first BG’s bandwidth, and the second BG’s bandwidth, are obtained and severed as inputs to the software of response surface methodology (RSM). The closed-form expressions of the three relationships are finally obtained to construct optimization models and result in the optimal band gaps (BGs) between 190–300 Hz and 500–600 Hz . It is expected that the present optimization scheme can be extended to material design of phononic/photonic structures in a reasonable way.

Highlights

The noise and vibration in human life disturb the residents and even do harmful to the mental of them [1]–[5]
Motivated by the finite element method (FEM) simulation-based optimization method, we develop a structural parameters optimization scheme to obtain relatively optimal locally resonant phononic crystal (LRPC) structures by combination of the FEM simulations and response surface methodology (RSM) analysis
We find that the thickness b of elastic beams is a key parameter to obtain a relative optimization band gaps (BGs)

Summary

INTRODUCTION

The noise and vibration in human life disturb the residents and even do harmful to the mental of them [1]–[5]. We find that the variation of the bandwidth can be neglected (the upper and the lower edges of the two BGs are nearly smooth), this parameter is not the key parameter to influence BGs. Fig. (b) shows the change of two BGs along with the length of elastic beam d, both the two BGs are monotonously increasing or decreased and the original selection d = 15 × 10−3 m is the relatively best one. I.e., the side length of square scatterer c, the length of each elastic beam ed, f , g, h, and i, the thickness of elastic beams b, and the radii of inner circles r2, are discussed to obtain the corresponding influences on BGs, and the significant influences of the late two key parameters b and r2 are determined. In view of these relationships, we can optimize the two key structural parameters r2 and b

THE OPTIMIZATION AND VERIFICATION OF THE STRUCTURE

CONCLUSION