Optimization Design for Minimization of Sound Radiation from Thin Plate Based on Acoustic Design Sensitivity Analysis

Abstract

In this paper, optimization design for minimization sound radiation from thin plate based on ADS (Acoustic Design Sensitivity) analysis is studied. Firstly, the velocity distribution of structure surface is solved by analytical method and the surface sound pressure is computed by Rayleigh integral respectively. The sound radiation power of structure can be expressed as a positive definite quadratic form of the Hermitian by impedance matrix. Then, the relationship between the sound radiation power and thickness of thin plate is analyzed. The ADS analysis of thin plate can be translated into the analysis of structure dynamic sensitivity and impedance matrix sensitivity. Finally, optimization design for sound power minimization of thin plate base on the gradient-based optimization algorithms is presented. Thicknesses are chosen as design variables. Taking a simple supported thin plate as a simulation example, the results show the validity of the presented method and give the optimal design of thin plate. Up to now, when we study ADS analysis about acoustic radiation, sound pressure is adopted for design objective, and the effect of design variable on sound pressure is studied. But sound pressure is different from spatial position and the calculation amount is too large. The sound power reveals itself as the most adequate mean for quantifying the radiation at the structure's surface, and it is related to the characteristics of structure and does not change as spatial position. Sound power is more suitable than sound pressure for ADS analysis. The present work focuses on the ADS analysis of thin plate with respect to sound radiation power and optimization design for minimization sound power of thin plate. We assume that air is the acoustic medium and a feedback coupling between the acoustic medium and the structure can be neglected. Proportional damping is assumed for material. The structural vibrations are excited by a time harmonic mechanical loading with prescribed excitation frequency, amplitude, direction, and spatial distribution. Firstly, the velocity distribution of structure is solved by analytical method and the surface sound pressure is computed by Rayleigh integral respectively. Secondly, the sound power can be expressed as a positive definite quadratic form of the Hermitian based on the sound radiation mode theory. Then, the ADS analysis of thin plate with respect to sound radiation power is transformed into the sensitivity of dynamic and impendance matrix with respect to design variables. Finally, optimization design for sound power minimization of thin plate base on the gradient-based optimization algorithms is presented. Thicknesses are chosen as design variables. Taking a simple supported thin plate as a simulation example, the results show the validity of the presented method and give the optimal design of thin plate with low sound radiation power.