Modeling of the tensioned membrane backed by a variable-shape cavity and research on acoustic characteristics

Abstract

The drum-type muffler comprises a rigid back cavity and a tensioned membrane, which utilizes the radiation sound field of a membrane and the superposition effect of the enclosed sound field to achieve noise reduction. However, most previous studies have been focused on idealized models, with little research on the sound radiation power from a membrane concerning a variable-shape back cavity. This article aims to establish a membrane vibration-acoustic model and investigate the impact of irregular shape and pre-tension conditions on the radiated sound energy. The microunits on the surface of the membrane and the pressure of the sound field are represented as cosine Fourier series. The variable-shape cavity is converted into a normal one by employing the coordinate transformation method. The analytical model of the coupling structure composed by a membrane and the enclosed sound fields is developed based on the energy principle. The acoustic and vibration characteristics of the membrane are solved based on the Rayleigh integral equation. This study also considers the difference in sound insulation performance between the thin plate and the membrane. The analytical results are compared with Finite Element Analysis (FEM) to verify the correctness of the theoretical model. In addition, based on the LMS Simcenter measurement system, experiments are designed to predict the sound pressure on both sides of the membrane. The test results closely correspond with the theoretical calculation results, which confirms the practicality of the theoretical approach.