Interior vibro-acoustic modeling and modal analysis of coupled panel-cavity systems using wavelet finite-element approach.

Abstract

A wavelet-based Galerkin weak form is developed in this paper to investigate the vibro-acoustic responses of a coupled panel-cavity system. The structural and acoustic models of the coupled panel-cavity system are constructed via the scaling function of a B-spline wavelet with multi-resolution analysis. Semi-orthogonal and compact support wavelet-based shape functions are employed as the wholly unknown displacement and sound pressure field variables in the vibro-acoustic systems. The similarity between the two-dimensional B-spline wavelet and three-dimensional (3D) B-spline wavelet on a bounded interval (BSWI) theory provides the potential for their integration and model at the fluid-structure interface. The panel is modeled according to both Kirchhoff and Mindlin theory using B-spline wavelets, with distinct coupling formulations derived by combining these plate theories with the 3D acoustic theory. In numerical examples, a parametric study, a convergence study, and an L-shaped panel-cavity system study are conducted using the proposed method and the standard finite-element method. The results demonstrate that the wavelet finite-element method effectively reduces the pollution error at a high wavenumber due to high order and multi-resolution of the B-spline wavelet and reveal that the coupled BSWI element is less sensitive to the irregular mesh, indicating that the proposed method provides more stable solutions for vibro-acoustic problems.