Vibro-Acoustic Analysis of Systems with Complex Geometries Using an Improved Wavelet-Based Finite Element Approach

Vibro-acoustic coupling systems between closed acoustic cavities with complex geometric shapes and elastic structures are commonly encountered in engineering applications. In the mid-frequency range, their dynamic characteristics are quite complex, and accurate deterministic analysis poses significant challenges. In this study, an improved wavelet finite element method is developed for complex cavity-plate coupling systems, aiming to maintain high precision for complex acoustic geometries while broadening the applicable frequency range and improving computational efficiency. The proposed method adopts the interval B-spline wavelet scaling functions as basis functions to formulate the discrete governing equations of the coupled acoustic-plate system, while enforcing physically consistent fluid-structure coupling conditions. The performance of this method is evaluated using a numerical validation example consisting of a semi-ellipsoidal acoustic cavity coupled with a fixed circular plate. Under different excitations, the results obtained using this method are systematically compared with reference finite element solutions. The results show good agreement within the studied frequency range, including regions with relatively high modal density. Furthermore, the relative error analysis indicates that the improved method significantly outperforms the traditional finite element method in terms of the accuracy per degree of freedom. These results demonstrate that the proposed method provides an effective and reliable alternative tool for deterministic mid-frequency vibro-acoustic analysis of coupled systems with complex geometric acoustic cavities.