Vibroacoustic analysis of baffled plate with elastic boundary conditions in heavy fluid near free surface based on Chebyshev spectral approach

Abstract

This study examines the vibroacoustic response of rectangular plates under point excitation, considering varying immersed depths near a free surface. A comprehensive model is developed using the Chebyshev spectral approach, the Helmholtz boundary integral equation, and the image source technique. The acoustic wave equation incorporates an infinite acoustic soft boundary to simulate the free surface. Plate motion and sound pressure distributions are defined through Chebyshev spectral expansions and Gauss-Chebyshev-Lobatto sampling. Penalty function techniques are introduced to simulate elastic boundary conditions. The proposed method, validated against established literature, demonstrates exponential convergence and provides insights into the effects of immersed depth and boundary conditions on vibroacoustic behavior. At shallow depths, a linear relationship is observed between the square of the natural frequencies. Furthermore, while standing waves influence the sound radiation pattern, they do not significantly affect the overall radiation magnitude. Beyond a critical depth, the natural frequencies stabilize, aligning with those characteristics of a semi-infinite domain with a heavy fluid.