This study aims to establish a vibro-acoustic coupling model for an underwater sandwich panel coupled with an acoustic cavity and a back plate under elastic boundary constraints. It further investigates the influence of back plate damping, back plate parameters, and acoustic cavity parameters on the structural and acoustic responses of the system subjected to mechanical excitation.

First, a dynamic model for rectangular plates is developed based on thin-plate theory, while Layerwise theory is applied to establish dynamic models for damped plates and sandwich panels. A modified Fourier series is employed as the displacement trial function for the plate structures, with elastic boundary constraints simulated using artificial boundary springs. Response functions for plates, damped plates, and sandwich plates under elastic boundary constraints are derived using energy variational principles. By coupling the sandwich panel and plate (damped plate) with a sealed acoustic cavity and a semi-infinite acoustic field, a coupled underwater sandwich panel-acoustic cavity-plate (damped plate) model is constructed. This model accommodates various structural boundary constraints and acoustic cavity configurations, and a solution method for evaluating the vibro-acoustic responses of the system is developed.

The damped plate effectively reduces system responses in the high-frequency range. Increasing the back plate thickness decreases the overall mean-square vibration velocity of the back plate and significantly reduces the mean-square acoustic pressure within the acoustic cavity at mid-to-low frequencies. The height of the acoustic cavity primarily affects the coupled structural-acoustic system response before the first-order resonance peak.

The proposed underwater sandwich panel-acoustic cavity-plate coupling model demonstrates high accuracy and provides a valuable reference for the acoustic design of sonar cavities.