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.

This paper aims to study the free vibration characteristics of complicated shape plate coupled with fluid under elastic boundary conditions.

To this end, the rectangular domain enveloping the complicated shape plate domain is selected, and the plate displacement is expressed by the improved Fourier series in the rectangular domain. Combined with the Rayleigh integral, the relationship between the plate displacement and the surface sound pressure is established, and the integral formula is transformed into polar coordinates to avoid singularity. Aiming at the problem that it is difficult to obtain the explicit expression of the boundary curve in the variable limit integral in local polar coordinates, the structural boundary curves are treated by "replacing curve with straight" to simplify the Rayleigh integral. Based on the energy principle, a semi analytical method for analyzing the free vibration characteristics of complicated shape plate contacting with water on one side is established.

The numerical examples of rectangular plate, circular plate and some complicated shape plates are given. Compared with the finite element method and literature results, the convergence and accuracy of the method are verified, and the influence of elastic boundary conditions on the added virtual mass incremental (AVMI) factor of plate is discussed. The AVMI factor of each mode reaches the maximum near the dimensionless displacement spring stiffness of 10³. At this time, the structure is relatively most affected by the fluid.

This method has strong adaptability and high calculation efficiency. It reveals the free vibration law of complicated shape plate coupled with fluid, and has certain engineering guiding significance.

Due to the larger length-to-diameter ratio of the stern bearing, it is difficult to reflect its actual operating conditions when simplified to the traditional equivalent model of single-point support. Therefore, the influence of the equivalent form of the stern bearing on the transverse vibration characteristics of the shafting is investigated.

The improved Fourier series is introduced to describe the lateral vibration displacement of propulsion shafting. Then, the calculation model of lateral vibration performance of propulsion shafting under various equivalent forms, such as single-point support, multi-point support or continuous distributed support, are constructed based on the energy principle. Thereby, the influence of the change of support stiffness equivalent to the liquid film pressure on the lateral vibration of the shafting and the influence of the propeller excitation on the vibration response of the shafting are further analyzed. Finally, the results acquired by the proposed model is compared with the results of related references and finite element method (FEM) to verify the validity of the calculation model.

The multi-point support calculation results converge to the continuous distributed support calculation results. The three-point support equivalent form can be used to study the influence of liquid film pressure distribution on the lateral vibration characteristics of the propulsion shafting. The shafting response under propeller excitation is affected by the revolution speed.

The research indicates that three-point support equivalent form can be used to analyze the influence of liquid film pressure on the shafting lateral vibration performance. The proposed model in this paper has advantages of good convergence, high accuracy, and less cost-consuming.