Objectives This paper investigates the vibration and acoustic characteristics of a floating raft-hull coupling system based on the generalized variational principle, aiming to enhance the acoustic performance of the floating raft vibration isolation system.

Methods The floating raft-hull coupling system is simplified as a reinforced cylindrical shell, double-layer plates, springs, and surrounding acoustic medium. The vibration energy equations of the structural domain are derived using the generalized variational method, and the discrete boundary element equations for the acoustic field domain are established based on the Helmholtz integral equation. The governing equations of the coupling system are developed by expanding the vibration displacement and acoustic pressure into Fourier series and orthogonal polynomials. The accuracy of the proposed semi-analytical model is validated through finite element method (FEM) simulations.

Results Results show that the proposed model is consistent with FEM analysis, offering high analytical efficiency and clear physical insights. Furthermore, this study systematically investigates the influence laws and optimization methods of various design parameters, including the stiffness of the isolator, the elastic modal of the raft, the mass ratio of the raft to the equipment, and the structural parameters of the hull, on the acoustic performance of the coupling system.

Conclusions It is found that reducing the stiffness of the isolator, increasing the stiffness of the raft structure, enlarging the mass ratio of the raft to the equipment, and increasing the height of the hull's ring ribs can significantly enhance the acoustic performance of the system. These conclusions provide theoretical support for the dynamic design, analysis, and optimization of floating raft vibration isolation systems and hold significant value for practical engineering applications.