A semi-analytical approach to predict the acoustic radiation of underwater inhomogeneous plates under turbulent boundary layer excitation

This paper proposes a semi-analytical method based on the spectral geometry approach for the rapid prediction of underwater vibration and acoustic radiation of in-plane inhomogeneous plates under turbulent boundary layer excitation. Arbitrary elastic boundary conditions are modeled by introducing two sets of virtual springs (linear and torsional), and a grid-based modal superposition framework is developed to handle plates with arbitrary geometries and multi-material embedded sub-plates. The turbulent boundary layer pressure field is synthesized by superimposing uncorrelated wall plane waves, enabling efficient coupling between the statistical wall-pressure model and the deterministic vibro-acoustic model. A simple and reproducible singularity treatment is proposed by analytically averaging the Rayleigh integral kernel over an equivalent-area circular domain. Numerical validations demonstrate that the proposed method achieves high accuracy while significantly reducing computational cost. The influence of acoustic–structural coupling on convergence is systematically analyzed, together with the effects of sub-plate materials, geometrical configurations, and boundary conditions on structural vibration and sound radiation characteristics. The results confirm that the developed method provides an efficient and reliable computational tool for analyzing flow-induced vibration and acoustic radiation of complex in-plane structures with arbitrary multi-material configurations.