Extension of a CUF-based vibroacoustic modal framework to fluid-loaded plates with simply-supported and free edges

This study extends a previously developed CUF-based frequency-domain framework for coupled vibroacoustic modal analysis to a rectangular fluid-loaded plate under simply-supported and free edge conditions. The physical system consists of an aluminum panel separating two surrounding air domains; the structural field is modeled by small-strain linear elasticity, and the acoustic field by linear, compressible acoustics. After enforcement of interface compatibility, the coupled displacement-pressure finite-element discretization yields a generalized eigenvalue problem. The spatial approximation combines cross-sectional Lagrange or Taylor expansions in the x-z plane with one-dimensional Lagrange interpolation along y, enabling systematic kinematic enrichment within the same CUF setting. The study focuses on the effect of non-clamped edges on the coupled spectrum, the comparison between Lagrange and Taylor cross-sectional expansions, and the MAC-based correlation between in vacuo and coupled modes. Validation against three-dimensional finite-element benchmarks is finally provided.