High-Order Vibroacoustic Modal Analysis of Fluid-Loaded Plates with Simply-Supported and Free Edges

A higher-order Carrera Unified Formulation is presented for fluid-loaded slender plates, employing orthogonal Lagrange and total-degree Taylor polynomials to capture cross-sectional kinematics. Comparison with three-dimensional finite-element models shows that moderate-order Lagrange expansions predict coupled eigenfrequencies with an error of less than 1%. In contrast, fourth- and fifth-order Taylor models achieve engineering accuracy with approximately 100 times fewer degrees of freedom. Parametric studies reveal that changing the lateral boundaries from simply supported to free lowers the fundamental frequency by approximately 3% and accentuates in-plane motion, especially in the mid-frequency range where plate and cavity modes coalesce. The method thus offers an efficient and validated alternative to complete 3-D analysis, with future extensions envisioned for nonlinear effects, damping layers, and gradient-based design optimization.