Analytical study on the vibration of spatial plate-plate coupled structures with combined simply supported and clamped edges

Spatial plate-plate coupled structures (cross, L, and T-shaped) are fundamental elements in engineering, yet a unified solution covering multiple coupling configurations, arbitrary coupling angles, and combined simply supported-clamped boundaries remains unavailable. This study develops a unified and rigorous analytical framework using the finite integral transform (FIT) method to obtain the closed-form solutions for free and forced vibrations of coupled plates, without shape function assumptions or numerical discretization. Validations against finite element analysis (FEA) show errors below 1%, demonstrating high accuracy. The main contributions of this study are the derivation of a unified analytical solution for coupled plates and the revelation of mechanistic insights based on the closed-form solution. These new insights include: rigid coupling makes free vibration independent of coupling angle; alternately distributed boundaries (CSCS) outperform adjacently distributed ones (CCSS) by uniformly suppressing rotation and deflection; low-order natural frequencies are sensitive only to the constraints of stiffness-dominant plates, enabling constraint simplification on non-dominant components; and rigid coupling at modal antinode lines maximizes the fundamental frequency by effectively suppressing the maximum modal deflection. These findings demonstrate that constraint spatial topology outweighs constraint number in dynamic regulation, providing an effective analytical tool for lightweight design and vibration control of coupled plate structures.