Hydroelastic vibration of two identical rectangular plates

A theoretical study is presented on the hydroelastic vibration of two identical rectangular plates coupled with a bounded fluid. It is assumed that the plates are clamped along the plate edges and an ideal fluid is surrounded by the two rectangular plates and a rigid rectangular container. The velocity potential satisfying the fluid boundary conditions is expanded in terms of a finite Fourier series and the modal displacements of the plates are also expanded by the finite Fourier series for the compatibility requirement along the contacting surface between the plates and the fluid. Two transverse vibration modes, in-phase and out-of-phase, are observed in the symmetric fluid-coupled structure. Each in-phase mode is assumed as a combination of the beam modes in air, but every out-of-phase mode is assumed as a combination of polynomials satisfying the plate boundary condition and fluid volume conservation. The coupled natural frequencies are obtained from the relationship between the reference kinetic energy of the structure including the fluid and the maximum strain energy of the two plates. The proposed analytical method was found to be in good agreement with the results of a three-dimensional finite element analysis.