Free vibration analysis of a laminated composite sandwich plate with compressible core placed at the bottom of a tank filled with fluid

The paper addresses the free vibration problem of a laminated composite sandwich plate with compressible core, placed at the bottom of a tank filled in with fluid. The analysis is performed based on the extended higher order sandwich plate theory (EHSAPT). First-order shear deformation theory (FSDT) is used for the face sheets. Cubic and quadratic polynomials are used to describe the in-plane and transverse displacements of the core, respectively. The fluid is assumed inviscid, incompressible, and irrotational. To obtain the kinetic energy of the fluid, its velocity potential is expressed by using the compatibility and boundary conditions. The governing differential equations and corresponding boundary conditions are derived from Hamilton’s principle. A single series expansion is considered with two-variable orthogonal polynomials as a set of admissible functions satisfying the boundary conditions. The natural frequencies of the coupled sandwich plate-fluid system are calculated by using the Rayleigh-Ritz method. Convergence of the adopted strategy is first investigated. Then, comparisons are conducted with previous results reported in the literature. Also, the effects are investigated of several parameters, such as the plate side-to-thickness ratio, the core-to-face sheets thickness ratio, the face sheet-to-core flexural modulus ratio, the height and aspect ratio of the tank.