Hydro-elastic vibration analysis of functionally graded circular plate vertically in contact with stationary fluid

This study investigates the free vibration of a thick FG circular plate in contact with an inviscid and incompressible fluid. Analysis of the plate is based on First-order Shear Deformation Plate Theory (FSDT) with consideration of rotational inertial effects and transverse shear stresses. Dynamic transverse displacements of the plate are approximated by set of admissible Chebyshev functions which is required to satisfy the geometric boundary conditions. Potential theory together Bernouli’s equation are utilized to obtain the fluid pressure on the free surface of the plate. The governing equation of the oscillatory behavior of the fluid is obtained by solving Laplace equation and satisfying its boundary conditions. The natural frequencies and mode shapes of the plate are determined using Rayleith-Ritz method based on minimizing the Rayleith quotient. The effects of the geometrical parameters such as height of the fluid, plate thickness to its radius ratio, fluid density, vessel height and volume fraction index on natural frequencies and mode shapes are investigated. Comparison of analytically outcome of this study is made with results of the experimental modal test for homogeneous Aluminum plate.