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

Abstract

This study investigates the free vibration of a moderately thick rectangular plate, which is composed of functionally graded materials and floating on incompressible fluid. Material properties are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fraction of the constituent. The governing equations of the plate are analytically derived based on the first-order shear deformation theory with consideration of rotational inertial effects and transverse shear stresses. Applied pressure on the free surface of the plate is obtained by the velocity potential function together with Bernoulli’s equation. The equation governing on the oscillatory behaviour of the fluid is obtained by solving Laplace equation with satisfying the boundary conditions. The natural frequencies and shape modes of the rectangular plate are determined by decoupling and solving the motion equations system. Then, analyses of the numerical results of free vibrations and the effects of the different parameters such as thickness to length of the plate, boundary conditions, fluid density, index of volume fraction and the height of the fluid on the frequencies are investigated. Finally, the results of this research in limit case is compared and validated with the results of other researchers and finite element model.

Divergence‐free finite elements for the numerical solution of a hydroelastic vibration problem

“…For instance, we mention [16] for a formulation in fluid displacement potential, [14,29] for an added mass formulation based on taking into account the effect of the fluid by means of a Neumann-to-Dirichlet operator and [6] for a BEM approach. We also mention [30,31,37,38] as examples of some more recent papers, which show a continuous interest on this subject.…”