Free Natural Frequency Analysis of an FG Composite Rectangular Plate Coupled with Fluid using Rayleigh-Ritz Method

Abstract

This study investigates natural frequency analysis of an FG composite rectangular plate partially contacting with a bounded fluid. The material properties are assumed to be varying continuously through the thickness direction according to a simple power law distribution in terms of volume fraction of material constituents. Wet dynamic transverse displacements of the plate are approximated by a set of admissible trial functions which are required to satisfy the clamped and simply supported geometric boundary conditions. Fluid velocity potential satisfying fluid boundary conditions is derived and wet dynamic modal functions of the plate are expanded in terms of finite Fourier series for compatibility requirement along the contacting surface between the plate and the fluid. Natural frequencies of the plate coupled with sloshing fluid modes are calculated using Rayleigh–Ritz method based on minimizing the Rayleigh quotient. The proposed analytical method is validated by available data in the literature. The numerical results show the effects of boundary conditions, aspect ratios, thickness ratios, gradient index, material properties of the FG plate, depth of the fluid and dimensions of the tank on the wet natural frequencies.