Free vibration of FGM Mindlin plates submerged in fluid

Abstract

This paper presents a free vibration analysis of functionally graded material (FGM) plates that are partially submerged in an incompressible, inviscid fluid. The FGM plates with four gradient types of continuously varying material properties along the thickness direction, including the power law, exponential, sinusoidal and cosine forms, are studied to examine various distributions of material properties. The plate is modeled based on the Mindlin Plate Theory (MPT), and the fluid loading effect on the FGM plates is modeled using the method of added mass. The variational principle is applied to derive the governing equations of this fluid-plate interaction system. The differential quadrature (DQ) method is used to solve this problem by converting the governing equations into a system of linear equations. The fundamental frequency and the corresponding mode shape are obtained using an iterative procedure. Numerical results for several examples are obtained and presented to investigate the vibration characteristics of the submerged FGM plates in terms of the gradient index, gradient type, immersed depth, fluid density, aspect ratio and slenderness ratio. Results indicate that the larger aspect ratio and immersed depth increase the fundamental frequency of the FGM plate, while larger gradient index, fluid density and slenderness ratio decrease the fundamental frequency. Among four different material gradient types, the FGM plate with power law type gradient has the smallest fundamental frequency, while the one with sinusoidal form has the largest value. The mode shape in fluid deviates from that in vacuum and shows an unsymmetrical shape for CCCC and SSSS FGM plates.