Free vibration analysis of a functionally graded rectangular plate in contact with a bounded fluid

Abstract

This study investigates the vibration analysis of a functionally graded (FG) rectangular plate partially in contact with a bounded fluid. The material properties are assumed to vary 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. The 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 the Rayleigh-Ritz method based on minimizing the Rayleigh quotient. The proposed analytical method is validated with available data in the literature. In the numerical results, 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 are investigated.

Nonlocal elasticity in plates using novel trial functions

“…The nonlocal differential model has been used with the Rayleigh-Ritz method to calculate the natural frequencies of uniform and non-uniform nonlocal plates for several possible boundary conditions (Chakraverty and Behera, 2014;Behera and Chakraverty, 2016). Rayleigh-Ritz method has been used for local vibration analysis of moderately thick rectangular plates (Hashemi et al 2009) and functionally graded rectangular plate (Khorshidi and Bakhsheshy, 2015). Faroughi and Goushegir (2016) studied the in-plane natural frequencies and mode shapes of non-uniform rectangular nanoplates using the Eringen nonlocal differential model along with the Rayleigh-Ritz method.…”

Buckling Analysis of a Functionally Graded unidirectional rectangular nanoPlate considering the surface effect

“…In fact, every material has different properties for surface parameters that each parameter has particular effect on the critical buckling load but in this research based on the properties that have been tabulated in table 1, the resultant effect of surface parameter leads to decreasing the critical buckling load. 7 Trigonometric shear deformation theory 8 Hyperbolic shear deformation theory 9 parabolic shear deformation theory 10 Local Petrov-Galerkin weak-formulation 11 Pasternak model 12 Strain gradient theory 13 Couple stress theory 14…”

The Rayleigh–Ritz method for linear dynamic, static and buckling behavior of beams, shells and plates: A literature review

“…Chakraverty and Pradhan (2014) studied free vibration of FGM thin rectangular plates resting on Winkler foundation using simple algebraic polynomials in the Rayleigh–Ritz method. Khorshidi and Bakhsheshy (2014, 2015) investigated free vibration of FGM rectangular plate in contact with a bounded fluid using the Rayleigh–Ritz method. Kinetic and strain energies of the system are obtained on the basis of CPT (classical plate theory), FSDT and TSDT.…”