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An Analytical Solution for Nonlinear Vibration Analysis of Functionally Graded Rectangular Plate in Contact with Fluid

An Analytical Solution for Nonlinear Vibration Analysis of Functionally Graded Rectangular Plate in Contact with Fluid
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Year:    2021

Author:    Soheil Hashemi, Ali Asghar Jafari

Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 4 : pp. 914–941

Abstract

In this paper, the nonlinear vibrations analysis of functionally graded (FG) rectangular plate in contact with fluid are investigated analytically using first order shear deformation theory (FSDT) for the first time. The pressure exerted on the free surface of the plate by the fluid is calculated using the velocity potential function and the Bernoulli equation. With the aid of von Karman nonlinearity strain-displacement relations and Galerkin procedure the partial differential equations of motion are developed. The nonlinear equation of motion is then solved by modified Lindstedt-Poincare method (MLPM). The effects of some system parameters such as vibration amplitude, fluid density, fluid depth ratio, volume fraction index and aspect ratio on the nonlinear natural frequency of the plate are discussed in detail.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2019-0333

Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 4 : pp. 914–941

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    28

Keywords:    Nonlinear vibration functionally graded materials fluid pressure first order shear deformation theory modified Lindstedt-Poincare method.

Author Details

Soheil Hashemi

Ali Asghar Jafari

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