An analytical study for nonlinear vibration analysis of two-directional functionally graded rectangular plate

Hashemi, Soheil; Jafari, Ali Asghar

doi:10.30506/jmee.2020.112273.1193

An analytical study for nonlinear vibration analysis of two-directional functionally graded rectangular plate

Document Type : Research Paper

Authors

Soheil Hashemi ¹

Ali Asghar Jafari ²

¹ Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran

² K.N Toosi University

10.30506/jmee.2020.112273.1193

Abstract

In this study, an analytical solution is presented for investigating the nonlinear vibration analysis of two-directional functionally graded rectangular plate for the first time. On the basis of first order shear deformation theory (FSDT) and Galerkin procedure, the equations of motion are developed. The nonlinear equation of motion is then solved analytically by modified Lindstedt-Poincare method. The volume fraction distribution is assumed to be symmetrical for characterizing the in-plane material inhomogeneity. Finally, the effects of some system parameters such as non-dimensional vibration amplitude, volume fraction indexes and aspect ratio on the nonlinear to linear frequency ratio are discussed in detail. To validate the analysis, the results of this paper are compared with the published data and good agreements are found.

Keywords

Nonlinear vibration

Rectangular plate

bi-directional functionally graded material

First order shear deformation theory

Modified Lindstedt-Poincare method