Vibration of 2D FG Higher Order Plates using Differential Integral Quadrature Method

Amr, E. Assie; Salwa, Mohamed

doi:10.21608/jest.2022.249536

Vibration of 2D FG Higher Order Plates using Differential Integral Quadrature Method

Document Type : Original Article

Authors

E. Assie Amr ¹^{, 2}
Mohamed Salwa ³

¹ Mechanical Engineering Department, Faculty of Engineering, Jazan University, P. O. Box 45142, Jazan, Kingdom of Saudi Arabia

² Department of Mechanical Design and Production, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt

³ Department of Engineering Mathematics, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt

10.21608/jest.2022.249536

Abstract

This article presented a mathematical model to investigate the free vibration behavior of bi-directional (2D) functionally graded plate (FGP) using higher order shear deformation theory. The gradation of the material through the thickness and axial directions is described by power distribution function, which derived based on Voigt rule of mixture. Kinematic higher order shear theory developed by Reddy, equivalent single layer 2D constitutive equation, and Hamilton’s principle are exploited to describe the strains, stress-strain relations, and equations of motions of 2D-FGP. Numerical differential integral quadrature method (DIQM) is manipulated to discretize the structure spatial domain and solve the system equations. Validation with previous work is presented. Numerical parametric studies are developed to illustrate the influence of gradation indices, slenderness ratio and aspect ratio on the natural frequencies of 2D-FG plate. The proposed model is economical in designing many applications used in nuclear, mechanical, aerospace, naval, dental, and medical fields.

Keywords