Three-Dimensional Solution for the Vibration Analysis of Functionally Graded Rectangular Plate with/without Cutouts Subject to General Boundary Conditions

Abstract

Functionally graded materials (FGMs) structures are increasingly used in engineering due to their superior mechanical and material properties, and the FGMs plate with cutouts is a common structural form, but research on the vibration characteristics of FGMs plate with cutouts is relatively limited. In this paper, the three-dimensional exact solution for the vibration analysis of FGMs rectangular plate with circular cutouts subjected to general boundary conditions is presented based on the three-dimensional elasticity theory. The displacement field functions are expressed as standard cosine Fourier series plus auxiliary cosine series terms satisfying the boundary conditions in the global coordinate system. The plate with circular cutout is discretized into four curve quadrilateral sub-domains using the p-version method, and then the blending function method is applied to map the closed quadrilateral region to the computational space. The characteristic equation is obtained based on the Lagrangian energy principle and Rayleigh–Ritz method. The efficiency and reliability of proposed method are verified by comparing the present results with those available in the literature and FEM methods. Finally, a parametric study is investigated including the cutout sizes, the cutout positions, and the cutout numbers from the free vibration characteristic analysis and the harmonic analysis. The results can serve as benchmark data for other research on the vibration of FGMs plates with cutouts.

Stress Analysis of 2D-FG Rectangular Plates with Multi-Gene Genetic Programming

“…In the last two decades, many studies have been conducted on the determination of the mechanical behavior of FGMs [1][2][3][4][5][6][7][8]. However, due to the difficulties encountered in production, the use of FGMs in the industry has been limited [9,10].…”

Three Dimensional Vibration of an Isotropic Plate Enclosed in a Rigid Body

“…Liew and Yang [18] investigated the vibrational characteristics of annular plates based on the three-dimensional elasticity theory. Recently, Huang et al [19] have developed a three-dimensional exact solution for the vibration analysis of functionally graded rectangular plates. The free vibrations of threedimensional orthotropic rectangular plates have been…”