Free vibration analysis of FGM plates on Winkler/Pasternak/Kerr foundation by using a simple quasi-3D HSDT

摘要

This paper introduces a simple quasi-3D theory with Reddy shear function and a new trigonometric shear func-tion to conduct free vibration analysis of the functionally graded plates resting on Winkler/Pasternak/Kerr elastic foundation. The proposed transverse shear strain functions satisfy the stress-free boundary conditions on the surfaces of the functionally graded plate without using any shear correction factors. The governing dif-ferential equation and boundary conditions are derived based on Hamilton's principle and Winkler/Pasternak/ Kerr type mathematical model. The material properties of FGM plates discussed in this paper are assumed to vary through the thickness according to the power-law distribution. The obtained results are compared with other 2D, quasi-3D and exact 3D solutions. The results show that the proposed trigonometric shear functions are more accurate than Reddy ones. Some interesting physical discussions of the recorded results are also given in this study.