Free Vibration of FGSW Plates Partially Supported by Pasternak Foundation Based on Refined Shear Deformation Theories

Cong Ich Le,Dinh Kien Nguyen,Vu Nam Pham

doi:10.1155/2020/7180453

Abstract

A refined third-order shear deformation theory (RTSDT), in which the transverse displacement is split into bending and shear parts, is employed to formulate a four-node quadrilateral finite element for free vibration analysis of functionally graded sandwich (FGSW) plates partially supported by a Pasternak foundation. An element based on the refined first-order shear deformation theory (RFSDT) which requires a shear correction factor is also derived for comparison purpose. The plates consist of a fully ceramic core and two functionally graded skin layers with material properties varying in the thickness direction by a power gradation law. The Mori–Tanaka scheme is employed to evaluate the effective moduli. The elements are derived using Lagrangian and Hermitian polynomials to interpolate the in-plane and transverse displacements, respectively. The numerical result reveals that the frequencies obtained by the RTSDT element are slightly higher than the ones using the RFSDT element. It is also shown that the foundation supporting area plays an important role on the vibration of the plates, and the effect of the material distribution on the frequencies is dependent on this parameter. A parametric study is carried out to highlight the effects of the material inhomogeneity, the foundation stiffness parameters, and the foundation supporting area on the frequencies and vibration modes. The influence of the layer thickness and aspect ratios on the frequencies is also examined and highlighted.

Highlights

With the development of advanced manufacturing methods [1], functionally graded materials (FGMs)—a new type of composite materials initiated by Japanese researchers in mid-1980 [2], can be incorporated into sandwich construction to improve performance of the structures
Graded sandwich (FGSW) structures can be designed to have a smooth variation of properties, which helps to avoid the interface separation problem as often seen in the conventional sandwich structures
Parametric studies carried out by the author show the importance of the material distribution, aspect ratio, and core thickness on the mechanical behaviour of the plates. e theory was employed in [5] to study the thermal buckling of Functionally graded sandwich (FGSW) plates

Summary

Introduction

With the development of advanced manufacturing methods [1], functionally graded materials (FGMs)—a new type of composite materials initiated by Japanese researchers in mid-1980 [2], can be incorporated into sandwich construction to improve performance of the structures. Zenkour [26, 27] used the trigonometric and hyperbolic functions to modify the displacement field to form the four-unknown shear deformation theories for bending analysis of FGM plates.

Results

Conclusion