Eigensolutions to functionally graded material plates covered with piezoelectric surface layers

Abstract

The transverse free vibration analysis of composite intelligent plates constituted by the functionally graded substrate and full size surface-attached piezoelectric laminae is conducted by means of the scaled boundary finite element method (SBFEM) in association with the precise integration algorithm (PIA). It is needful to point out that material coefficients of the functionally graded host layer are altered across the single direction or both in-plane coordinate axes and changed as any form of polynomial or non-polynomial formulae. In the suggested methodology, only the outer surface parallel with the x-O-y coordinate plane is required to be meshed with two dimensional spectral elements. Moreover, three and four degrees of freedom for non-homogeneous and piezoelectric laminae respectively are adopted, which is convenient to decrease the calculation expense and increase the computational efficiency. Supported by the scaled boundary coordinate system z-η-ζ, the governing equation of the hybrid plate is expressed as an ordinary differential one. Aided by the highly accurate PIA, the stiffness matrix of each layer from the analytical matrix exponential function can be acquired. Eigensolutions to laminated coupling plates are derived from the eigenvalue equation composed of stiffness and mass matrices. From tabular and graphical comparisons with available data provided by open works, the brilliant correctness and broad utilization of the exploited procedure are revealed. Finally, numerical exercises are implemented to examine impacts of gradient functions, constraint conditions, gradation parameters and aspect ratios on free vibration responses of composite smart plates.