Static, Dynamic, and Free Vibration Analysis of Functionally Graded Piezoelectric Panels Using Finite Element Method

Abstract

In this article, analysis of the static bending, free vibration, and dynamic response of functionally graded piezoelectric panels have been carried out by finite element method under different sets of mechanical, thermal, and electrical loadings. The temperature field is assumed to be of uniform distribution over the panel surface and through the thickness of panel. The governing equations are obtained using potential energy and Hamilton’s principle based on the first-order shear deformation theory that includes thermo-piezoelectric effects. The finite element model is derived on the basis of constitutive equation of piezoelectric material accounting for coupling between elasticity and electric effect by four node elements. The present finite element is modeled with displacement components and electric potential as nodal degrees of freedom. The temperature field is calculated by post-computation through constitutive equation. Results are presented for two constituent FGPM panels under different mechanical boundary conditions. Numerical results for PZT-4/PZT-5H panels are given in both dimensionless tabular and graphical forms. Effects of material composition and boundary conditions on static bending, free vibration, and dynamic response are also studied. The numerical results obtained by the present model are in good agreement with the available solutions reported in the literature.

A review of theories for the modeling and analysis of functionally graded plates and shells

“…Further studies on geometrically nonlinear bending behavior of FSDT shells were carried out by Barbosa and Ferreira [116] and Sheng and Wang [117] using Marguerre shell element and fourorder Runge-Kutta numerical method, respectively. Behjat et al [118] …”

Viscoelastic material damping characteristics of carbon nanotubes based functionally graded composite shell structures

“…Sheng and Wang 15 studied the effects of the thermal load based on the first-order shear deformation theory (FSDT) on the vibration, buckling, and dynamic stability of FG cylindrical shells surrounded by an elastic medium. Behjat et al 16 carried out static bending, free vibration, and dynamic responses of FG piezoelectric panels for various mechanical, thermal, and electrical loadings using FE-based FSDT. Kiani et al 17 performed free vibration and dynamic behavior of an FG doubly curved shell panel with FSDTbased and modified Sanders assumptions.…”

Optimum material gradient composition for the functionally graded piezoelectric beams

“…A comprehensive study on the static, dynamic and free vibration response of functionally graded piezoelectric panels under different sets of mechanical, thermal and electrical loadings using the finite element method was presented by Behjat et al (2009). Behjat et al (2011) investigated also the static bending; free vibration and dynamic response of functionally graded piezoelectric plates under mechanical and electrical loads using the first order shear deformation theory.…”