Static Analysis of Functionally Graded Piezoelectric Beams under Thermo-Electro-Mechanical Loads

Abstract

This paper presents the analysis of static bending of beams made of functionally graded piezoelectric materials (FGPMs) under a combined thermo-electro-mechanical load. The Euler Bernoulli theory (EBT), first-order shear deformation theory (FSDT) and third-order shear deformation theory (TSDT) were employed to compare the accuracy and the reliability of each theory in applications. The material properties vary continuously through the thickness direction. The material compositions were selected from the PZT family. The governing equations were derived from Hamilton's principle and solved using the finite element method and Fourier series method. Cubic Hermit interpolation shape function was used for estimating the transverse deflection, and the linear interpolation function was used for the axial displacement and the shear rotation as well. Fourier series expansion, based on the boundary conditions, were employed to solve the governing equations analytically. The accuracy of the method was validated by comparing the results with the previous studies. Finite element results were compared with the analytical results presented in this paper. A comprehensive parametric study is conducted to show the influence of the voltage, shear deformation, material composition, end supports, and the slenderness ratio on the thermo-electro-mechanical characteristic.

A Multi-Parameter Perturbation Solution for Functionally Graded Piezoelectric Cantilever Beams under Combined Loads

“…Zhong and Yu obtained a solution for FGPM cantilever beams under different loadings by assuming that the mechanical and electrical properties of the material have the same variations along the thickness direction [ 20 ], and proposed a general solution for FGPM cantilever beams with arbitrary graded material properties along the beam thickness direction by expressing the Airy stress function and the electric potential function in finite power series [ 21 ]. Yang and Xiang [ 22 ] and Komeili et al [ 23 ] investigated the static bending FGPM beams under combined thermo-electro-mechanical loads. Based on the modified strain gradient theory and Timoshenko beam theory, Li et al [ 24 ] developed a size-dependent FGPM beam model by using variational formulation, and solved the static bending and free vibration problems of a simply supported FGPM beam.…”

Finite element modelling to assess the effect of position and size of the piezoelectric layer of a hybrid beam

“…They used an N-order polynomial approximation of the displacement unknown variables to impose kinematic field above the cross-section. Komeili et al 2011 presented the static bending analysis of functionally graded piezoelectric beams under thermo-electro-mechanical load. They derived the governing equations from Hamilton's principle and used the finite element method and Fourier series method as solution technique.…”

A numerical efficiency study on the active vibration control for a FGPM beam

“…These FGPM are generally made of a mixture of two piezoelectric materials. Several authors studied FGPM beams or plates under thermo-electro-mechanical loads: static analysis have been performed in [4][5][6][7] and modal analysis in [8][9][10][11][12]. The geometrically non linear transient thermo-elastic response of FGM beam integrated with a pair of FGPM sensors has been investigated in [13].…”