Iranian Society of Mechanical Engineering Iranian Journal of Mechanical Engineering Transactions of the ISME 1605-9727 11 1 2010 03 01 Finite Element Analysis of Functionally Graded‎ ‎Piezoelectric Beams 45 73 20572 EN A. Armin Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran B. Behjat Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran M. Abbasi Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran M. R. Eslami Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran Journal Article 2010 10 01 In this paper‎, ‎the static bending‎, ‎free vibration‎, ‎and dynamic response of functionally graded‎ ‎piezoelectric beams have been carried out by finite element method‎‎under different sets of mechanical‎, ‎thermal‎, ‎and electrical‎ ‎loadings‎. ‎The beam with functionally graded piezoelectric material‎ ‎(FGPM) is assumed to be graded across the thickness with a simple‎ ‎power law distribution in terms of the volume fractions of the‎ ‎constituents‎. ‎The electric potential is assumed linear across the‎ ‎FGPM beam thickness‎. ‎The temperature field is assumed to be of‎ ‎uniform distribution over the beam surface and through the beam‎ ‎thickness‎. ‎The governing equations are obtained using potential‎ ‎energy and Hamilton's principle based on the Euler-Bernoulli beam‎ ‎theory that includes thermo-piezoelectric effects‎. ‎The finite‎ ‎element model is derived based on the constitutive equation of‎ ‎piezoelectric material accounting for coupling between the‎ ‎elasticity and the electric effect by two nodes Hermitian beam‎ ‎element‎. ‎The present finite element is modelled with displacement‎ ‎components and electric potential as nodal degrees of freedom‎. ‎The‎ ‎temperature field is calculated by post-computation through the‎ ‎constitutive equation‎. ‎Results are presented for two-constituent‎ ‎FGPM beam under different mechanical boundary conditions‎. ‎Numerical results include the influence of the different power law‎ ‎indexes‎, ‎the effect of mechanical‎, ‎thermal‎, ‎and electrical‎ ‎loadings and the type of in-plane boundary conditions on the‎ ‎deflection‎, ‎stress‎, ‎natural frequencies‎, ‎and dynamic response‎. ‎The‎ ‎numerical results obtained by the present model are in good‎ ‎agreement with the available solutions reported in the‎ ‎literature. https://jmee.isme.ir/article_20572_3889837143074f2ccb5989d34dc6e82b.pdf