Exact Electroelastic Field of a Functionally Graded Piezoelectric Cantilever Beam Subjected to Pure Body Force Loading

The electroelastic response of functionally graded piezoelectric cantilever beams which includes the effect of body force is presented in this paper. The material properties such as elastic compliance, piezoelectric and dielectric impermeability are assumed to be graded with different indices in the thickness direction according to exponential distributions. Systems of fourth order inhomogeneous partial differential equations (PDEs) which are satisfied by the stress and induction functions and involve the body force terms are derived. Spectral forms for electrical and mechanical variables in the x-axis are employed to convert the partial differential governing equations and the associated boundary conditions into sets of ordinary differential equations, and the resulting equations are solved in a closed form manner. Subsequently, in numerical studies, the effects of the material property graded indices are examined upon the electroelastic response of FGP cantilever beams under pure body force loadings.