Size-dependent static bending and free vibration analysis of porous functionally graded piezoelectric nanobeams

According to electric enthalpy variation and Hamilton's principle, governing differential equations and boundary conditions of functionally gradient piezoelectric nanobeams with porosities are established. The generalized differential quadrature method plays the role of transforming governing differential equations into a group of linear algebraic equations. Based on the strain gradient theory, a size-dependent functionally gradient piezoelectric nanobeam formulation including additional material length scale parameters is established. The static bending and free vibration analysis of a nanobeam made up of porous functionally gradient piezoelectric materials is researched. Two kinds of porosity distributions are considered in this paper. The influencess of power law index, porosity parameter, porosity distribution, external electrical voltage, flezoelectric effect, length scale parameter and boundary conditions on static deformation and natural frequencies of the nanobeam are researched in detail.