Size-dependent free vibration analysis of functionally graded porous piezoelectric sandwich nanobeam reinforced with graphene platelets with consideration of flexoelectric effect

This paper investigates the effect of flexoelectricity on the vibration responses of functionally graded porous piezoelectric sandwich nanobeam reinforced by graphene platelets (GPLs). The Euler-Bernoulli beam theory and the general modified strain gradient theory are employed to formulate the constitutive equations. Different distributions of porosity and GPLs dispersion patterns are considered and the Halpin-Tsai model is used to predict Young's modulus and density of the nanobeam. The governing equations and boundary conditions are derived based on the general strain gradient theory and solved by differential quadrature method. A parametric study is accomplished to investigate the effects of flexoelectricity, size-dependence, porosity coefficient, GPLs weight fraction, porosity distributions as well as GPLs dispersion patterns on the fundamental frequency of composite nanobeam. Numerical results indicate that the porosity, GPLs and flexoelectricity can effectively influence the vibration behavior of nanobeam.