Parametric study on damped nonlinear vibration of FG-GPLRC dielectric beam with edge crack

In this paper, we investigate the damped nonlinear vibration of cracked functionally graded (FG) graphene platelets (GPLs)-reinforced composite (FG-GPLRC) dielectric beam. The effective material properties of the composites are evaluated by effective medium theory (EMT) and rule of mixture. Governing equations incorporating damping and dielectric properties are derived from an energy method with the framework of Timoshenko beam theory and nonlinear von Kármán strain–displacement relationship. Stress intensity factor (SIF) of cracked FG-GPLRC beam at the crack tip is obtained via finite element method (FEM). Differential quadrature (DQ) and direct iterated methods are utilized to discretize and solve the nonlinear system. Accuracy and convergence of the model and the solution are verified. An extensive numerical study is performed to examine the effects of crack location and depth, damping and attributes of GPL and the applied electric field on the nonlinear vibration behavior of the cracked FG-GPLRC beam. It is found that the frequency ratios of cracked FG-GPLRC beams are more sensitive to the applied electric field when the crack with larger depth is located close to the mid-span. The cracked FG-GPLRC beams with FG distribution profiles exhibit better stability.