Nonlinear static and dynamic responses of edge-cracked FG-GPLRC dielectric beams with internal pores

The dielectric properties of functionally graded (FG) graphene platelets (GPLs) reinforced composite (FG-GPLRC) beams enable tunable mechanical responses under external electric fields and hence offer an effective way for enhanced control of structural performance. This paper investigates nonlinear static and dynamic responses of FG-GPLRC dielectric beams with internal pores and an open edge crack. A two-step hybrid mechanical model is developed to determine the material properties of the multiphase composites. The governing equations, incorporating damping and dielectric properties, are derived within the framework of Timoshenko beam theory and the nonlinear von Kármán strain-displacement relationship. The stress intensity factor (SIF) at the crack tip of the cracked FG-GPLRC beam is obtained via finite element method (FEM). Differential quadrature (DQ) and incremental harmonic balance (IHB) methods combined with the arc-length algorithm methods are utilized to solve the nonlinear system. After the present analysis has been verified, a comprehensive parametric study is conducted to examine the effects of internal pore attributes, crack location and depth, damping, GPL properties and the applied electric field on the nonlinear bending, free and forced vibrations of the cracked FG-GPLRC beam. The study indicates that the internal pore attributes and crack location and depth have a significant impact on the nonlinear frequency, dimensionless amplitude, and peak amplitude excitation frequency of the cracked FG-GPLRC beam under an applied voltage.