Numerical study on damped nonlinear dynamics of cracked FG-GNPRC dielectric beam with active tuning

Abstract

Functionally graded (FG) graphene nanoplatelets (GNPs) reinforced composite (FG-GNPRC) is widely used in various engineering fields due to its high-performance and multifunctional features. Cracks generated in complex environments have a significant impact on the structural behavior of FG-GNPRC structures. This paper studies the damped nonlinear dynamics of cracked FG-GNPRC dielectric beam subjected to mechanical excitation and electrical field. The effective material properties of the composites are determined by the effective medium theory (EMT). Based on Timoshenko beam theory and nonlinear von Kármán strain–displacement relationship, the governing equations which incorporate damping and dielectric properties are derived by using energy method. Stress intensity factor (SIF) of cracked FG-GNPRC beam at the crack tip is calculated via finite element method. Differential quadrature (DQ) and incremental harmonic balance (IHB) methods combined with arc-length algorithm are utilized to discretize and solve the nonlinear system. After validation of the model and solution, the effects of crack depth and location, damping, FG distribution and the attributes of GNP and the electric field on the dynamic response of the system are comprehensively investigated. The study indicates that when an electric field is applied, the amplitude ratio of cracked FG-GNPRC beam with profile V is the largest when the crack is close to the edge, whereas profile A exhibits the largest value when the crack is near the mid-span. In addition, the generated bending moment enables profiles A and V to transit into profile U at a certain voltage or GNP aspect ratio due to the existence of electrostatic stress.