Damped Nonlinear Dynamics of FG-GPLRC Dielectric Beam with Active Tuning Using DQ and IHB Methods

The composites reinforced by graphene and its derivatives have demonstrated great potential in developing high-performance and smart materials and structures. This paper numerically studies the dynamic characteristics of functionally graded (FG) graphene platelets (GPLs) reinforced composite (FG-GPLRC) dielectric beam subjected to damping, mechanical excitation and electrical field. Required mechanical and physical properties of the composites are evaluated by effective medium theory (EMT). Governing equations for the structure are established based on Timoshenko beam theory and nonlinear von Kármán strain-displacement relationship. Differential quadrature (DQ) and incremental harmonic balance (IHB) together with an arc-length algorithm are combined to discretize and solve the highly nonlinear equations. The effects of the geometry and concentration of GPLs, attributes of electrical field, FG distribution profile, excitation and damping on the dynamic characteristics of the beam are comprehensively investigated. Two transition regions for the effect of AC (alternating current) frequency of the electrical field on the dynamic performances of the beam are identified. There exist thresholds for GPL concentration, FG slope factor and aspect ratio for the dynamic response of the composite beam. It is indicated that the dynamic performances of the FG composite beam can be actively tuned by changing the attributes of the electrical field. The numerical investigation is envisaged to provide guidelines for the design and optimization of developing smart engineering structures.