Magneto-elastic vibration of axially moving graphene nanocomposite current-carrying beam with variable speed and axial force

Lightweight, high-strength, conductive carbon nanocomposites are widely used in axial moving systems, and the primary parametric resonance and primary resonance due to variable axial velocity and tension are quite disturbing when they work in complex electromagnetic environments. In this paper, a theoretical model for predicting Young’s modulus and electrical conductivity of graphene nanocomposites is developed by combining equivalent medium theory, shear-leg theory, and Mori–Tanaka theory. The magnetoelastic vibration equations of axially moving graphene nanocomposite current-carrying beam with variable speed and axial force are then derived and solved analytically and numerically. The amplitude-frequency response equations are derived to describe the parametric resonance of the nanocomposite beam with different graphene volume concentrations. The coupled effect of graphene fillers, electric–magnetic field, and external citation on the system’s primary parametric resonance are deeply investigated. The results showed that the concentration of graphene filler could significantly affect the amplitude response of the system by controlling Young’s modulus and electrical conductivity of the nanocomposite. It can provide a theoretical basis for structure design and vibration control in engineering applications.