Stability of an axially moving laminated composite beam reinforced with graphene nanoplatelets

This study investigates the dynamic stability of an axially moving laminated composite beam reinforced by graphene nanoplatelets (GPLs) under constant and harmonically varying velocities. It is assumed that GPLs are distributed into the beam in different patterns through the thickness symmetrically, and the GPL distribution in each layer is uniformly and randomly oriented. The effective Young's modulus of the nanocomposite is predicated on Halpin-Tsai's model. The partial differential equations of motion for the axially moving laminated composite beam are derived using Hamilton's principle, and the ordinary differential governing equations are obtained by Galerkin method. According to the eigenvalues of the coefficient matrix of the ordinary differential equations, the linear stability of the axially moving beam reinforced with GPLs at constant velocity is studied. Finally, the instability region of the axially moving beam in the perspective of resonance under harmonically varying velocity is discussed in detail by utilizing the multiscale method. Governing equations of motion for the axially moving beam are established.Instability regions are obtained considering the damping.Reinforcement of GPLs on the stability of axially moving beam is analyzed.