Dynamic stability of axially moving graphene reinforced laminated composite plate under constant and varied velocities

Abstract

The dynamic stability of an axially moving graphene reinforced laminated composite plate is studied. The graphene nanoplatelets (GPLs) are distributed in each polyvinylidene fluoride (PVDF) layer uniformly and in the whole plate symmetrically. The volume fraction of the first layer is used as the control variable to determine the distribution pattern of the GPLs. Halpin–Tsai’s model is used to predict the effective Young’s modulus of the axially moving graphene reinforced laminated composite plate. The effective mass density and Poisson’s ratio are calculated by using the rule of mixture. Based on von Kármán plate theory and Hamilton’s principle, the governing equations of motion are derived for the axially moving graphene reinforced laminated composite plate. To evaluate the stability of the axially moving graphene reinforced laminated composite plate with the constant velocity, the ordinary differential equations of motion are obtained by using Galerkin method. The effect of the graphene reinforcement on the critical and flutter velocities of the axially moving laminated composite plate is analyzed based on the eigenvalue of the coefficient matrix. The influence of the graphene reinforcement on the instability region for the axially moving laminated composite plate with the varied velocity is also evaluated by using the direct multiscale method.