Nonlinear dynamic buckling of a simply supported imperfect nanocomposite shear deformable plate under the effect of in-plane velocities

•An analytical scheme is offered to consider the non-linear dynamic stability problem of an imperfect nanocomposite Plate subjected to axial constant velocity.•Three distribution patterns of carbon nanotubes (CNTs) are conducted.•The shear deformation theory is generalized to the dynamic nonlinear buckling (DNB) problem of CNTs plate.•Outcome of several axial velocity, initial imperfection, damping and the volume fraction of CNT on the dynamic behavior are discussed. Due to its lightweight design and high load-bearing capacity, the nanocomposite plate structure is extensively applied in flight wings, ship hulls and aerospace structures. In particular, there is a lack of research on the nonlinear dynamic response of the shear deformable plates with initial geometric imperfection and damping ratio. Inspired by this, this article investigates the nonlinear stability behavior of an imperfect nanocomposite plate under axial compression loading. Material properties are presumed to vary in thickness directions according to three different CNT distributions patterns, in which the material properties are calculated with the help of the mixing rule. Subsequently, considering the effect of shear stresses, initial geometrical imperfections and damping ratio, the dynamic model is constructed according to the shear deformation theory (SDT) and Von Karman-form of the nonlinearity. Then, the nonlinear equations of motion are of the plate is derived based on the Hamilton principle. Then, the procedure of the superposition and Galerkin-based method are applied in order to convert the non-linear partial differential expressions of CNTs plate for the non-linear ordinary differential form. The resulted non-linear differential expressions are numerically solved via fourth-order Runge-Kutta-based scheme. Simultaneously, the analytical results of the presented expression are compared with other published literatures to verify the accuracy of this article, and the comparisons show that there is no notable variation between the present data and existing literature. In addition, a parametric investigation is presented to reveal the impacts of axial velocities, initial imperfections, damping, CNTs distribution and volume fraction, geometry parameters and buckling modes on the non-linear dynamic buckling responses of the CNTs plate. It can be found that the presence of initial imperfection will significantly affect the nonlinear dynamic behavior of the nanocomposite plates.