Analytical Modeling of Impact loading of Nanoparticles on the Nano-curved Plate

In this paper an analytical model is presented to investigate the dynamic response of the nano-curved plate under impact loading of nanoparticles. Unlike the macroscale, long-range interatomic interactions, such as the Van der Waals (vdW) force, are considered at the nanoscales. The impact load on the nano- curved plate is considered as an interaction between the nanoparticle and the nano-plate. The vdW force between the carbon nanoparticle and silicon nano-curved plate is determined by the Lennard-Jones potential. The Love-Kirchhoff plate theory and Double Fourier series are used for determining the displacement field of the nano-plate. Also the governing equations of the nano-curved plate are derived by considering the residual surface stress, Gurtin and Murdoch relations and Hamilton's principle and are solved for a simply supported nano-curved plate by using the Rung-Kutta’s fourth order method in MATLAB. The analytical model results are validated with an analytical model that has investigated the dynamic response of the nanoparticle impact on a rectangular nano-plate. The effects of geometrical parameters such as curvature, thickness, mass and velocity are investigated. Also the surface effects of the nano-plate on the vdW force and the dynamic response of the nano-curved plate are studied. The results show that by increasing the radius of curvature, the maximum deformation at a constant curvature angle is decreased. Also, by considering the surface effect, the maximum displacement of the center of the nano-plate is reduced and the role of the surface effect on the maximum deflection of the nano-plate decreases with increasing nano-plate thickness.