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

Document Type : Solid Mechanics

Authors

Dept. of Mechanical Engineering, Razi University, Kermanshah, I. R. of Iran

Abstract

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.

Keywords

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References

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History

  • Receive Date: 23 September 2019
  • Revise Date: 28 January 2020
  • Accept Date: 23 May 2021
  • Publish Date: 21 April 2021

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