Structural Engineering and Mechanics

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A nonlocal strain gradient theory for nonlinear free and forced vibration of embedded thick FG double layered nanoplates

  • Mahmoudpour, E. (Department of Mechanical Engineering, Science and Research Branch, Islamic Azad University) ;
  • Hosseini-Hashemi, SH. (School of Mechanical Engineering, Iran University of Science and Technology) ;
  • Faghidian, S.A. (Department of Mechanical Engineering, Science and Research Branch, Islamic Azad University)
  • Received : 2018.04.09
  • Accepted : 2018.07.21
  • Published : 2018.10.10
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Abstract

In the present research, an attempt is made to obtain a semi analytical solution for both nonlinear natural frequency and forced vibration of embedded functionally graded double layered nanoplates with all edges simply supported based on nonlocal strain gradient elasticity theory. The interaction of van der Waals forces between adjacent layers is included. For modeling surrounding elastic medium, the nonlinear Winkler-Pasternak foundation model is employed. The governing partial differential equations have been derived based on the Mindlin plate theory utilizing the von Karman strain-displacement relations. Subsequently, using the Galerkin method, the governing equations sets are reduced to nonlinear ordinary differential equations. The semi analytical solution of the nonlinear natural frequencies using the homotopy analysis method and the exact solution of the nonlinear forced vibration through the Harmonic Balance method are then established. The results show that the length scale parameters give nonlinearity of the hardening type in frequency response curve and the increase in material length scale parameter causes to increase in maximum response amplitude, whereas the increase in nonlocal parameter causes to decrease in maximum response amplitude. Increasing the material length scale parameter increases the width of unstable region in the frequency response curve.

Keywords

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