Advances in nano research

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A hybrid conventional computer simulation via GDQEM and Newmark-beta techniques for dynamic modeling of a rotating micro nth-order system

  • Fan, Linyuan (College of Mathematics and Data Science (College of Software), Minjiang University) ;
  • Zhang, Xu (Information Technology Center, Jingchu Institute of Technology) ;
  • Zhao, Xiaoyang (Birmingham City University, School of Computing and Digital Technology)
  • Received : 2021.08.14
  • Accepted : 2021.12.05
  • Published : 2022.02.25
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Abstract

In this paper, the free and forced vibration analysis of rotating cantilever nanoscale cylindrical beams and tubes is investigated under the external dynamic load to examine the nonlocal effect. A couple of nonlocal strain gradient theories with different beams and tubes theories, involving the Euler-Bernoulli, Timoshenko, Reddy beam theory along with the higher-order tube theory, are assumed to the mathematic model of governing equations employing the Hamilton principle in order to derive the nonlocal governing equations related to the local and accurate nonlocal boundary conditions. The two-dimensional functional graded material (2D-FGM), made by the axially functionally graded (AFG) in conjunction with the porosity distribution in the radial direction, is considered material modeling. Finally, the derived Partial Differential Equations (PDE) are solved via a couple of the generalized differential quadrature element methods (GDQEM) with the Newmark-beta techniques for the time-dependent results. It is indicated that the boundary conditions equations play a crucial task in responding to nonlocal effects for the cantilever structures.

Keywords

Acknowledgement

This work was supported by Special Fund granted by Minjiang University.

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