Bending, Buckling and Vibrations Analysis of the Graphene Nanoplate Using the Modified Couple Stress Theory

Authors

  • Majid ESKANDARI SHAHRAKI Ferdowsi University of Mashhad
  • Mahmoud SHARIATI Ferdowsi University of Mashhad
  • Naser ASIABAN Ferdowsi University of Mashhad
  • Jafar ESKANDARI JAM Malek-Ashtar University of Technology

DOI:

https://doi.org/10.5755/j02.mech.25298

Keywords:

Modified couple stress theory, Mindlin's plate, rectangular nanoplates, Navier's solution method.

Abstract

In this paper using the modified couple stress theory, to study the bending, buckling and vibration characteristics of the rectangular Mindlin's nanoplates with graphene material was investigated. With the aim of considering the effects of small scales, the modified couple stress theory, which has only one parameter of length scale and also was presented by Yang in 2002, was used. In the modified couple stress theory; the strain energy density is a function of the components of the strain tensor, curvature tensor, stress tensor and the symmetric part of the couple stress tensor. After obtaining the strain energy, external work, and buckling equation and placing them in the Hamilton's equation, the basic and auxiliary equations of the nanoplates were obtained. Then, by applying boundary and force conditions in the governing equations, the bending, buckling and vibration of the rectangular graphene nanoplates with thickness h and simply-supported conditions were explored. Also, the solution method was the Navier's solution.

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Published

2021-10-12

Issue

Section

MECHANICS OF SOLID BODIES