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Free vibration analysis of circular graphene sheet with centric circular defect based on two-phase local/nonlocal elasticity theory

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Abstract

In this work, for the first time, the mixed local/nonlocal elasticity theory is employed for the free axisymmetric vibration of an annular single-layer graphene sheet. According to the insufficiency of pure Eringen's nonlocal elasticity, recently researchers have been fascinated by the two-phase elasticity theory to study nanostructures. Some of the imperfections on a graphene sheet can happen due to the manufacturing process and limitation conditions, and lots of them can be considered as a hole. So, in this study, a defect is assumed as the centric perforation on a circular graphene sheet. Dynamic equilibrium equations, in Newtonian formulation, are derived as an integrodifferential equation of motion, which are properly transformed in differential form. Clamped boundary conditions are assumed at the both outer and inner edges and two constitutive boundary conditions are extracted. An analytical procedure is employed to solve the motion equations. Validation of the solution is verified by comparing our obtained results with those addressed in the pertinent literature, and the precision of the presented approach is approved. The influence of the mixture parameter, nonlocal parameter, and radius of imperfection on the natural frequency is examined. The results show that increasing the mixture parameter causes to increase in the natural frequency.

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran

    Pejman Ayoubi & Habib Ahmadi

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  1. Pejman Ayoubi
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  2. Habib Ahmadi
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Ayoubi, P., Ahmadi, H. Free vibration analysis of circular graphene sheet with centric circular defect based on two-phase local/nonlocal elasticity theory. Acta Mech 234, 5425–5435 (2023). https://doi.org/10.1007/s00707-023-03667-3

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  • DOI: https://doi.org/10.1007/s00707-023-03667-3

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