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Advances in Nano Research
  Volume 8, Number 4, May 2020 , pages 265-276

Investigating vibrational behavior of graphene sheets under linearly varying in-plane bending load based on the nonlocal strain gradient theory
Ali Shariati, Mohammad Reza Barati, Farzad Ebrahimi, Abhinav Singhal and Ali Toghroli

    A study that primarily focuses on nonlocal strain gradient plate model for the sole purpose of vibration examination, for graphene sheets under linearly variable in-plane mechanical loads. To study a better or more precise examination on graphene sheets, a new advance model was conducted which carries two scale parameters that happen to be related to the nonlocal as well as the strain gradient influences. Through the usage of two-variable shear deformation plate approach, that does not require the inclusion of shear correction factors, the graphene sheet is designed. Based on Hamilton's principle, fundamental expressions in regard to a nonlocal strain gradient graphene sheet on elastic half-space is originated. A Galerkin's technique is applied to resolve the fundamental expressions for distinct boundary conditions. Influence of distinct factors which can be in-plane loading, length scale parameter, load factor, elastic foundation, boundary conditions, and nonlocal parameter on vibration properties of the graphene sheets then undergo investigation.
Key Words
    graphene sheets; free vibration; in-plane bending; nonlocal strain gradient; refined plate theory
(1) Ali Shariati:
Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, 758307, Vietnam;
(2) Ali Shariati:
Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, 758307, Vietnam;
(3) Mohammad Reza Barati, Farzad Ebrahimi:
Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran;
(4) Abhinav Singhal:
Department of Mathematics, Madanapalle Institute of Technology and Science, Madanapalle, Andhra Pradesh, 517325, India;
(5) Ali Toghroli:
Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam.

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