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Structural Engineering and Mechanics Volume 66, Number 6, June25 2018 , pages 693-701 DOI: https://doi.org/10.12989/sem.2018.66.6.693 |
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A nonlocal strain gradient refined plate model for thermal vibration analysis of embedded graphene sheets via DQM |
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Farzad Ebrahimi and Mohammad Reza Barati
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| Abstract | ||
| This paper develops a nonlocal strain gradient plate model for vibration analysis of graphene sheets under thermal environments. For more accurate analysis of graphene sheets, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. Graphene sheet is modeled via a two-variable shear deformation plate theory needless of shear correction factors. Governing equations of a nonlocal strain gradient graphene sheet on elastic substrate are derived via Hamilton\'s principle. Differential quadrature method (DQM) is implemented to solve the governing equations for different boundary conditions. Effects of different factors such as temperature rise, nonlocal parameter, length scale parameter, elastic foundation and aspect ratio on vibration characteristics a graphene sheets are studied. It is seen that vibration frequencies and critical buckling temperatures become larger and smaller with increase of strain gradient and nonlocal parameter, respectively. | ||
| Key Words | ||
| thermal vibration; refined plate theory; graphene sheets; nonlocal strain gradient theory | ||
| Address | ||
| Farzad Ebrahimi and Mohammad Reza Barati: Mechanical Engineering Department, Faculty of Engineering, Imam Khomeini International University, Qazvin, P.O.B. 3414916818, Iran | ||