Determination of vibration of single-layered graphene sheets using nonlocal modified couple stress theory

F. Attar, R. Khordad and A. Zarifi
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F. Attar: Department of Physics, College of Sciences, Yasouj University, Yasouj 75918, Iran
R. Khordad: Department of Physics, College of Sciences, Yasouj University, Yasouj 75918, Iran
A. Zarifi: Department of Physics, College of Sciences, Yasouj University, Yasouj 75918, Iran

International Journal of Modern Physics C (IJMPC), 2022, vol. 33, issue 01, 1-19

Abstract: The free vibration of single-layered graphene sheet (SLGS) has been studied by nonlocal modified couple stress theory (NMCS), analytically. Governing equation of motion for SLGS is obtained via thin plate theory in conjunction with Hamilton’s principle for two cases: (1) using nonlocal parameter only for stress tensor, (2) using nonlocal parameter for both stress and couple stress tensors. Navier’s approach has been used to solve the governing equations for simply supported boundary conditions. It is found that the frequency ratios decrease with increasing nonlocal parameter and also with enhancing vibration modes, but increase with raising length scale parameter. The nonlocal and length scale parameters are more prominent in higher vibration modes. The obtained results have been compared with the previous studies obtained by using classical plate theory, the modified couple stress theory and nonlocal elasticity theory, separately.

Keywords: Nonlocal elasticity theory; graphene sheet; vibration (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0129183122500115

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