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A comprehensive computer simulation of the size-dependent sector or complete microsystem via two-dimensional generalized differential quadrature method

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Abstract

This article presents the mode shape and frequency analysis of graphene nanoplatelets reinforced composite (GPLRC) microdisk surrounded by viscoelastic foundation using a non-classical continuum theory called modified couple stress theory (MCST). The boundary conditions and non-classical governing equations of size-dependent GPLRC microstructure are derived by adding the higher-order stress and symmetric rotation gradient tensors to the strain energy. The current non-classical model is capable of capturing the size-dependency in the composite microsystem using only one material length scale parameter. Moreover, the mathematical formulation of the GPLRC microdisk based on the classical model can be recovered from the present model by neglecting the material length scale parameter. Finally, the generalized differential quadrature element method (GDQEM) is applied for solving the governing equations are solved using various sets of boundary conditions. Afterward, a parametric study is carried out to study the impacts of the radius ratio, length scale parameter, radial and circumferential mode number, geometry of GPLRC material, and boundary conditions on the frequency responses of the current microsystem by considering MCST. The results demonstrate that when the material length scale factor improves, the impact of the damping factor on the natural frequency of the microsystem decreases.

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Acknowledgements

This work was supported by Doctoral foundation of Mudanjiang Normal University (MNUB201608).

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Authors and Affiliations

  1. College of Physics and Electronics Engineering, Mudanjiang Normal University, Mudanjiang, 157000, Heilongjiang, China

    Wulin Zhang, Zirui Liu & Zeyu Liang

  2. Faculty of Mechanical Engineering, Tabriz University, Tabriz, Iran

    Khaled Oslub

  3. Department of Mechanics, Imam Khomeini International University, Qazvin, Iran

    Hamed Safarpour

Authors
  1. Wulin Zhang
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  2. Zirui Liu
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  3. Zeyu Liang
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  4. Khaled Oslub
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  5. Hamed Safarpour
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Corresponding author

Correspondence to Zirui Liu.

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Zhang, W., Liu, Z., Liang, Z. et al. A comprehensive computer simulation of the size-dependent sector or complete microsystem via two-dimensional generalized differential quadrature method. Engineering with Computers 38 (Suppl 5), 4239–4255 (2022). https://doi.org/10.1007/s00366-021-01440-5

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  • DOI: https://doi.org/10.1007/s00366-021-01440-5

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