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A comprehensive mathematical simulation of the composite size-dependent rotary 3D microsystem via two-dimensional generalized differential quadrature method

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Abstract

In this study, frequency simulation and critical angular velocity of a size-dependent laminated rotary microsystem using modified couple stress theory (MCST) as the higher-order elasticity model is undertaken. The centrifugal and Coriolis impacts due to the spinning are taken into account. The size-dependent thick annular microsystem's computational formulation, non-classical governing equations, and corresponding boundary conditions are obtained by using the higher-order stress tensors and symmetric rotation gradient to the strain energy. By using a single material length scale factor, the most recent non-classical approach captures the size-dependency in the annular laminated microsystem. Furthermore, by ignoring the length scale element of the material, an annular microsystem’s mathematical formulation based on the classical model can be retrieved from the current model. Ultimately, the governing equations, which are non-classic, have been solved for various boundary conditions (BCs) using the two-dimensional generalized differential quadrature (2D-GDQ) approach. The effects of Young's modulus ratio the, rotating speed, radius ratio, laminated layers’ number, length scale element, and laminated types on the critical rotating speed and frequency responses of the laminated spinning microdisk are then investigated using MCST. The outcomes reveal that the negative influence from spinning velocity on the system’s dynamics is more significant than the negative influence from radius ratio, and the mentioned problem is more considerable for the vertical laminated pattern. Finally, the critical radius ratio and rotating speed increase by changing the laminated pattern from vertical to longitudinal.

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Author information

Authors and Affiliations

  1. Mathematics and Physics Teaching Department, Yantai Nanshan University, Yantai, 265713, Shandong, China

    Hui Liu

  2. School of Mechatronics and Vehicle Engineering, Chongqing Jiaotong University, Chongqing, 400074, China

    Yao Zhao

  3. Department of Computer Engineering, Faculty of Engineering, Larestan Branch, Technical and Vocational University (TVU), P.O. Box 7437148575, Lar, Iran

    Mohammad Pishbin

  4. Institute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam

    Mostafa Habibi

  5. Faculty of Electrical-Electronic Engineering, Duy Tan University, Da Nang, 550000, Vietnam

    Mostafa Habibi

  6. Center of Excellence in Design, Robotics, and Automation, Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, P.O. Box 11365-9567, Tehran, Iran

    Mostafa Habibi

  7. Department of Civil Engineering, Faculty of Engineering Sciences, Omdurman Islamic University, Omdurman, Sudan

    M-O Bashir

  8. Al-Farabi Kazakh National University, Almaty, Kazakhstan

    Alibek Issakhov

  9. Kazakh-British Technical University, Almaty, Kazakhstan

    Alibek Issakhov

Authors
  1. Hui Liu
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  2. Yao Zhao
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  3. Mohammad Pishbin
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  4. Mostafa Habibi
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  5. M-O Bashir
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  6. Alibek Issakhov
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Corresponding author

Correspondence to Mostafa Habibi.

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Liu, H., Zhao, Y., Pishbin, M. et al. A comprehensive mathematical simulation of the composite size-dependent rotary 3D microsystem via two-dimensional generalized differential quadrature method. Engineering with Computers 38 (Suppl 5), 4181–4196 (2022). https://doi.org/10.1007/s00366-021-01419-2

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  • DOI: https://doi.org/10.1007/s00366-021-01419-2

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