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Size-dependent nonlinear vibration of functionally graded composite micro-beams reinforced by carbon nanotubes with piezoelectric layers in thermal environments

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Abstract

Nonlinear free vibration characteristics of functionally graded (FG) composite micro-beams reinforced by carbon nanotubes (CNTs) with piezoelectric layers in thermal environment are investigated in this work. The uniform distribution and four nonuniform distribution types of the CNTs reinforcements are examined. The equations of motion are derived based on the Euler–Bernoulli beam theory with von Karman’s assumption, the nonlocal strain gradient theory and the Hamilton’s principle. The approximate nonlinear frequencies of FG-carbon nanotube-reinforced composite (CNTRC) micro-beams for simply supported and clamped–clamped boundary conditions are obtained by using two analytical methods including the equivalent linearization method and the energy balance method. The accuracy of the obtained results has been verified. The influences of the nonlocal parameter, material length scale parameter, geometric property of micro-beam, temperature change, applied voltage, distribution pattern and volume fraction of the CNTs on the nonlinear free vibration behaviors of the FG-CNTRC micro-beams are performed and discussed in detail.

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Acknowledgements

This research is funded by University of Transport Technology (UTT) under Grant Number ĐTTĐUTT2021-20.

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Authors and Affiliations

  1. University of Transport Technology, Hanoi, Vietnam

    Bui Gia Phi

  2. Department of Mechanics, Faculty of Automotive and Power Machinery Engineering, Thai Nguyen University of Technology, Thainguyen, Vietnam

    Dang Van Hieu

  3. Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran

    Hamid M. Sedighi

  4. Drilling Center of Excellence and Research Center, Shahid Chamran University of Ahvaz, Ahvaz, Iran

    Hamid M. Sedighi

  5. Department of Civil Engineering, Engineering Faculty of Suleyman Demirel University, 32260, Isparta, Turkey

    Abdullah H. Sofiyev

  6. Information Technology Research and Application Center Member of Consultancy Board of ITRAC Center, Istanbul Commerce University, 34445, Beyoglu, Istanbul, Turkey

    Abdullah H. Sofiyev

  7. Scientific Research Centers for Composition Materials of UNEC-Azerbaijan State Economic University, 1001, Baku, Azerbaijan

    Abdullah H. Sofiyev

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  1. Bui Gia Phi
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  2. Dang Van Hieu
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  4. Abdullah H. Sofiyev
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Gia Phi, B., Van Hieu, D., Sedighi, H.M. et al. Size-dependent nonlinear vibration of functionally graded composite micro-beams reinforced by carbon nanotubes with piezoelectric layers in thermal environments. Acta Mech 233, 2249–2270 (2022). https://doi.org/10.1007/s00707-022-03224-4

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