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Wave Analysis of Thick Rectangular Graphene Sheets: Thickness and Small-Scale Effects on Natural and Bifurcation Frequencies

Author

Listed:
  • Seyyed Mostafa Mousavi Janbeh Sarayi

    (Department of Mechanical Engineering, College of Engineering, State University of New York at Buffalo, Buffalo, NY 14203, USA)

  • Amir Rajabpoor Alisepahi

    (Department of Mechanical Engineering, College of Engineering and Mathematical Science, University of Vermont, Burlington, VT 05401, USA)

  • Arian Bahrami

    (Department of Mechanical Engineering, Cyprus International University, Mersin 10, Nicosia 99258, Turkey)

Abstract

Free vibration and wave analysis of thick rectangular graphene are studied by employing the wave propagation method. To consider small-scale effects and thickness of a plate in nanoscales, equations of motions are represented by the Eringen nonlocal theory coupled with the Mindlin plate theory of thick plates. To solve the governing equations of motion with the wave propagation technique, propagation and reflection matrices are derived. These matrices are combined to obtain exact natural frequencies of graphene sheets for all six possible boundary conditions. To check the accuracy and reliability of the method, natural frequencies are compared with the results of the literature, and excellent agreement is observed. Additionally, wave analysis of the graphene sheet is performed and different types of waves in the graphene sheet are captured. Deriving the dispersion relation of the graphene sheet, bifurcation frequencies (cut-off and escape frequencies) are analytically found. Finally, the effects of graphene sheet thickness and nonlocal parameter on the natural frequencies and bifurcation frequencies are investigated. It is observed that natural frequencies are highly dependent on the graphene sheet’s thickness and nonlocal parameter. More importantly, the number and order of bifurcation frequencies depend on these two parameters as well. Our findings are valuable for the sustainable design and fabrication of graphene-based sensors, in which structural health monitoring of embedded graphene sheets is of great importance.

Suggested Citation

  • Seyyed Mostafa Mousavi Janbeh Sarayi & Amir Rajabpoor Alisepahi & Arian Bahrami, 2022. "Wave Analysis of Thick Rectangular Graphene Sheets: Thickness and Small-Scale Effects on Natural and Bifurcation Frequencies," Sustainability, MDPI, vol. 14(19), pages 1-22, September.
    • Handle: RePEc:gam:jsusta:v:14:y:2022:i:19:p:12329-:d:927730
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    References listed on IDEAS

    as
    1. Duong Duc La & Tuan Anh Nguyen & Thanh Tung Nguyen & Ha Duc Ninh & Hoai Phuong Nguyen Thi & Tham Thi Nguyen & Duy Anh Nguyen & Trung Dung Dang & Eldon R. Rene & Soon Woong Chang & Hien Tran Thi & Dinh, 2019. "Absorption Behavior of Graphene Nanoplates toward Oils and Organic Solvents in Contaminated Water," Sustainability, MDPI, vol. 11(24), pages 1-9, December.
    2. Tengteng Guo & Hao Fu & Chaohui Wang & Haijun Chen & Qian Chen & Qing Wang & Yuanzhao Chen & Zhenxia Li & Aijiu Chen, 2021. "Road Performance and Emission Reduction Effect of Graphene/Tourmaline-Composite-Modified Asphalt," Sustainability, MDPI, vol. 13(16), pages 1-21, August.
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