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Modelling of the flexoelectric effect on rotating nanobeams with geometrical imperfection

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Abstract

Flexoelectricity is the phenomenon of electric polarization caused by the strain gradient, which usually has a huge effect on nanoscale structures. This paper firstly combines the finite element method (FEM) with a novel third-order shear deformation beam theory (TSDT) to simulate the static bending and free vibration responses of rotating (around one fixed axis) piezoelectric nanobeams with geometrical imperfection considering flexoelectric effects, where the structures are placed on the Pasternak’s elastic foundations. Based on two-node beam elements, the Lagrange and Hermit interpolation functions, the proposed approach shows high accuracy through the comparative results of this work and published references. A wide range of parameter studies is conducted such as the rotational speed, shape imperfection, flexoelectric effect, and so on to evaluate the influences on the static bending and free vibration behaviors of the structures. The novel investigation points out that when the beams are rotating around one fixed axis, the mechanical responses, in this case, are not similar to those of normal cases when the rotational speed is zero. This is a new study that can be referenced when designing nanoscale beam structures in practice.

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Acknowledgements

NCT gratefully acknowledges the support of Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 107.10-2020.100.

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Authors and Affiliations

  1. Institute of Techniques for Special Engineering, Le Quy Don Technical University, Hanoi City, Vietnam

    Nguyen Chi Tho

  2. Academy of Military Science and Technology, Hanoi City, Vietnam

    Nguyen Truong Thanh

  3. Faculty of Special Equipment, Le Quy Don Technical University, Hanoi City, Vietnam

    To Duc Tho

  4. Faculty of Mechanical Engineering, Le Quy Don Technical University, Hanoi City, Vietnam

    Phung Van Minh

  5. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Le Kha Hoa

  6. Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Le Kha Hoa

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  1. Nguyen Chi Tho
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  2. Nguyen Truong Thanh
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  3. To Duc Tho
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  4. Phung Van Minh
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Correspondence to Le Kha Hoa.

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Technical Editor: Aurelio Araujo.

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Tho, N.C., Thanh, N.T., Tho, T.D. et al. Modelling of the flexoelectric effect on rotating nanobeams with geometrical imperfection. J Braz. Soc. Mech. Sci. Eng. 43, 510 (2021). https://doi.org/10.1007/s40430-021-03189-w

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  • DOI: https://doi.org/10.1007/s40430-021-03189-w

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