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Nonlinear vibration of microbeams based on the nonlinear elastic foundation using the equivalent linearization method with a weighted averaging

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Abstract

We investigate the nonlinear vibration of microbeams based on the nonlinear elastic foundation through the modified couple stress theory. The equivalent linearization method with a weighted averaging is used to solve approximately the ordinary differential equation that describes the equation of motion of the microbeam. The effects of length scale parameter, the flexural rigidity ratio, the slenderness ratio, the Winkler parameter, the Pasternak parameter and the nonlinear foundation parameter on the nonlinear vibration of the microbeam are studied and discussed.

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Acknowledgements

This work was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 107.04-2018.12.

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Authors and Affiliations

  1. Department of Mechanics, Thai Nguyen University of Technology, 3/2 Street, Thainguyen City, Vietnam

    Van-Hieu Dang

  2. Institute of Mechanics, No. 264, Doi Can, Ba Dinh, Hanoi, Vietnam

    Dong-Anh Nguyen

  3. Department of Mechanics of Materials and Structures, School of Mechanical Engineering, Hanoi University of Science and Technology, No. 1, Dai Co Viet Road, Hanoi, Vietnam

    Minh-Quy Le

  4. Ha Noi Architectural University, Nguyen Trai Street, Hanoi, Vietnam

    Quang-Hai Ninh

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  1. Van-Hieu Dang
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Dang, VH., Nguyen, DA., Le, MQ. et al. Nonlinear vibration of microbeams based on the nonlinear elastic foundation using the equivalent linearization method with a weighted averaging. Arch Appl Mech 90, 87–106 (2020). https://doi.org/10.1007/s00419-019-01599-w

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