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Nonlinear Vibration Analysis of Fractional Viscoelastic Nanobeam

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Abstract

Purpose

Considering the size-dependent influence ignored by classical continuum mechanics, a new non-classical Euler–Bernoulli beam model is proposed in this paper. The new fractional viscoelastic nanobeam model is set up using the fractional Kelvin–Voigt viscoelastic model and Hamilton’s principle. And the new model studies the total effects of nonlocal elasticity, modified couple stress, and surface energy.

Methods

The model represented the fractional integral-partial differential governing equation is solved by Galerkin’s and predictor–corrector methods. First, the effects of nonlocal elasticity, modified couple stress, surface energy, and their coupling impact on the nonlinear time response of free vibration of fractional viscoelastic nanobeam are analyzed. Then, in the frame of nonlocal couple-stress elasticity and surface energy theory, the effects of different parameters on the nonlinear time responses of free and forced vibration of fractional viscoelastic nanobeam are discussed.

Results and Conclusion

The numerical results show that the fractional order must be considered in the modeling of viscoelastic nanobeam, and the system’s damping enhances by the increase of fractional order. Moreover, owing to the correlation between fractional order and excitation frequency, the nonlinear time responses of fractional order to free and forced vibration are different.

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Data Availability

The data for the results of this study are available from the corresponding author.

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Funding

This work is supported by the National Natural Science Foundation of China (11862014).

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  1. School of Science, Lanzhou University of Technology, Lanzhou, Gansu, People’s Republic of China

    Meifeng Qiu, Dongxia Lei & Zhiying Ou

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  1. Meifeng Qiu
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  2. Dongxia Lei
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Correspondence to Zhiying Ou.

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Qiu, M., Lei, D. & Ou, Z. Nonlinear Vibration Analysis of Fractional Viscoelastic Nanobeam. J. Vib. Eng. Technol. 11, 4015–4038 (2023). https://doi.org/10.1007/s42417-022-00799-z

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