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Wave propagation of functionally graded porous nanobeams based on non-local strain gradient theory

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Abstract.

In this paper, attention is paid to the prediction of wave propagation behaviors of functionally graded materials (FG) porous nanobeams based on Reddy’s higher-order shear deformation beam theory in conjunction with the non-local strain gradient theory. The governing equations of the porous nanobeams are derived with the help of the Hamilton principle. By solving an eigenvalue problem, the analytic dispersion relation is obtained. The results of Euler-Bernoulli beam and Timoshenko beam models are also presented. The influences of non-local parameter, strain gradient parameter, power law index and porosity volume fraction on the wave propagation are discussed in detail.

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Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, 410082, Changsha, China

    Gui-Lin She, Yan-Long Zhang, Hai-Bo Liu & Yi-Ru Ren

  2. China Aviation Changsha Design and Research Co. Ltd, 410018, Changsha, China

    Kun-Ming Yan

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  1. Gui-Lin She
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  2. Kun-Ming Yan
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  3. Yan-Long Zhang
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Correspondence to Yi-Ru Ren.

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She, GL., Yan, KM., Zhang, YL. et al. Wave propagation of functionally graded porous nanobeams based on non-local strain gradient theory. Eur. Phys. J. Plus 133, 368 (2018). https://doi.org/10.1140/epjp/i2018-12196-5

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