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Small-scale effects on the dynamic response of inhomogeneous nanobeams on elastic substrate under uniform dynamic load

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Abstract.

In this article, forced vibration and resonance frequencies of functionally graded (FG) nanobeams resting on Winkler-Pasternak foundation are investigated employing a higher-order refined beam theory which captures shear deformation influences without the need for any shear correction factor. The nanobeam is subjected to a uniform dynamic load with a finite length. The two-parameter elastic medium consists of parallel springs and a shear layer. Gradation of the material properties of the nanobeam is described via the Mori-Tanaka distribution model. The governing equations of embedded higher-order FG nanobeams under dynamic loading are obtained by employing Eringen’s elastic differential law and Hamilton’s principle. These equations are solved for simply-supported-simply-supported (S-S) and clamped-clamped (C-C) boundary conditions. It is indicated that forced vibration characteristics and resonance frequencies of embedded FG nanobeams are significantly influenced by material composition, nonlocality, foundation parameters and boundary conditions. A nonlocal FG beam has lower resonance frequency compared with a local beam. However, the presence of elastic foundation leads to a significant delay in the occurrence of resonance frequencies.

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Authors and Affiliations

  1. Aerospace Engineering Department & Center of Excellence in Computational Aerospace, University of Technology, 15875-4413, Tehran, Iran

    Mohammad Reza Barati & Hossein Shahverdi

Authors
  1. Mohammad Reza Barati
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  2. Hossein Shahverdi
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Correspondence to Mohammad Reza Barati.

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Reza Barati, M., Shahverdi, H. Small-scale effects on the dynamic response of inhomogeneous nanobeams on elastic substrate under uniform dynamic load. Eur. Phys. J. Plus 132, 167 (2017). https://doi.org/10.1140/epjp/i2017-11441-9

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