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Vibration and buckling characteristics of nonlocal beam placed in a magnetic field embedded in Winkler–Pasternak elastic foundation using a new refined beam theory: an analytical approach

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Abstract

In this article, a new refined beam theory, namely one variable first-order shear deformation theory, has been employed to study the vibration and buckling characteristics of nonlocal beam. The beam is exposed to an axial magnetic field and embedded in Winkler–Pasternak foundation. The von Kármán hypothesis along with Hamilton’s principle has been implemented to derive the governing equations for both the vibration and buckling studies, and closed-form solutions are obtained for simply supported beam using the Navier’s approach. Further, a parametric study has been conducted to explore the impacts of small-scale parameter, Winkler modulus, shear modulus and magnetic field intensity on natural frequencies and critical buckling loads.

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Acknowledgement

The first two authors acknowledge to Defence Research & Development Organization (DRDO), New Delhi, India (Sanction Code: DG/TM/ERIPR/GIA/17-18/0129/020), for the funding to carry out the present research work.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Rourkela, Rourkela, 769008, India

    Subrat Kumar Jena & S. Chakraverty

  2. Department of Mechanics of Materials and Structures, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, Gdansk, Poland

    Mohammad Malikan

Authors
  1. Subrat Kumar Jena
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  2. S. Chakraverty
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  3. Mohammad Malikan
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Correspondence to S. Chakraverty.

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Jena, S.K., Chakraverty, S. & Malikan, M. Vibration and buckling characteristics of nonlocal beam placed in a magnetic field embedded in Winkler–Pasternak elastic foundation using a new refined beam theory: an analytical approach. Eur. Phys. J. Plus 135, 164 (2020). https://doi.org/10.1140/epjp/s13360-020-00176-3

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