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Free vibration of functionally graded beams resting on Winkler-Pasternak foundation

  • ICCESEN 2017
  • Published:
Arabian Journal of Geosciences Aims and scope Submit manuscript

Abstract

In the present study, the free vibration of functionally graded beams resting on two parameter elastic foundation was examined. The properties of the functionally graded materials were presumed to vary continuously along the thickness direction. The foundation medium was assumed to be linear, homogeneous, and isotropic, and it was modeled by the Winkler-Pasternak model with two parameters for describing the reaction of the elastic foundation on the beam. The functionally graded beam was modeled with classical beam theory. The governing equation including the effects of functionally graded material properties, Winkler-Pasternak elastic foundation was solved using separation of variables. The eigenvalues of yielding fundamental equation versus clamped-clamped, clamped-free, clamped-simply supported, and simply supported-simply supported boundary conditions were found. To corroborate the results, comparisons were carried out with available results for homogeneous and functionally graded beams. The effects of Winkler-Pasternak type elastic foundation and functionally graded material properties on the values of dimensionless frequency parameter of beams were discussed. Briefly, it was found that the dimensionless frequency parameters of beam change according to material properties, presence of elastic foundation, and boundary conditions; moreover, the separate effects of these quantities on each other are interesting.

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Funding

The financial support of the Suleyman Demirel University Scientific Research Projects Unit (SDU-BAP) with Grant No. 4912-YL1-17 is gratefully acknowledged. The authors would like to thank institution.

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Authors and Affiliations

  1. Department of Civil Engineering, Faculty of Engineering, Suleyman Demirel University, Cunur, Isparta, Turkey

    Mehmet Avcar

  2. Graduate School of Natural and Applied Sciences, Suleyman Demirel University, Cunur, Isparta, Turkey

    Waleed Khalid Mohammed Mohammed

Authors
  1. Mehmet Avcar
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  2. Waleed Khalid Mohammed Mohammed
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Correspondence to Mehmet Avcar.

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This article is part of the Topical Collection on Geo-Resources-Earth-Environmental Sciences

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Avcar, M., Mohammed, W.K.M. Free vibration of functionally graded beams resting on Winkler-Pasternak foundation. Arab J Geosci 11, 232 (2018). https://doi.org/10.1007/s12517-018-3579-2

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  • DOI: https://doi.org/10.1007/s12517-018-3579-2

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