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Free vibration analysis of non-homogeneous orthotropic plates resting on Pasternak elastic foundation by Rayleigh-Ritz method

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Abstract

Free vibration analysis of non-homogeneous orthotropic plates resting on a Pasternak type of elastic foundation is investigated. A set of admissible orthogonal polynomials are generated with Gram-Schmidt orthogonalization procedure and adopted in the Rayleigh-Ritz method. Accuracy and applicability of the method are examined by comparison of the results for different boundary conditions and material types with those available in literature. It is found that this method has good accuracy regardless of type of boundary condition and yields very accurate results even with low number of terms of orthogonal polynomials for the first mode of vibration. For higher modes of vibration, higher terms of orthogonal polynomials should be used. The effects of foundation parameter, density and non-homogeneity parameters on natural frequency are examined. It is concluded that natural frequency of plates are more sensitive to shearing layer coefficient rather than Winkler coefficient and density parameter has weakening effect on natural frequency.

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Authors and Affiliations

  1. Department of Ocean Engineering, AmirKabir University of Technology, Hafez Ave., Tehran, 15914, Iran

    Ahmad Rahbar-Ranji & Arash Shahbaztabar

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  1. Ahmad Rahbar-Ranji
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  2. Arash Shahbaztabar
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Correspondence to Ahmad Rahbar-Ranji.

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Rahbar-Ranji, A., Shahbaztabar, A. Free vibration analysis of non-homogeneous orthotropic plates resting on Pasternak elastic foundation by Rayleigh-Ritz method. J. Cent. South Univ. 23, 413–420 (2016). https://doi.org/10.1007/s11771-016-3086-0

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  • DOI: https://doi.org/10.1007/s11771-016-3086-0

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