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Flexural vibration of functionally graded thin skew plates resting on elastic foundations

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Abstract

In this investigation, free vibration of functionally graded (FG) thin skew plates subjected to different classical edge supports with various skew angles has been studied. The plate is also assumed to lay on Winkler and Pasternak elastic foundations. Material properties of FG constituents vary spatially along thickness direction in power-law form. The constitutive relation is obtained on the basis of classical plate theory and further numerical modeling is performed in terms of Rayleigh–Ritz method to obtain the generalized eigenvalue problem. Trail functions denoting the transverse displacement are expressed as linear combination of simple algebraic polynomials (generated from Pascal’s triangle). The main aim of this study is to find the effect of aspect ratio, skew angles, elastic foundation moduli and volume fractions on free vibration frequencies of the concerned plate. Consequently, the validation of present results is carried out after checking the convergence to report the natural frequencies.

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Acknowledgements

The authors are thankful to the anonymous reviewer(s) for the constructive suggestions, which have certainly improved the contents of the article. The second author is grateful to Science and Engineering Research Board (DST), India for the financial support against Sanction No. PDF/2015/000751 and also to the CSIR-Central Building Research Institute, Roorkee for the brilliant laboratory provisions.

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  1. Karan K. Pradhan

    Present address: AIMS Group, BPPP Division, CSIR-CBRI, Roorkee, Roorkee, Haridwar, Uttarakhand, 247667, India

Authors and Affiliations

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

    S. Chakraverty

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  1. S. Chakraverty
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Correspondence to S. Chakraverty.

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Chakraverty, S., Pradhan, K.K. Flexural vibration of functionally graded thin skew plates resting on elastic foundations. Int. J. Dynam. Control 6, 97–121 (2018). https://doi.org/10.1007/s40435-017-0308-8

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  • DOI: https://doi.org/10.1007/s40435-017-0308-8

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