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Natural frequencies of shear deformed functionally graded beams using inverse trigonometric functions

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Abstract

In this paper, free vibration of functionally graded (FG) beam subjected to all sets of boundary conditions has been investigated using Rayliegh-Ritz method. Different higher-order shear deformation beam theories (SDBTs) have also been incorporated, out of which three SDBTs are proposed in the form of inverse trigonometric functions. The proposed deformation theories satisfy the transverse shear stress conditions at the bottom and top surfaces of the beam. The material properties of FG beam are assumed to vary along thickness direction in power-law form and trial functions denoting the displacement components are expressed as linear combination of algebraic polynomials. Rayleigh–Ritz method is used to estimate frequency parameters in order to handle to all sorts of boundary conditions at the edges with ease. Comparison of frequency parameters is carried out with the available literature in special cases and new results are also provided after checking the convergence of frequency parameters.

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Acknowledgements

The authors are thankful to the anonymous reviewer(s) for their constructive suggestions, which have certainly improved the contents of the paper. The first author is grateful to CSIR-Central Building Research Institute, Roorkee for the excellent laboratory provisions.

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Authors and Affiliations

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

    Karan K. Pradhan & S. Chakraverty

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  1. Karan K. Pradhan
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  2. S. Chakraverty
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Correspondence to S. Chakraverty.

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Technical Editor: Fernando Alves Rochinha.

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Pradhan, K.K., Chakraverty, S. Natural frequencies of shear deformed functionally graded beams using inverse trigonometric functions. J Braz. Soc. Mech. Sci. Eng. 39, 3295–3313 (2017). https://doi.org/10.1007/s40430-016-0701-9

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  • DOI: https://doi.org/10.1007/s40430-016-0701-9

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