Generalized power-law exponent based shear deformation theory for free vibration of functionally graded beams

Karan K. Pradhan and S. Chakraverty

Applied Mathematics and Computation, 2015, vol. 268, issue C, 1240-1258

Abstract: Present study deals with free vibration of functionally graded (FG) beams subject to different sets of boundary conditions. The analysis is carried out on the basis of a newly proposed generalized power-law exponent based shear deformation beam theory (PESDBT). The proposed theory exactly satisfies the transverse stress boundary conditions on the bottom and top surfaces of the beam. Material properties of the beam vary continuously in the thickness direction according to the power-law exponent form. The displacement components of the cross-sections of the beam are expressed in simple algebraic polynomials. Rayleigh–Ritz method is used to estimate frequency parameters in order to handle various sets of boundary conditions at the edges. The objective is to study the effects of constituent volume fractions, slenderness ratios and the beam theories on the natural frequencies. New results for frequency parameters are also incorporated after checking the convergence pattern and validation of results computed for previously published shear deformation beam theories.

Keywords: Vibration; Shear deformation theory; Rayleigh–Ritz method; Frequency parameter (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:268:y:2015:i:c:p:1240-1258

DOI: 10.1016/j.amc.2015.07.032

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