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Free vibration analysis of functionally graded beams is carried out for various classical boundary conditions. Two separate finite element formulations, one based on Euler-Bernoulli beam theory and other based on Timoshenko beam theory are developed. Principle of virtual work is used to obtain the finite element system of equations. Numerical results are provided to demonstrate the effect of transverse shear on the natural frequencies and mode shapes for different length-to-thickness ratios and volume fraction exponents of functionally graded material (FGM) beams for the boundary conditions considered. It was observed that transverse shear significantly affects the fundamental frequency and mode shape for lower length to thickness ratios of FGM beams. Further, the effect was observed to be more prominent at higher modes for all the volume fraction exponents of FGM beam.
Defence Science Journal, 2012, 62(3), pp.139-146, DOI:http://dx.doi.org/10.14429/dsj.62.1326