Free Vibration Analysis of Functionally Graded Rotating Double Tapered Beam by using Euler-bernoulli Beam Theory and Differential Transform Method

In this study, the free vibration analysis of a functionally graded rotating double tapered beam is performed. The analysis is based on Euler-Bernoulli beam theory. The Material properties of the beam vary continuously in the thickness direction according to the power-law function. The governing differential equation of motion is derived using the Hamilton’s principle. Natural frequencies are obtained using differential transformation (DTM) technique. The effects of the taper ratios, nondimensional rotational speed, nondimensional hub radius and material volume fraction index on the natural frequencies are discussed. Numerical results are tabulated in several tables and figures. To verify the present analysis, the results of this study are compared with the available results from the existing literature. It is shown that the natural frequencies of a functionally graded rotating double tapered Euler-Bernoulli beam can be obtained with high accuracy by using DTM. It was observed that nondimensional rotational speed, height taper ratio and power-law exponent significantly affect the natural frequency. The effects of hub radius and breadth taper ratio on the natural frequencies are negligible.