Free vibration analysis of a rotating non-uniform functionally graded beam

Abstract

In this paper, free vibration characteristics of a rotating double tapered functionally graded beam is investigated. Material properties of the beam vary continuously through thickness direction according to the power-law distribution of the volume fraction of the constituents. The governing differential equations of motion are derived using the Hamilton's principle and solved utilizing an efficient and semi-analytical technique called the Differential Transform Method (DTM). Several important aspects such as taper ratios, rotational speed, hub radius, as well as the material volume fraction index which have impacts on natural frequencies of such beams are investigated and discussed in detail. Numerical results are tabulated in several tables and figures. In order to demonstrate the validity and accuracy of the current analysis, some of present results are compared with previous results in the literature and an excellent agreement is observed. It is showed that the natural frequencies of an FG rotating double tapered beam can be obtained with high accuracy by using DTM. It is also observed that nondimensional rotational speed, height taper ratio, power-law exponent significantly affect the natural frequencies of the FG double tapered beam while the effects of hub radius and breadth taper ratio are negligible.