Dynamic analysis of rotating tapered Rayleigh beams using two general approaches.

The free vibration characteristics of a rotating tapered Rayleigh beam is analysed in this study. Two approaches to the dynamic analysis of a rotating beam. The first proposed approach is the discretization “CDM” method, the structure is reduced to rigid bars, connected together by means of elastic hinges, and lower bound to the true frequencies is obtained. The second approach is a variational Rayleigh–Ritz like method, in which the vibration modes are expressed as a linear combination of orthogonal polynomials. The results are presented for Rayleigh beams with rotatory inertia effects and compared with existing solution. The parameters for the hub radius, rotational speed and taper ratio are incorporated. Numerous numerical examples are proposed for the calculation of the free frequencies of vibration to vary some parameter of taper of the beams. Good agreement with the finite element method is obtained. In the end the results are compared with those reported by other authors.