Free vibration analysis of a system of elastically interconnected rotating tapered Timoshenko beams using differential transform method

Abstract

A new procedure for determining natural frequencies and mode shapes of a system of elastically connected multiple rotating tapered beams is presented through a differential transform method. These identical double tapered beams are assumed to rotate at a constant speed and their deformation is obeying the Timoshenko beam theory. The motion of the system is described by a coupled set of 2n partial differential equations. A substantial change of variables is employed to uncouple the governing differential equations. Thereafter, a new equivalent system of n decoupled Timoshenko beams is formed where each beam appears elastically connected to the ground, resulting to a bunch of similar equations. The inverse transform is applied to extract the solution of the original system in terms of the original variables. The results are validated against those reported in the literature and then the effects of the rotational speed, hub radius, taper ratios, rotary inertia, shear deformation, slenderness ratio and elastic layers stiffness coefficients on the natural frequencies are discussed. The natural frequencies are in excellent agreement with the reported results.