Dynamic Response of a Spinning Timoshenko Shaft With Coupled Bending and Torsion

Abstract

The dynamic behavior of a simply-supported spinning Timoshenko shaft with coupled bending and torsion is analyzed. This is accomplished by transforming the set of nonlinear partial differential equations of motion into a set of linear ordinary differential equations. This set of ordinary differential equations is a time-varying system and the solution is obtained analytically in terms of Chebyshev series. The analytical method is a viable alternative to numerical methods and can provide the full range of the required solutions. A beating phenomenon is observed from the numerical simulations. This phenomenon occurs when the system has two natural frequencies close to each other. It is also shown that the period of torsional vibrations is much shorter than the period of oscillations in transverse deflections and in bending angles.