Torsional vibration analyses of a damped shafting system using tapered shaft element

The objective of this paper is to present a tapered shaft element such that the torsional vibration characteristics of a damped shafting system can be easily determined with effect of continuous non-uniformity of the shaft cross-sections being considered. To this end, the shape functions of the tapered shaft element are firstly derived. Then, the stiffness and mass matrices of the last shaft element are determined by means of the Lagrangeʹs equations. To confirm the reliability of the presented theory, the numerical results obtained from the presented technique are compared with those obtained from the existing literature and good agreement is achieved. Finally, the torsional vibration analysis of a hybrid (tapered) shaft, composed of multiple uniform and tapered shaft segments and carrying multiple disks, is performed to show the applicability of the presented technique.