CONTINUOUS MODELLING OF THE TORSIONAL VIBRATIONS OF THE DRIVE SHAFT OF MECHANISMS

Abstract

The torsional vibrations of crankshafts, input and output shafts of mechanisms having variable inertia characteristics are generally modelled as discrete systems, and the governing equations of the motion are described by ordinary differential equations. The stability and the forced response of the shafts are examined by solving these ordinary differential equations. In this study, the torsional vibrations of the drive shaft of the mechanisms having variable inertia characteristics are studied by modelling the shaft as a continuous element. As a result of the continuous element modelling, a non-linear boundary value problem is obtained. The non-linear problem is linearized by a suitable transformation and the forced response of the shaft is examined. For this purpose, a well-known solution technique, the perturbation method, is adapted to the problem and the resonance conditions of the torsional vibrations are investigated.