THREE-DIMENSIONAL RESPONSE AND INTENSITY OF TORSIONAL VIBRATION IN A STEPPED SHAFT

In this paper, a method is presented for predicting the three-dimensional dynamic response, shear stresses and structural intensity of torsional vibration in a finite shaft with stepped cross-sections. The series expansion techniques is employed to express the dynamic responses and shear stresses in terms of the eigenfunctions of torsional vibration in uniform cylindrical rods. The coefficients of the series are determined by enforcing the boundary conditions through the least-squares fitting. The effectiveness of this proposed method is assessed and illustrated by numerical results. The numerical results also revealed the characteristics of dynamic response, shear stresses and intensity vector fields in a finite stepped shaft and showed that the application of the one-dimensional torsional vibration theory to a finite stepped shaft not only misses out radial modal responses, but also results in a large error for the prediction of responses of axial modes when the resonance frequencies of all the segments (in free–free end conditions) do not coincide.