Three-dimensional response and intensity of torsional vibration in a stepped shaft

In this paper, a method is presented for predicting the three-dimensional d ynamic response, shear stresses and structural intensity of torsional vibra tion in a finite shaft with stepped cross-sections. The series expansion te chniques 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 bounda ry conditions through the least-squares fitting. The effectiveness of this proposed method is assessed and illustrated by numerical results. The numer ical results also revealed the characteristics of dynamic response, shear s tresses and intensity vector fields in a finite stepped shaft and showed th at the application of the one-dimensional torsional vibration theory to a f inite stepped shaft not only misses out radial modal responses, but also re sults in a large error for the prediction of responses of axial modes when the resonance frequencies of all the segments tin free-free end conditions) do not coincide. (C) 2000 Academic Press.