Vibration of straight-curved-straight hollow shafts

This work presents the governing equations for both the in-plane motion and out-of-plane motion of a curved hollow shaft. Two types of shaft structure s, which are a curved hollow shaft and a straight-curved-straight hollow sh aft, are considered. An analytical method is also presented to examine the free vibration of the two types of shaft structures. The orthogonality of a ny two distinct sets of mode shape functions for both the in-plane motion a nd out-of-plane motion of the structures is also derived. The first in-plan e modal frequency of a structure is greater than the first out-of-plane mod al frequency of the same structure. (C) 2000 Academic Press.