DYNAMIC STABILITY OF AN AXIALLY MOVING BAND

This paper determines approximate stability-instability region boundaries for two cases of parametric excitation. The first problem considers periodic, axial, tension variation of slender, axially moving materials such as band saws, belts, tapes, strings and chains; the second case investigates instability caused by periodic, in-plane, edge loading in axially moving materials. The governing equation of motion is reduced by means of a coordinate function expansion and Galerkin's method to a set of coupled Mathieu equations. The methods of Hsu and Bolotin are used to construct stability boundaries for the two cases. Results are compared with analog computer stability boundaries for a moving string; the string was spatially discretized by replacing spatial derivatives by equivalent difference expressions. Boundaries predicted by the two methods are close for moderate material axial velocities but separate as the axial velocity increases. © 1968.