Dynamic stability of an axially moving band

✍ Scribed by C.D. Mote Jr.

• Publisher: Elsevier Science
• Year: 1968
• Tongue: English
• Weight: 664 KB
• Volume: 285
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(68)90482-1

✦ Synopsis

This paper determines approximate stability~inetability reoion boundaries for two eases of parametric excitation. The first problem considers periodicj axial, tension variation of slender, a.vially 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 meYwde of Hsu and Bolotin are used to construct stability boundaries for the two eases. 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.