Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, Jan. 2, 2001, final revision, May 6, 2003. Associate Editor: N. Triantafyllidis.

Whirling rods in a constrained environment are encountered in a variety of industrial applications, e.g., rotating drill strings confined to narrow boreholes in oilwell drilling (see, e.g., 1,2 for recent references) and in textile yarn manufacturing processes such as two-for-one twisting where the yarn is constrained by a cylindrical guide surface, 3.

Most analytical studies on the buckling of drill strings have assumed continuous contact between the drill string and the borehole wall. In fact, in most cases a helical shape for the drill string is assumed, 2. In previous work by one of us, 4, continuous contact was considered but no...

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