The Free Vibrations of Stiffened Drill Strings With Static Curvature

[+] Author and Article Information
D. A. Frohrib, R. Plunkett

University of Minnesota, Minneapolis, Minn.

J. Eng. Ind 89(1), 23-29 (Feb 01, 1967) (7 pages) doi:10.1115/1.3610000 History: Received May 19, 1966; Online August 25, 2011


The natural frequencies of lateral vibration of a long drill string in static tension under its own weight are primarily the same as those of the equivalent catenary. These frequencies and the mode shapes are affected to a certain extent by the bending stiffness and to a greater extent by the static deflection curve due to lateral deflection of the bottom end. In this paper, the governing equations are derived and general solutions are given in an asymptotic expansion with the bending stiffness as the parameter. Specific numerical results are given in dimensionless form for the first three natural frequencies for a very wide range of horizontal tension and several appropriate values of bending stiffness for zero vertical static force at the bottom.

Copyright © 1967 by ASME
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