We consider the dynamics of a closed loop of inextensible string which is undergoing an axial motion. At each instant, one material point of the string is in contact with a singular supply of linear momentum (also known as an external constraint). Several peculiar features of this problem which have not been previously discussed are presented. These include the possible presence of an arbitrary number of kinks, the vanishing nature of the singular supply of momentum, and the critical nature of the tension in the string. When the linear momentum is supplied by a mass-spring-dashpot system, we are also able to establish an exact expression for the frequency of the resulting vibrations, prove that dissipation cannot be present, show that these vibrations only occur for discrete speeds of axial motion, and establish that Coulomb friction is absent.
On Some Peculiar Aspects of Axial Motions of Closed Loops of String in the Presence of a Singular Supply of Momentum
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 Applied Mechanics Division, May 12, 2003; final revision, October 23, 2003. Editor: R. M. McMeeking. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Journal of Applied Mechanics, Department of Mechanical and Environmental Engineering, University of California–Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication in the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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O’Reilly, O. M., and Varadi, P. C. (September 7, 2004). "On Some Peculiar Aspects of Axial Motions of Closed Loops of String in the Presence of a Singular Supply of Momentum ." ASME. J. Appl. Mech. July 2004; 71(4): 541–545. https://doi.org/10.1115/1.1756139
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