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Nonlinear eigenvalue problems for the whirling of heavy elastic strings

Published online by Cambridge University Press:  14 November 2011

Stuart S. Antman
Stuart S. Antman
Affiliation:
Lefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University, Providence, Rhode Island, U.S.A. and Department of Mathematics, University of Maryland, College Park, Maryland, U.S.A.
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Synopsis

This paper combines the global bifurcation theory of Rabinowitz with Sturmian theory and careful estimates to obtain a detailed qualitative description of bifurcating branches of solutions to the equations for whirling nonuniform, nonlinearly elastic strings. These results generalize earlier work of Kolodner and Stuart on inextensible strings. It is shown that the location of solution branches for the generalization of Kolodner's problem is especially sensitive to the material properties of the string, whereas that for Stuart's problem is not. The analysis of a third problem illuminates the source of this dichotomy.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 85 , Issue 1-2 , 1980 , pp. 59 - 85
Copyright
Copyright © Royal Society of Edinburgh 1980

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