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Large amplitude whirling of an elastic string -- a nonlinear eigenvalue problem

Caughey, T. K. (1970) Large amplitude whirling of an elastic string -- a nonlinear eigenvalue problem. SIAM Journal on Applied Mathematics, 18 (1). pp. 210-237. ISSN 0036-1399.

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The whirling of a string is a problem of some antiquity, the linearized solutions to a number of such problems having been derived by D. Bernoulli (1700-1782) and L. Euler (1707-1783). The nonlinear theory of whirling of inextensible strings has been discussed by Kolodner [1] and Caughey [2], [3]. Carrier [4], [5] has discussed the theory of nonlinear vibration of an elastic string using perturbation methods. In the present paper exact solutions will be presented for the whirling of an elastic string with fixed ends, and it will be shown that the modes of free whirling are orbitally stable.

Item Type:Article
Additional Information:© 1970 Society for Industrial and Applied Mathematics. Received by the editors June 13, 1968, and in revised form November 1, 1968.
Issue or Number:1
Record Number:CaltechAUTHORS:CAUsiamjam70
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:363
Deposited By: Thomas Kirk Caughey
Deposited On:06 Jun 2005
Last Modified:02 Oct 2019 22:33

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