Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



The vibrations of a random elastic string: the method of integral equations

Authors: Bruce E. Goodwin and William E. Boyce
Journal: Quart. Appl. Math. 22 (1964), 261-266
DOI: https://doi.org/10.1090/qam/99949
MathSciNet review: QAM99949
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Abstract | References | Additional Information

Abstract: The theory of Fredholm integral equations is applied to the problem of determining the natural frequencies of transverse vibrations of a tightly stretched elastic string whose mass per unit length varies with position in a stationary random manner. Upper and lower bounds for the statistical moments of the frequencies are given in terms of corresponding moments and appropriate correlation functions for the random linear density. The adequacy of the bounds decreases for the higher frequencies. Extensions to more general random boundary value problems are also indicated.

References [Enhancements On Off] (What's this?)

  • [1] K. Hohenemser, Die Methoden zur angenäherten Lösung von Eigenwert-problemen in der Elastokinetik, Chelsea Publishing Co., New York, 1949
  • [2] R. Courant and D. Hilbert, Methods of mathematical physics, Vol. 1, Chap. 6, Interscience Publishers, Inc., New York, 1953 MR 0065391
  • [3] L. Brand, Advanced calculus, John Wiley and Sons, Inc., New York, 1955, pp. 486-489 MR 0068595
  • [4] W. E. Boyce, Random vibration of elastic strings and bars, Proceedings of the Fourth U. S. National Congress of Applied Mechanics, Berkeley, 1962, pp. 77-85 MR 0152193
  • [5] L. Collatz, Eigenwertprobleme und ihre numerische Behandlung, Chelsea Publishing Co., New York, 1948, pp. 305-308

Additional Information

DOI: https://doi.org/10.1090/qam/99949
Article copyright: © Copyright 1964 American Mathematical Society

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