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 |
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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.
K. Hohenemser, Die Methoden zur angenäherten Lösung von Eigenwert-problemen in der Elastokinetik, Chelsea Publishing Co., New York, 1949
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
- Louis Brand, Advanced calculus. An introduction to classical analysis, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1955. MR 0068595
- W. E. Boyce, Random vibration of elastic strings and bars, Proc. 4th U.S. Nat. Congr. Appl. Mech. (Univ. California, Berkeley, Calif., 1962) Amer. Soc. Mech. Engrs., New York, 1962, pp. 77–85. MR 0152193
L. Collatz, Eigenwertprobleme und ihre numerische Behandlung, Chelsea Publishing Co., New York, 1948, pp. 305–308
K. Hohenemser, Die Methoden zur angenäherten Lösung von Eigenwert-problemen in der Elastokinetik, Chelsea Publishing Co., New York, 1949
R. Courant and D. Hilbert, Methods of mathematical physics, Vol. 1, Chap. 6, Interscience Publishers, Inc., New York, 1953
L. Brand, Advanced calculus, John Wiley and Sons, Inc., New York, 1955, pp. 486–489
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
L. Collatz, Eigenwertprobleme und ihre numerische Behandlung, Chelsea Publishing Co., New York, 1948, pp. 305–308
Additional Information
Article copyright:
© Copyright 1964
American Mathematical Society