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
Full-text PDF Free Access

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. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
  • [3] Louis Brand, Advanced calculus. An introduction to classical analysis, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1955. MR 0068595
  • [4] 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
  • [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


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website