The transverse vibrations of a pipe containing flowing fluid: Methods of integral equations-Reference-Cited by-同舟云学术

The transverse vibrations of a pipe containing flowing fluid: Methods of integral equations

Published:1971 Issue:3 Volume:29 Page:363-374
ISSN:0033-569X
Container-title:Quarterly of Applied Mathematics
language:en
Short-container-title:Quart. Appl. Math.

Author:

Jones Louise H.,Goodwin Bruce E.

Abstract

Methods are developed to study the problem described in the title. Improvable lower bounds for the first eigenvalue are obtained for the low velocity-thin pipe wall case. It is shown that the eigenvalue changes from real to imaginary as the fluid velocity increases through a “critical” velocity. It is the methods which we wish to emphasize in that while we discuss them only for the present problem they are very general and especially powerful when applied to differential equations with constant coefficients.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics

Link

http://www.ams.org/qam/1971-29-03/S0033-569X-1971-99757-6/S0033-569X-1971-99757-6.pdf

Reference15 articles.

1. L. H. Jones, The transverse vibrations of a pipe containing flowing fluid, Master’s Thesis, University of Delaware, Newark, Delaware

2. E. P. Hamilton and B. E. Goodwin, The inverse problem of the calculus of variations, in Analytic methods in mathematical physics (ed. R. P. Gilbert and R. G. Newton), Gordon and Breach, New York, 1970

3. On the realization of the eigenvalues of integral equations whose kernels are entire or meromorphic in the eigenvalue parameter;Goodwin, Bruce E.;SIAM J. Appl. Math.,1966

4. Über lineare Integralgleichungen mit vom Parameter abhängigem Kern;Iglisch, Rudolf;Math. Ann.,1939

5. G. W. Housner, Bending vibrations of a pipeline containing flowing fluid, J. Appl. Mech. 19, 205–208 (1952)

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