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

Authors:
Louise H. Jones and Bruce E. Goodwin

Journal:
Quart. Appl. Math. **29** (1971), 363-374

DOI:
https://doi.org/10.1090/qam/99757

MathSciNet review:
QAM99757

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Abstract | References | Additional Information

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.

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Additional Information

DOI:
https://doi.org/10.1090/qam/99757

Article copyright:
© Copyright 1971
American Mathematical Society