Hostname: page-component-84b7d79bbc-7nlkj Total loading time: 0 Render date: 2024-07-25T10:28:42.699Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear resonant oscillations in open tubes

Published online by Cambridge University Press:  29 March 2006

Brian R. Seymour  and
Michael P. Mortell
Brian R. Seymour
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver
Michael P. Mortell
Affiliation:
Department of Mathematical Physics, University College, Cork, Ireland
Get access Rights & Permissions [Opens in a new window]

Abstract

A gas in a tube, one end of which is open, is driven by a periodic applied velocity or pressure at or near a resonant frequency. Damping is introduced into the system by radiation of energy through the open end. It is shown that shocks are possible at an open end and that there is a critical level of damping which ensures a continuous gas response for all frequencies. At the critical level the amplitude of the response is O(ε1/3), where ε is the amplitude of the input, and it is bounded by the amplitude predicted by linear theory. There is agreement with the qualitative experimental results available.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 60 , Issue 4 , 9 October 1973 , pp. 733 - 749
Copyright
© 1973 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Collins, W. D. 1971 Forced oscillations of systems governed by one-dimensional nonlinear wave equations Q. J. Mech. Appl. Math. 24, 129–153.Google Scholar
Jimenez, J. 1973 Nonlinear gas oscillations in pipes. Part 1. Theory J. Fluid Mech. 59, 23–46.Google Scholar
Lettau, E. 1939 Dtsch. Kraftfahrtforsch. 39, 1.
Levine, H. & Schwinger, J. 1948 On the radiation of sound from an unflanged circular pipe Phys. Rev. 73, 383–406.Google Scholar
Lin, C. C. 1954 On a perturbation method based on the method of characteristics J. Math. Phys. 33, 117–134.Google Scholar
Mortell, M. P. 1971 Resonant thermal-acoustic oscillations Int. J. Engng Sci. 9, 175–192.Google Scholar
Mortell, M. P. & Seymour, B. R. 1972 Pulse propagation in a nonlinear viscoelastic rod of finite length SIAM J. App. Math. 22, 209–224.Google Scholar
Mortell, M. P. & Seymour, B. R. 1973 The evolution of a self-sustained oscillation in a nonlinear continuous system J. Appl. Mech., Trans. A.S.M.E. 95, 53–60.Google Scholar
Mortell, M. P. & Varley, E. 1970 Finite amplitude waves in a bounded media: nonlinear free vibrations of an elastic panel. Proc. Roy. Soc A 318, 169–196.Google Scholar
Seymour, B. R. & Mortell, M. P. 1973 Resonant acoustic oscillations with damping: small rate theory. J. Fluid Mech. 58, 353–374.Google Scholar
van Wijngaarden, L. 1968. On the oscillations near and at resonance in open pipes. J. Engng Math. 2, 225–240.