Hostname: page-component-77c89778f8-m8s7h Total loading time: 0 Render date: 2024-07-19T14:47:31.397Z Has data issue: false hasContentIssue false
  • English
  • Français

Geometrical effects in resonant gas oscillations

Published online by Cambridge University Press:  26 April 2006

H. Ockendon ,
J. R. Ockendon ,
M. R. Peake  and
W. Chester
Get access Rights & Permissions [Opens in a new window]

Abstract

It is known that the response of a cylindrical acoustic resonator to excitation by an oscillating piston can contain shock waves if the detuning is sufficiently small. However, the response of a spherical annular resonator is continuous, with an amplitude that depends on the detuning in the same way as does a Duffing equation. This paper discusses the response in resonators that deviate from being cylindrical and shows that, in general, the detuning range in which shocks are possible decreases as the geometrical imperfection increases.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 257 , December 1993 , pp. 201 - 217
Copyright
© 1993 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

Barcilon, V. 1983 Explicit solutions of the inverse problem for a vibrating string. Math. Anal. 93, 222–234.Google Scholar
Can, M. & Askar, A. 1990 Nonlinear surface waves. Wave Motion 12, 485–495.Google Scholar
Chester, W. 1964 Resonant oscillations in closed tubes. J. Fluid Mech. 18, 44–64.Google Scholar
Chester, W. 1968 Resonant oscillations of water waves. Proc. R. Soc. Lond. A 306, 5–22.Google Scholar
Chester, W. 1981 Resonant oscillations of a gas in an open ended tube. Proc. R. Soc. Lond. A 377, 449–467.Google Scholar
Chester, W. 1991 Acoustic resonance in spherically symmetric waves. Proc. R. Soc. Lond. A 434, 459–463.Google Scholar
Chester, W. 1993 Nonlinear acoustic resonance in tubes of varying cross-section. Proc. R. Soc. Lond. A (to appear.)Google Scholar
Chester, W. & Bones, J. A. 1968 Resonant oscillations of water waves. Proc. R. Soc. Lond. A 306, 23–39.Google Scholar
Ellermeier, W. 1993 Nonlinear acoustics in non-uniform infinite and finite layers. J. Fluid Mech. 257, 183–200.Google Scholar
Keller, J. B. & Ting, L. 1966 Periodic vibrations of systems governed by nonlinear partial differential equations. Commun. Pure Appl. Maths. 19, 371–420.Google Scholar
Keller, J. J. 1976a Resonant oscillations in closed tubes: the solution of Chester's equation. J. Fluid Mech. 77, 279–304.Google Scholar
Keller, J. J. 1976b Third order resonances in closed tubes. Z. Angew. Math. Phys. 27, 303–323.Google Scholar
Keller, J. J. 1977 Nonlinear acoustic resonances in shock tubes with varying cross-sectional area. Z. Angew. Math. Phys. 28, 107–122.Google Scholar
Lighthill, M. J. 1978 Waves in Fluids. Cambridge University Press.
Moiseyev, N. N. 1958 On the theory of nonlinear vibrations of a liquid of finite volume. Prikl. Mat. Mech. 22, 612–621.Google Scholar
Ockendon, J. R. & Ockendon, H. 1973 Resonant surface waves. J. Fluid Mech. 59, 397–413.Google Scholar
Ockendon, H., Ockendon, J. R. & Johnson, A. D. 1986 Resonant sloshing in shallow water. J. Fluid Mech. 167, 465–479.Google Scholar
Ockendon, H. & Tayler, A. B. 1983 Inviscid Fluid Flows. Springer.
Peake, M. 1993 Resonance in nonlinear gas dynamics. DPhil thesis, Oxford University.