Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T14:11:06.600Z Has data issue: false hasContentIssue false
  • English
  • Français

Spatial resonance of a liquid-filled vibrating beaker

Published online by Cambridge University Press:  11 April 2006

Ian Huntley
Ian Huntley
Affiliation:
Department of Mathematics and Computing, Paisley College of Technology, Renfrewshire PA1 2BE, Scotland
Get access Rights & Permissions [Opens in a new window]

Abstract

Mahony & Smith (1972) put forward a model to explain the phenomenon of energy transfer between nearly resonant oscillations at greatly differing frequencies. However, their model of ‘spatial resonance’ is restricted to situations where the geometry of the system is very simple. The present paper shows how to derive Mahony & Smith's equations in a general manner, and compares the theoretical predictions for a situation with circular symmetry with existing experimental results (Huntley 1972). In addition, it suggests a simple method for evaluating the resonance frequencies when a liquid-filled beaker is vibrated in one of its bell modes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 80 , Issue 1 , 4 April 1977 , pp. 81 - 97
Copyright
© 1977 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

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.
Bickley, W. G. & Talbot, A. 1961 An Introduction to the Theory of Vibrating Systems. Oxford University Press.
Case, K. M. & Parkinson, W. C. 1957 Damping of surface waves in an incompressible liquid. J. Fluid Mech. 2, 172–184.Google Scholar
Huntley, I. D. 1972 Observations on a spatial-resonance phenomenon. J. Fluid Mech. 53, 209–216.Google Scholar
Huntley, I. D. 1973 Aspects of nonlinear wave interactions. Ph.D. thesis, University of Essex.
Mahohy, J. J. & Smith, R. W. 1972 On a model representation for certain spatialresonance phenomena. J. Fluid Mech. 53, 193–207.Google Scholar
Timoshenko, S. P. & Woinowsky-Krieger, S. 1969 Theory of Plates and Shells. McGraw-Hill.