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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
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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

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References

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