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Hysteresis and nonlinear detuning in a spatial-resonance phenomenon

Published online by Cambridge University Press:  29 March 2006

Ian Huntley  and
Ronald Smith
Ian Huntley
Affiliation:
Fluid Mechanics Research Institute, University of Essex Present address: Engineering Department, University of Leicester.
Ronald Smith
Affiliation:
Fluid Mechanics Research Institute, University of Essex
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Abstract

The experimental work of Franklin, Price & Williams (1973) shows that for moderately large driving amplitudes there are features of spatial resonance that are not predicted by the model representation of Mahony & Smith (1972). We here derive an alternative model, which remains valid for moderately large driving amplitudes, and we are able to obtain a theoretical description of both hysteresis and nonlinear detuning of the low frequency wave response. An experiment in which surface waves were generated by a sinusoidal pressure field at the free surface (and which corresponds almost exactly to the theoretical problem) was conducted in order to test these predictions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 61 , Issue 2 , 6 November 1973 , pp. 401 - 413
Copyright
© 1973 Cambridge University Press

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References

Cole, J. D. 1968 Perturbation Methods in Applied Mathematics. Waltham, Mass.: Blaisdell.
Franklin, R. E., Price, M. & Williams, D. C. 1973 Acoustically driven water waves. J. Fluid Mech. 57, 257–268.Google Scholar
Huntley, I. 1972 Observations on a spatial-resonance phenomenon. J. Fluid Mech. 53, 209–216.Google Scholar
Mahony, J. J. & Smith, R. 1972 On a model representation for certain spatial-resonance phenomena. J. Fluid Mech. 53, 193–208.Google Scholar