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Finite amplitude analysis of a flow-structure interaction problem

Published online by Cambridge University Press:  29 March 2006

A. O. St Hilaire  and
P. G. Vaidya
A. O. St Hilaire
Affiliation:
Department of Mechanical Engineering, Tufts University, Medford, Massachusetts Present address: United Aircraft Research Laboratories, East Hartford, Connecticut.
P. G. Vaidya
Affiliation:
Department of Mechanical Engineering, Tufts University, Medford, Massachusetts Present address: R. W. Herrick Laboratories, Purdue University, Lafayette, Indiana.
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Abstract

The interaction between a vibrating structure and an unsteady potential flow-field disturbance induced by the motion of the structure itself is investigated, and is shown to be a significant source of both nonlinear excitation and nonlinear dissipation. An approximate analysis, based on small nonlinear disturbance theory, is presented of the forces that influence the characteristic behaviour of self-excited harmonium reeds vibrating at finite amplitudes. It is demonstrated that the ideas brought forth by this example can be generalized to apply to other flow-induced vibrating systems, regardless of the excitation mechanism, provided that certain basic assumptions about the flow can be made. For the case of the harmonium reed, it is shown that, taken by itself, an account of the feedback forces arising from induced higher-order unsteady disturbances in the surrounding potential flow field is sufficient for predicting the net nonlinear dissipative force that eventually causes the reed to reach and maintain a finite limiting amplitude. In particular, it is demonstrated that the nonlinear energy drain from the motion of the reed is a consequence of the net effect of the higher-harmonic disturbances that are generated near the structure.

A result of the analysis is the development of a functional dependence of the interactive forces on the system geometry and the flow velocity. One of the advantages of obtaining a functional expression is the ability to carry out parametric studies in the context of vibration and noise control.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 67 , Issue 2 , 28 January 1975 , pp. 377 - 396
Copyright
© 1975 Cambridge University Press

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