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The Application of the Vincent Circle to Vibro-Acoustic and Duct Acoustic Problems

Journal Article
2009-01-2215
ISSN: 1946-3995, e-ISSN: 1946-4002
Published May 19, 2009 by SAE International in United States
The Application of the Vincent Circle to Vibro-Acoustic and Duct Acoustic Problems
Sector:
Citation: Herrin, D. and Liu, J., "The Application of the Vincent Circle to Vibro-Acoustic and Duct Acoustic Problems," SAE Int. J. Passeng. Cars – Mech. Syst. 2(1):1505-1510, 2009, https://doi.org/10.4271/2009-01-2215.
Language: English

Abstract:

Over 30 years ago, A. H. Vincent of Westland Helicopters demonstrated that if a structure is excited harmonically, the response at another position (at a fixed frequency) will trace a circle in the complex plane as a result of a dynamic stiffness modification between two points. As either the real or imaginary part of an introduced dynamic stiffness is varied from minus infinity to plus infinity, the structural or acoustic response on any position will map a circle in the complex plane. This paper reviews the basis for this little known principle for vibro-acoustics problems and illustrates the viability for a cantilevered plate example. The applicability of the method is then considered for strictly acoustic systems like intake and exhaust systems. Specifically, it is shown that the response traces a circle in the complex plane if either the real or imaginary parts of the source or termination impedance are varied from minus to plus infinity.