The vincent circle

David W. Herrin, Jinghao Liu

Research output: Contribution to specialist publicationArticle

12 Scopus citations


More than 30 years ago, A. H. Vincent of Westland Helicopters demonstrated that if a structure is excited harmonically at a fixed frequency, the response at another position will trace a circle in the complex plane as a result of a stiffness modification between two points. This can be more generally expressed in the following manner. The structural or acoustical response at any position will map a circle in the complex plane for any straight line impedance modification in the complex plane. This article reviews the basis for this little-known principle and illustrates its usefulness for vibro-acoustics problems. The principle is demonstrated for noise radiation from a cantilevered plate and operator equipment cab. The technique can also be applied to waveguides.

Original languageEnglish
Number of pages4
Specialist publicationSound and Vibration
StatePublished - Oct 2011

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Acoustics and Ultrasonics
  • Mechanical Engineering


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