Application of the Vincent Circle to vibro-acoustic systems

D. W. Herrin, G. Sampath, J. Liu, H. Song

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


The Vincent Circle [1-2] principle may be stated as follows. 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 summarizes the basis for this little known principle, and then three examples are included to demonstrate how the principle can be applied to noise suppression. In the first example, a cantilevered plate is used to confirm that the principle is amenable to noise problems. A similar analysis is then performed on a construction cab to illustrate the applicability of the method if the structure is excited at multiple locations. Finally, the method is shown to be applicable to muffler and silencer systems for a modification of the source or termination impedance.

Original languageEnglish
Title of host publicationIMAC-XXVII
Subtitle of host publicationConference and Exposition on Structural Dynamics - Model Verification and Validation
StatePublished - 2009
Event27th Conference and Exposition on Structural Dynamics 2009, IMAC XXVII - Orlando, FL, United States
Duration: Feb 9 2009Feb 12 2009

Publication series

NameConference Proceedings of the Society for Experimental Mechanics Series
ISSN (Print)2191-5644
ISSN (Electronic)2191-5652


Conference27th Conference and Exposition on Structural Dynamics 2009, IMAC XXVII
Country/TerritoryUnited States
CityOrlando, FL

ASJC Scopus subject areas

  • General Engineering
  • Computational Mechanics
  • Mechanical Engineering


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