Exploting the complex plane: The moebius transformation and vibro-acoustic optimization

D. W. Herrin, Y. Zhang, J. Liu

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

Abstract

If a mechanical or acoustical impedance modification is introduced between two positions, the effect of that modification can be plotted in the complex plane at a given frequency. It has been shown that the mechanical or acoustical response will trace a circle in the complex plane for straightline modifications to impedance in the complex plane. In that case, the equations relating the response to an impedance modification are in a form consistent with the Moebius transformation, which maps straight lines or circles in one complex domain into straight lines or circles in another complex plane. It is demonstrated that the equations for muffler transmission loss and mount insertion loss are in a form consistent with the Moebius transformation for certain design changes. Accordingly, the usefulness of this linear system property will be illustrated for both muffler and mount design.

Original languageEnglish
Title of host publication41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012
Pages5714-5720
Number of pages7
StatePublished - 2012
Event41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012 - New York, NY, United States
Duration: Aug 19 2012Aug 22 2012

Publication series

Name41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012
Volume7

Conference

Conference41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012
Country/TerritoryUnited States
CityNew York, NY
Period8/19/128/22/12

ASJC Scopus subject areas

  • Acoustics and Ultrasonics

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