Nonlinear asymptotic impedance model for a Helmholtz resonator liner

D.K. Singh, S.W. Rienstra

Research output: Book/ReportReportAcademic

26 Citations (Scopus)
126 Downloads (Pure)

Abstract

The usual nonlinear corrections for a Helmholtz resonator type impedance do not seem to be based on a systematic asymptotic solution of the pertaining equations. We aim to present a systematic derivation of a solution of the nonlinear Helmholtz resonator equation, in order to obtain analytically expressions for impedances close to resonance, while including nonlinear effects. The amplitude regime considered is such that when we stay away from the resonance condition, the nonlinear terms are relatively small and the solution obtained is of the linear equation (formed after neglecting the nonlinear terms). Close to the resonance frequency, the nonlinear terms can no longer be neglected and algebraic equations are obtained that describe the corresponding nonlinear impedance. Sample results are presented including a few comparisons with measurements available in the literature. The validity of the model is understood in the near resonance and non- resonance regimes.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages14
Publication statusPublished - 2014

Publication series

NameCASA-report
Volume1418
ISSN (Print)0926-4507

Fingerprint

Helmholtz resonators
linings
impedance
nonresonance
linear equations
derivation

Cite this

Singh, D. K., & Rienstra, S. W. (2014). Nonlinear asymptotic impedance model for a Helmholtz resonator liner. (CASA-report; Vol. 1418). Eindhoven: Technische Universiteit Eindhoven.
Singh, D.K. ; Rienstra, S.W. / Nonlinear asymptotic impedance model for a Helmholtz resonator liner. Eindhoven : Technische Universiteit Eindhoven, 2014. 14 p. (CASA-report).
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Singh, DK & Rienstra, SW 2014, Nonlinear asymptotic impedance model for a Helmholtz resonator liner. CASA-report, vol. 1418, Technische Universiteit Eindhoven, Eindhoven.

Nonlinear asymptotic impedance model for a Helmholtz resonator liner. / Singh, D.K.; Rienstra, S.W.

Eindhoven : Technische Universiteit Eindhoven, 2014. 14 p. (CASA-report; Vol. 1418).

Research output: Book/ReportReportAcademic

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T1 - Nonlinear asymptotic impedance model for a Helmholtz resonator liner

AU - Singh, D.K.

AU - Rienstra, S.W.

PY - 2014

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N2 - The usual nonlinear corrections for a Helmholtz resonator type impedance do not seem to be based on a systematic asymptotic solution of the pertaining equations. We aim to present a systematic derivation of a solution of the nonlinear Helmholtz resonator equation, in order to obtain analytically expressions for impedances close to resonance, while including nonlinear effects. The amplitude regime considered is such that when we stay away from the resonance condition, the nonlinear terms are relatively small and the solution obtained is of the linear equation (formed after neglecting the nonlinear terms). Close to the resonance frequency, the nonlinear terms can no longer be neglected and algebraic equations are obtained that describe the corresponding nonlinear impedance. Sample results are presented including a few comparisons with measurements available in the literature. The validity of the model is understood in the near resonance and non- resonance regimes.

AB - The usual nonlinear corrections for a Helmholtz resonator type impedance do not seem to be based on a systematic asymptotic solution of the pertaining equations. We aim to present a systematic derivation of a solution of the nonlinear Helmholtz resonator equation, in order to obtain analytically expressions for impedances close to resonance, while including nonlinear effects. The amplitude regime considered is such that when we stay away from the resonance condition, the nonlinear terms are relatively small and the solution obtained is of the linear equation (formed after neglecting the nonlinear terms). Close to the resonance frequency, the nonlinear terms can no longer be neglected and algebraic equations are obtained that describe the corresponding nonlinear impedance. Sample results are presented including a few comparisons with measurements available in the literature. The validity of the model is understood in the near resonance and non- resonance regimes.

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BT - Nonlinear asymptotic impedance model for a Helmholtz resonator liner

PB - Technische Universiteit Eindhoven

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Singh DK, Rienstra SW. Nonlinear asymptotic impedance model for a Helmholtz resonator liner. Eindhoven: Technische Universiteit Eindhoven, 2014. 14 p. (CASA-report).