A systematic impedance model for non-linear Helmholtz resonator liner

D.K. Singh; S.W. Rienstra

doi:10.2514/6.2013-2223

A systematic impedance model for non-linear Helmholtz resonator liner

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

The usual non-linear 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 non-linear Helmholtz resonator equation, in order to obtain analytically expressions for impedances close to resonance, while including non-linear effects. The amplitude regime considered is such that when we stay away from the resonance condition, the non-linear terms are relatively small and the solution obtained is of the linear equation (formed after neglecting the non-linear terms). Close to the resonance frequency, the non-linear terms can no longer be neglected and algebraic equations are obtained that describe the corresponding non-linear impedance.

Original language	English
Title of host publication	19th AIAA/CEAS Aeroacoustics Conference (Berlin, Germany, May 27-29, 2013)
Place of Publication	Reston
Publisher	American Institute of Aeronautics and Astronautics Inc. (AIAA)
Number of pages	12
ISBN (Print)	978-1-62410-213-4
DOIs	https://doi.org/10.2514/6.2013-2223
Publication status	Published - 2013
Event	19th AIAA/CEAS Aeroacoustics Conference - Berlin, Germany Duration: 27 May 2013 → 29 May 2013

Conference

Conference	19th AIAA/CEAS Aeroacoustics Conference
Country/Territory	Germany
City	Berlin
Period	27/05/13 → 29/05/13

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10.2514/6.2013-2223

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title = "A systematic impedance model for non-linear Helmholtz resonator liner",

abstract = "The usual non-linear 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 non-linear Helmholtz resonator equation, in order to obtain analytically expressions for impedances close to resonance, while including non-linear effects. The amplitude regime considered is such that when we stay away from the resonance condition, the non-linear terms are relatively small and the solution obtained is of the linear equation (formed after neglecting the non-linear terms). Close to the resonance frequency, the non-linear terms can no longer be neglected and algebraic equations are obtained that describe the corresponding non-linear impedance.",

author = "D.K. Singh and S.W. Rienstra",

year = "2013",

doi = "10.2514/6.2013-2223",

language = "English",

isbn = "978-1-62410-213-4",

booktitle = "19th AIAA/CEAS Aeroacoustics Conference (Berlin, Germany, May 27-29, 2013)",

publisher = "American Institute of Aeronautics and Astronautics Inc. (AIAA)",

address = "United States",

note = "19th AIAA/CEAS Aeroacoustics Conference ; Conference date: 27-05-2013 Through 29-05-2013",

}

Singh, DK & Rienstra, SW 2013, A systematic impedance model for non-linear Helmholtz resonator liner. in 19th AIAA/CEAS Aeroacoustics Conference (Berlin, Germany, May 27-29, 2013)., AIAA-2013-2223, American Institute of Aeronautics and Astronautics Inc. (AIAA), Reston, 19th AIAA/CEAS Aeroacoustics Conference, Berlin, Germany, 27/05/13. https://doi.org/10.2514/6.2013-2223

A systematic impedance model for non-linear Helmholtz resonator liner. / Singh, D.K.; Rienstra, S.W.
19th AIAA/CEAS Aeroacoustics Conference (Berlin, Germany, May 27-29, 2013). Reston: American Institute of Aeronautics and Astronautics Inc. (AIAA), 2013. AIAA-2013-2223.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - A systematic impedance model for non-linear Helmholtz resonator liner

AU - Singh, D.K.

AU - Rienstra, S.W.

PY - 2013

Y1 - 2013

N2 - The usual non-linear 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 non-linear Helmholtz resonator equation, in order to obtain analytically expressions for impedances close to resonance, while including non-linear effects. The amplitude regime considered is such that when we stay away from the resonance condition, the non-linear terms are relatively small and the solution obtained is of the linear equation (formed after neglecting the non-linear terms). Close to the resonance frequency, the non-linear terms can no longer be neglected and algebraic equations are obtained that describe the corresponding non-linear impedance.

AB - The usual non-linear 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 non-linear Helmholtz resonator equation, in order to obtain analytically expressions for impedances close to resonance, while including non-linear effects. The amplitude regime considered is such that when we stay away from the resonance condition, the non-linear terms are relatively small and the solution obtained is of the linear equation (formed after neglecting the non-linear terms). Close to the resonance frequency, the non-linear terms can no longer be neglected and algebraic equations are obtained that describe the corresponding non-linear impedance.

U2 - 10.2514/6.2013-2223

DO - 10.2514/6.2013-2223

M3 - Conference contribution

SN - 978-1-62410-213-4

BT - 19th AIAA/CEAS Aeroacoustics Conference (Berlin, Germany, May 27-29, 2013)

PB - American Institute of Aeronautics and Astronautics Inc. (AIAA)

CY - Reston

T2 - 19th AIAA/CEAS Aeroacoustics Conference

Y2 - 27 May 2013 through 29 May 2013

ER -

A systematic impedance model for non-linear Helmholtz resonator liner

Abstract

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