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.
title = "Nonlinear asymptotic impedance model for a Helmholtz resonator liner",
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.",
T1 - Nonlinear asymptotic impedance model for a Helmholtz resonator liner
AU - Singh, D.K.
AU - Rienstra, S.W.
PY - 2014
Y1 - 2014
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.
M3 - Report
T3 - CASA-report
BT - Nonlinear asymptotic impedance model for a Helmholtz resonator liner