Treatment of frequency-dependent admittance boundary conditions in transient acoustic finite/infinite-element models

Nieuwenhof, Benoı̂t Van den; Coyette, Jean‐Pierre

doi:10.1121/1.1404436

Cited by 11 publications

(9 citation statements)

References 14 publications

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“…For a positive reactance they made the choice of K = 0 (in our notation), and expressed p in v and v . For a negative reactance they took m = 0, used the split form (18), and expressed p in v and v . The causality condition of the impedance Z was correctly associated with the location of the pole at ω = 0, but the causality condition of the admittance Z −1 was called "stability" condition, which is confusing.…”

Section: A 3-parameter Modelmentioning

confidence: 99%

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Impedance Models in Time Domain, Including the Extended Helmholtz Resonator Model

Rienstra

2006

12th AIAA/CEAS Aeroacoustics Conference (27th AIAA Aeroacoustics Conference)

143

123

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The problem of translating a frequency domain impedance boundary condition to time domain involves the Fourier transform of the impedance function. This requires extending the definition of the impedance not only to all real frequencies but to the whole complex frequency plane. Not any extension, however, is physically possible. The problem should remain causal, the variables real, and the wall passive. This leads to necessary conditions for an impedance function.Various methods of extending the impedance that are available in the literature are discussed. A most promising one is the so-called z-transform by Ozyoruk & Long, which is nothing but an impedance that is functionally dependent on a suitable complex exponent e −iωκ . By choosing κ a multiple of the time step of the numerical algorithm, this approach fits very well with the underlying numerics, because the impedance becomes in time domain a delta-comb function and gives thus an exact relation on the grid points.An impedance function is proposed which is based on the Helmholtz resonator model, called Extended Helmholtz Resonator Model. This has the advantage that relatively easily the mentioned necessary conditions can be satisfied in advance. At a given frequency, the impedance is made exactly equal to a given design value. Rules of thumb are derived to produce an impedance which varies only moderately in frequency near design conditions. An explicit solution is given of a pulse reflecting in time domain at a Helmholtz resonator impedance wall that provides some insight into the reflection problem in time domain and at the same time may act as an analytical test case for numerical implementations, like is presented at this conference by the companion paper AIAA-2006-2569 by N. Chevaugeon, J.-F. Remacle and X. Gallez.The problem of the instability, inherent with the Ingard-Myers limit with mean flow, is discussed. It is argued that this instability is not consistent with the assumptions of the Ingard-Myers limit and may well be suppressed. wherev = (v · n),v is the acoustic velocity vector and n denotes the normal vector of the wall that points into the wall. Pressure is scaled on ρ 0 c 2 0 , velocity on c 0 and impedance on ρ 0 c 0 , while we use throughout the e +iωt * Associate professor,

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Section: A 3-parameter Modelmentioning

confidence: 99%

“…In [16,17] and [18] this form was used for N = 4 and M = 3, in [19] with N = M = 2, and in [20] with N = M = 2 and N = M = 4. Care is required that the zeros and poles are located in the correct part of the complex plane (i.e.…”

Section: B Rational Functions In ωmentioning

confidence: 99%

Impedance Models in Time Domain, Including the Extended Helmholtz Resonator Model

Rienstra

2006

12th AIAA/CEAS Aeroacoustics Conference (27th AIAA Aeroacoustics Conference)

143

123

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“…This phenomenon also shows up in acoustic experiments 9 as well as in the pertaining Finite-Difference Time-Domain method ͑FDTD͒ and field emission microscopy Finite Element Method ͑FEM͒ studies. 10,11 A careful analysis of the structure of our reflection function shows, however, that this phenomenon is not in the same category as the Rayleigh wave 12 along the planar boundary of a traction free elastic solid, the Scholte wave 3 along the planar fluid/ solid interface, or the Stoneley waves 13 along the interface of two different solids. The analytic CdH method employed, further provides the changes in wave shape that the reflected wave undergoes, in their dependence on the parameters 14 occurring in the expression for the boundary's acoustic impedance.…”

Section: Introductionmentioning

confidence: 93%

Impulsive sound reflection from an absorptive and dispersive planar boundary

Lam

Kooij

Hoop

2004

The Journal of the Acoustical Society of America

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The impulsive sound reflection from a planar boundary with absorptive and dispersive properties is investigated. The acoustic properties of the boundary are modeled via a local impedance transfer function whose complex frequency domain representation is taken to be a Padé ͑2,2͒ expression. The coefficients in this representation are matched to frequency domain acoustic wave reflection measurements. With the aid of the Cagniard-De Hoop method, a closed-form space-time expression is derived for the acoustic pressure of the reflected wave arising from the incidence of a point-source monopole excited spherical pulse. Depending on the acoustic impedance properties of the boundary, large-amplitude oscillating surface effects can occur. These surface phenomena differ in nature from the true surface waves like the Rayleigh, Scholte, and Stoneley waves in elastodynamics. Illustrative numerical results are presented.

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“…At this point, it is convenient to comment that the impedance of the vocal tract wall is not actually frequency independent (e.g., see Ishizaka et al, 1975). However, implementing frequency dependent boundary conditions in the time domain is not a straightforward task [see Nieuwenhof and Coyette (2001) for some steps toward this goal], so that the constant frequency assumption is usually adopted (e.g., see Takemoto et al, 2010). On the other hand, the homogeneous Neumann boundary condition in Eq.…”

Section: The Wave Equation For Vocal Tract Acousticsmentioning

confidence: 99%

Effects of head geometry simplifications on acoustic radiation of vowel sounds based on time-domain finite-element simulations

Arnela

Guasch

Álías

2013

The Journal of the Acoustical Society of America

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One of the key effects to model in voice production is that of acoustic radiation of sound waves emanating from the mouth. The use of three-dimensional numerical simulations allows to naturally account for it, as well as to consider all geometrical head details, by extending the computational domain out of the vocal tract. Despite this advantage, many approximations to the head geometry are often performed for simplicity and impedance load models are still used as well to reduce the computational cost. In this work, the impact of some of these simplifications on radiation effects is examined for vowel production in the frequency range 0-10 kHz, by means of comparison with radiation from a realistic head. As a result, recommendations are given on their validity depending on whether high frequency energy (above 5 kHz) should be taken into account or not.

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Treatment of frequency-dependent admittance boundary conditions in transient acoustic finite/infinite-element models

Cited by 11 publications

References 14 publications

Impedance Models in Time Domain, Including the Extended Helmholtz Resonator Model

Impedance Models in Time Domain, Including the Extended Helmholtz Resonator Model

Impulsive sound reflection from an absorptive and dispersive planar boundary

Effects of head geometry simplifications on acoustic radiation of vowel sounds based on time-domain finite-element simulations

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