Implementation and Experimental Validation of a New Viscothermal Acoustic Finite Element for Acousto-Elastic Problems

Beltman, W.M.; Hoogt, P.J.M. van der; Spiering, R.M.E.J.; Tijdeman, H.

doi:10.1006/jsvi.1998.1708

Cited by 68 publications

(64 citation statements)

References 15 publications

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“…A direct application of these methods is not appropriate for the system considered in this study because the viscous boundary layer occupies a large fraction of the 110-m duct height, causing these approaches to underestimate the viscous fluid damping. The finite element model described herein is taken from Beltman et al (23). This model couples a thin, viscous, compressible acoustic medium to a structure, differing from the majority of cochlear models by focusing on viscous fluid effects.…”

Section: Modelingmentioning

confidence: 99%

Microengineered hydromechanical cochlear model

White

Grosh

2005

Proc. Natl. Acad. Sci. U.S.A.

100

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Micromachined fluid-filled variable impedance waveguides intended to mimic the mechanics of the passive mammalian cochlea have been fabricated and experimentally examined. The structures were microfabricated with dimensions similar to those of the biological system. Experimental tests demonstrate acoustically excited traveling fluid-structure waves with phase accumulations between 1.5 and 3 radians at the location of maximum response. The resulting measured frequency-position mapping function, with similarities to that observed in the cochlea, is presented. Results for both isotropic and orthotropic membranes are reported, demonstrating that the achieved orthotropy ratio of 8:1 in tension is insufficient to produce the sharp filtering observed in animal experiments and many computational models that use higher ratios. It is also shown experimentally that high viscosity fluids must be used to provide sufficient damping to avoid the formation of a nonphysiological standing wave pattern. A mathematical model incorporating a thin-layer viscous, compressible fluid approximation coupled to an orthotropic membrane model is validated against experimental results. The work presented herein is motivated by the possibility of producing microfabricated cochlear-like filters, thus the structure is designed for production in a scalable microfabrication process.acoustic ͉ micro-electro-mechanical systems ͉ sensor ͉ viscosity T he cochlea is the organ in the inner part of the mammalian ear that is responsible for the transduction of acoustic signals into neurological signals. The typical human cochlea operates over a 3-decade frequency band, from 20 Hz to 20 kHz, covers 120 dB of dynamic range, and can distinguish tones that differ by Ͻ0.5% (1). The cochlea is also very small, occupying a volume of Ϸ1 cm 3 . Perhaps most importantly, the cochlea uses a mechanical process to separate audio signals into Ϸ3,500 channels of frequency information. Thus, the cochlea is a sensitive real-time mechanical frequency analyzer.The effectiveness of the cochlea as a time-frequency analyzer motivates our efforts to construct a hydromechanical analog that can be fabricated repeatably and in a batch fashion. Integration of sensing elements with the mechanical structure would result in a combined acoustic sensor͞filter with a unique operating modality. During the design of the mechanical structure, we also learn more about some aspects of the biological cochlea. von Békésy's (2, 3) observation of traveling waves on the basilar membrane (BM) of cadaver cochleae motivated the construction of a number of physical models of the cochlea. The first group of these models involved scaled-up versions of the cochlea. Helle's (4) model is seven times life size and exhibits tonotopic structure in the 25-to 800-Hz band. Chadwick et al. (5) built a 24 times life-size model and clearly show strong standing wave patterns and the resulting discrete resonances. Because of the standing wave nature of their response, a tonotopic map is not demonstrated (5). Lechner'...

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Section: Modelingmentioning

confidence: 99%

Microengineered hydromechanical cochlear model

White

Grosh

2005

Proc. Natl. Acad. Sci. U.S.A.

100

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“…Beltman et al [37] also presented an acoustic Finite Element (FE) for layers based on the LRF model. In this formulation, the velocity and temperature profiles across the thickness of the layer are solved analytically from the LRF equations while the equation for propagation behavior is discretized using a finite element method.…”

Section: (Lrf) Model With a Numerical Solution Tomentioning

confidence: 99%

“…The equation for pressure, describing behavior in propagation direction, can be solved analytically. In contrast, for straight layers of arbitrary shape the equations for pressure have to be solved numerically (for instance with FE [37] or Trefftz [21] method), while the equations describing the temperature and velocity profiles across the layer can be solved analytically. Naturally, obtaining the solution to the full set of equations in these ways requires more computational effort than solving a purely analytical LRF model.…”

Section: (B)(c)(d) Lrf Modelsmentioning

confidence: 99%

“…Note that the propagation constant k t is related to the dimensionless propagation constant Γ, by k t = kΓ. The propagation constant kΓ in the finite element formulation for viscothermal wave propagation in flat layers proposed by Beltman et al [37] can be substituted by solutions for k t to obtain a model for flat layers of arbitrary shape.…”

Section: Pilot Vector and Surface Normal Coincidementioning

confidence: 99%

“…Using separation of variables for arbitrary geometries and boundary conditions leads to the Trefftz method (for an example see [21]). A more general approach based on FE methods, which is suitable for layers of arbitrary shape is presented in [37]. An overview of the literature on viscothermal wave propagation in plain layers is given in references [10,36].…”

Section: Plain Layersmentioning

confidence: 99%

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Viscothermal wave propagation

Nijhof¹

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SummaryIn engineering practice, the simplest, most efficient model that yields the desired level of accuracy is usually the model of choice. This is particulary true if an optimization process is involved, in which case the choice of the underlying models is often a trade-off between efficiency and accuracy. It is therefore important to know not only how efficient a model is, but also how accurate.In this work, the accuracy, efficiency and range of applicability of various (approximate) models for viscothermal wave propagation are investigated in a general setting. Models for viscothermal wave propagation describe the wave behavior of fluids including viscous and thermal effects. Cases where viscothermal effects are significant generally involve small fluid domains, low frequencies, or fluid systems near resonance. Examples of practical applications of these models are, for instance, describing the behavior of in-ear hearing aids, MEMS devices, microphones, inkjet printheads and muffler systems involving acoustic resonators.Amongst the various models for viscothermal wave propagation that are considered, a prominent role is taken by the family of approximate models known as Low Reduced Frequency (or LRF) models. These are the most efficient approximate models available and they have been used extensively to model a wide variety of problems involving viscothermal wave propagation. Nevertheless, LRF models are only available for a limited number of geometries and can become inaccurate under certain conditions. A second family of models that is considered consists of exact solutions to the equations describing viscothermal wave propagation. These models, which are less efficient than the LRF models, provide reference solutions which can be used to determine the accuracy of the LRF models. A drawback of the exact models is that they are only available for a small number of geometries. Therefore a third family of models is considered, which is based on a newly developed Finite Element (or FE) approximation of the equations for viscothermal wave propagation. The main attraction of these FE models is that they can be used to model arbitrary geometries and boundary conditions. A drawback is that obtaining a solution requires much more computing power than needed for the LRF or exact models. The vi numerical stability and convergence properties of the developed FE methods are investigated to ensure that they can yield reference solutions of a desired accuracy for cases where an exact solution is not available.Using these three families of models, a number of parameter studies are carried out that yield detailed information on accuracy of the highly efficient LRF models for a range of geometries and boundary conditions. The gathered data provides a means of estimating the accuracy of simple coupled LRF models a priori.Besides the investigation into the accuracy of LRF models, two engineering applications where viscothermal wave propagation takes a prominent role are described. The first application involves the passive si...

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Implementation and Experimental Validation of a New Viscothermal Acoustic Finite Element for Acousto-Elastic Problems

Cited by 68 publications

References 15 publications

Microengineered hydromechanical cochlear model

Microengineered hydromechanical cochlear model

Viscothermal wave propagation

Viscothermal Wave Propagation Including Acousto-Elastic Interaction, Part I: Theory

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