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Jul 2004

Volume 116, Issue 1, pp. 1-603

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The Laplace transform to describe bounded inhomogeneous waves

Nico F. Declercq, Joris Degrieck, and Oswald Leroy

J. Acoust. Soc. Am. Volume 116, Issue 1, pp. 51-60 (2004); (10 pages) | Cited 3 times

Online Publication Date: 01 Jul 2004

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The inhomogeneous waves theory deals with plane waves having complex valued wave vectors and with their superposition to form bounded beams. Since infinite inhomogeneous plane waves cannot be formed experimentally, verifications of the theory have to be performed using bounded inhomogeneous waves. In this paper we clarify how a bounded inhomogeneous wave is described as a superposition of inhomogeneous waves. This is done by applying the Laplace transform. The paper also shows from a theoretical point of view why bounded inhomogeneous waves behave like infinite inhomogeneous waves in numerous experiments. © 2004 Acoustical Society of America.
Show PACS
43.20.Bi Mathematical theory of wave propagation
43.20.El Reflection, refraction, diffraction of acoustic waves
43.35.Pt Surface waves in solids and liquids

Ultrasonic wave propagation in human cancellous bone: Application of Biot theory

Z. E. A. Fellah, J. Y. Chapelon, S. Berger, W. Lauriks, and C. Depollier

J. Acoust. Soc. Am. Volume 116, Issue 1, pp. 61-73 (2004); (13 pages) | Cited 27 times

Online Publication Date: 01 Jul 2004

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Ultrasonic wave propagation in human cancellous bone is considered. Reflection and transmission coefficients are derived for a slab of cancellous bone having an elastic frame using Biot’s theory modified by the model of Johnson et al. [J. Fluid Mech. 176, 379–402 (1987)] for viscous exchange between fluid and structure. Numerical simulations of transmitted waves in the time domain are worked out by varying the modified Biot parameters. The variation is applied to the governing parameters and is about 20%. From this study, we can gain an insight into the sensitivity of each physical parameter used in this theory. Some parameters play an important role in slow-wave wave form, such as the viscous characteristic length Λ and pore fluid bulk modulus Kf. However, other parameters play an important role in the fast-wave wave form, such as solid density ρs and shear modulus N. We also note from these simulations that some parameters such as porosity ϕ, tortuosity α∞, thickness, solid bulk modulus Ks, and skeletal compressibility frame Kb, play an important role simultaneously in both fast and slow wave forms compared to other parameters which act on the wave form of just one of the two waves. The sensitivity of the modified Biot parameters with respect to the transmitted wave depends strongly on the coupling between the solid and fluid phases of the cancellous bone. Experimental results for slow and fast waves transmitted through human cancellous bone samples are given and compared with theoretical predictions. © 2004 Acoustical Society of America.
Show PACS
43.20.Bi Mathematical theory of wave propagation
43.20.Hq Velocity and attenuation of acoustic waves
43.20.Jr Velocity and attenuation of elastic and poroelastic waves
43.80.Cs Acoustical characteristics of biological media: molecular species, cellular level tissues

Analysis and design of conical concentric tube resonators

T. Kar and M. L. Munjal

J. Acoust. Soc. Am. Volume 116, Issue 1, pp. 74-83 (2004); (10 pages) | Cited 5 times

Online Publication Date: 01 Jul 2004

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The concept of perforate impedance and its exploitation for acoustic attenuation through several elements including concentric tube resonators, is common in practice. Variable cross-sectional area ducts are often used for better performance at lower frequencies (like in horns), whereas concentric tube resonators are often used to provide attenuation at relatively higher frequencies. A combination of the two leads to conical concentric-tube resonators. Using a one-dimensional control volume approach, a mathematical model is presented that accounts for waves in an incompressible mean flow in the center tube, wave propagation in the cavity, and an acoustic coupling between the two due to the impedance of the perforate. The matrizant model results have been validated for self consistency. In the sections dealing with discussion and parametric study, the effect of the moving medium has been neglected so as to bring out clearly the physical effect of the variable area ducts. A few notable effects have been found that include an effective length shorter than the geometric length for an inhomogeneous duct. Some useful features like the absence of pass bands are noticed in the transmission loss spectrum. Finally, results of a parametric study are presented for use by the noise control engineers. © 2004 Acoustical Society of America.
Show PACS
43.20.Bi Mathematical theory of wave propagation
43.20.Hq Velocity and attenuation of acoustic waves
43.20.Mv Waveguides, wave propagation in tubes and ducts

Effectiveness of acoustic power dissipation in lossy layers

Daniel Razansky, Pinchas D. Einziger, and Dan R. Adam

J. Acoust. Soc. Am. Volume 116, Issue 1, pp. 84-89 (2004); (6 pages) | Cited 1 time

Online Publication Date: 01 Jul 2004

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The effect of losses in the dissipative object becomes crucial when maximal power absorption of the incident wave is of top priority. In order to assess the phenomenon of acoustic power absorption in finite size dissipative medium, a prototype model of linear pressure waves absorption in dissipative layer is considered. The conditions, parameters and bounds for the optimal (maximal) incident power absorption within the layer have been found analytically and explicitly versus its normalized thickness. These conditions are presented in terms of the basic wave propagation parameters, namely sound velocity and attenuation constant. It is shown that, for thin layers (in terms of acoustic wavelength), the upper bound on the absorptivity tends to the value of 50%, when prescribed resonant dispersion/absorption conditions, characterized by the so-called Kramers–Kronig relations, are met within the layer. For sufficiently thick layers absorption of close to 100% of the incident wave power can be achieved, when specific optimal values are selected for the corresponding real and imaginary parts of dissipative layer wave number. The model may serve as a canonical prototype problem for engineered dissipative materials design and optimization of the sound/ultrasound absorption in lossy targets, e.g., biological tissues. © 2004 Acoustical Society of America.
Show PACS
43.20.El Reflection, refraction, diffraction of acoustic waves
43.35.Bf Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in liquids, liquid crystals, suspensions, and emulsions
43.80.Sh Medical use of ultrasonics for tissue modification (permanent and temporary)
43.55.Ev Sound absorption properties of materials: theory and measurement of sound absorption coefficients; acoustic impedance and admittance

Determining the pulse-echo electromechanical characteristic of a transducer using flat plates and point targets

Thomas L. Szabo, Başak Ülker Karbeyaz, Robin O. Cleveland, and Eric L. Miller

J. Acoust. Soc. Am. Volume 116, Issue 1, pp. 90-96 (2004); (7 pages) | Cited 4 times

Online Publication Date: 01 Jul 2004

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A common technique to determine the electromechanical response of a spherically focusing transducer is to use a reference pulse echo from a flat plate in the focal plane of the transducer. We show that when the pressure focusing gain of the transducer is much greater than unity, the focal plane reflection is a valid approximation of the desired electromechanical response. An alternative calibration target is a point scatterer and we show theoretically and experimentally that this waveform is the double time differential of the flat-plate response. The use of calibration to describe general scatterers through a Born approximation (Jensen, J. A. (1991), J. Acoust. Soc. Am. 89, 182–190) is discussed. © 2004 Acoustical Society of America.
Show PACS
43.20.Fn Scattering of acoustic waves
43.20.Rz Steady-state radiation from sources, impedance, radiation patterns, boundary element methods
43.20.Bi Mathematical theory of wave propagation
43.35.Bf Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in liquids, liquid crystals, suspensions, and emulsions

Spectral estimation for characterization of acoustic aberration

Trond Varslot, Bjørn Angelsen, and Robert C. Waag

J. Acoust. Soc. Am. Volume 116, Issue 1, pp. 97-108 (2004); (12 pages) | Cited 2 times

Online Publication Date: 01 Jul 2004

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Spectral estimation based on acoustic backscatter from a motionless stochastic medium is described for characterization of aberration in ultrasonic imaging. The underlying assumptions for the estimation are: The correlation length of the medium is short compared to the length of the transmitted acoustic pulse, an isoplanatic region of sufficient size exists around the focal point, and the backscatter can be modeled as an ergodic stochastic process. The motivation for this work is ultrasonic imaging with aberration correction. Measurements were performed using a two-dimensional array system with 80×80 transducer elements and an element pitch of 0.6 mm. The f number for the measurements was 1.2 and the center frequency was 3.0 MHz with a 53% bandwidth. Relative phase of aberration was extracted from estimated cross spectra using a robust least-mean-square-error method based on an orthogonal expansion of the phase differences of neighboring wave forms as a function of frequency. Estimates of cross-spectrum phase from measurements of random scattering through a tissue-mimicking aberrator have confidence bands approximately ±5° wide. Both phase and magnitude are in good agreement with a reference characterization obtained from a point scatterer. © 2004 Acoustical Society of America.
Show PACS
43.20.Fn Scattering of acoustic waves
43.80.Vj Acoustical medical instrumentation and measurement techniques
43.60.Cg Statistical properties of signals and noise

Ultrasonic attenuation due to grain boundary scattering in copper and copper-aluminum

X.-G. Zhang, W. A. Simpson, Jr., J. M. Vitek, D. J. Barnard, L. J. Tweed, and J. Foley

J. Acoust. Soc. Am. Volume 116, Issue 1, pp. 109-116 (2004); (8 pages) | Cited 3 times

Online Publication Date: 01 Jul 2004

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Ultrasonic attenuation in copper and copper-aluminum samples is measured as a function of frequency and average grain size. At low frequencies the attenuation scales quadratically with the frequency and linearly with average grain size. In addition, there is a large difference in attenuation between powder metallurgy samples and cast-and-wrought samples, although their qualitative behaviors are similar both in terms of frequency dependence and grain size dependence. Such difference and the discrepancy with the existing theory may point to mechanisms of scattering by grain boundaries that are not included in the current theoretical model. © 2004 Acoustical Society of America.
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43.20.Hq Velocity and attenuation of acoustic waves

Quantitative analysis of the vibration modes in a finite set of coupled spheres

Anne-Christine Hladky-Hennion, Arnaud Devos, and Michel de Billy

J. Acoust. Soc. Am. Volume 116, Issue 1, pp. 117-124 (2004); (8 pages) | Cited 5 times

Online Publication Date: 01 Jul 2004

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This paper deals with the propagation of waves along a one-dimensional chain made up of welded spheres. First, a theoretical analysis allows the vibration modes of the chain to be quantitatively described. It has been validated by a comparison between numerical results, using the finite element method and experimental results, restricted to sets of two or three coupled spheres. It is numerically and experimentally verified that the peaks associated with the Rayleigh modes broaden out as the mode number increases and that the passband structure is strongly influenced by the characteristics of the welding between the cells of the periodic structure. The interest of such an approach is then illustrated by the examination of an inverse problem, in which the analytical model is used to deduce the characteristics of the welding. © 2004 Acoustical Society of America.
Show PACS
43.20.Ks Standing waves, resonance, normal modes

On the feasibility of elastic wave visualization within polymeric solids using magnetic resonance elastography

Anthony J. Romano, Joseph A. Bucaro, Brian H. Houston, Jennifer L. Kugel, Phillip J. Rossman, Roger C. Grimm, and Richard L. Ehman

J. Acoust. Soc. Am. Volume 116, Issue 1, pp. 125-132 (2004); (8 pages)

Online Publication Date: 01 Jul 2004

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In this paper, the feasibility of extending previously described magnetic resonance elastography (MRE) dynamic displacement (and associated elasticity) measurement techniques, currently used successfully in tissue, to solid materials which have much higher shear rigidity and much lower nuclear spin densities, is considered. Based on these considerations, the MRE technique is modified in a straightforward manner and used to directly visualize shear wave displacements within two polymeric materials, one of which is relatively stiff. © 2004 Acoustical Society of America.
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43.20.Ye Measurement methods and instrumentation
43.58.-e Acoustical measurements and instrumentation

Transient modeling of Lamb waves generated in viscoelastic materials by surface bonded piezoelectric transducers

Laurent Duquenne, Emmanuel Moulin, Jamal Assaad, and Sébastien Grondel

J. Acoust. Soc. Am. Volume 116, Issue 1, pp. 133-141 (2004); (9 pages) | Cited 6 times

Online Publication Date: 01 Jul 2004

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In order to help optimize health monitoring systems based on Lamb wave propagation, a hybrid finite element–normal mode expansion modeling technique has been developed. This technique allows one to predict the Lamb waves generated in a structure as a function of the transducer parameters (size, location, material, etc.). The present paper shows how this hybrid modeling, initially valid for nonlossy materials and harmonic excitation, can be extended to lossy (viscoelastic) materials and transient excitation. For this purpose, simplifying assumptions have been proposed and validity conditions have been established and verified. Moreover, numerical results concerning Lamb wave generation have been successfully compared to experimental ones. As a result, the method has proved to be pertinent and practically unrestrictive. © 2004 Acoustical Society of America.
Show PACS
43.20.Ks Standing waves, resonance, normal modes
43.35.Mr Acoustics of viscoelastic materials
43.40.Le Techniques for nondestructive evaluation and monitoring, acoustic emission

Time domain holography: Forward projection of simulated and measured sound pressure fields

Ombeline de La Rochefoucauld, Manuel Melon, and Alexandre Garcia

J. Acoust. Soc. Am. Volume 116, Issue 1, pp. 142-153 (2004); (12 pages) | Cited 8 times

Online Publication Date: 01 Jul 2004

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In this article, the fundamental principles of forward projecting time domain acoustic pressure fields are summarized. Four different numerical approaches are presented and compared both with simulated and measured signals. The approaches differ in their definition domain: Frequency/time and space/wave vector domains. The simulated source is a planar baffled piston excited with a Gaussian pulsed velocity. The pressure radiated by two different real sources has been measured: The first source is made up of two baffled loudspeakers (a Gaussian white noise can be radiated by a third loudspeaker). The second one is a baffled aluminum plate excited by a short impact at its center. The influence of parameters such as the sound source radius, the array size, the number of microphones and the propagation distance is studied. Finally, results concerning the optimization of the sampling of the sound field are presented. © 2004 Acoustical Society of America.
Show PACS
43.20.Px Transient radiation and scattering
43.60.Pt Signal processing techniques for acoustic inverse problems
43.60.Sx Acoustic holography

Mindlin plate theory for damage detection: Source solutions

L. R. F. Rose and C. H. Wang

J. Acoust. Soc. Am. Volume 116, Issue 1, pp. 154-171 (2004); (18 pages) | Cited 5 times

Online Publication Date: 01 Jul 2004

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A consideration of the relevant length scales and time scales suggests that Mindlin plate theory provides a judicious model for damage detection. A systematic investigation of this theory is presented that emphasizes its mixed vector-scalar character and analogies with 3D elasticity. These analogies lead to the use of Helmholtz potentials, and to compact statements of the reciprocal theorem and the representation theorem. The plate response for a point moment is derived using a direct source specification, rather than an indirect specification through boundary conditions. Solutions are presented for combinations of such point moments (doublets) that represent, respectively, a center of bending, a center of twist and a center of inplane twist. The flexural response due to finite sources, such as piezoelectric actuators, can be modeled by distributions of centers of bending. Detailed results are presented for a circular, and for a narrow rectangular actuator. The far-field radiation pattern for an array of equally spaced actuators parallel to a straight boundary is derived. The solutions presented for the point moment and the point force constitute the components of a dyadic Green’s function which is required, along with its spatial derivatives, for a representation of plate-wave scattering by flexural inhomogeneities. © 2004 Acoustical Society of America.
Show PACS
43.20.Rz Steady-state radiation from sources, impedance, radiation patterns, boundary element methods
43.35.Cg Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in solids; elastic constants
43.40.Dx Vibrations of membranes and plates

A partial field decomposition algorithm and its examples for near-field acoustic holography

Kyoung-Uk Nam and Yang-Hann Kim

J. Acoust. Soc. Am. Volume 116, Issue 1, pp. 172-185 (2004); (14 pages) | Cited 6 times

Online Publication Date: 01 Jul 2004

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In this paper we introduce a practical algorithm that can accurately implement partial field decomposition for near-field acoustic holography (NAH). Unlike other methods, the algorithm does not require sensors near sources because it uses calculations rather than measured signals in order to decompose a holography image into the images of individual sources. Therefore it makes holography measurement easier than other methods. The algorithm is composed of five steps: measurement of pressure on a hologram plane, estimation of pressure on a source plane, selection of maximum pressure, estimation of the sound field from one source, and estimation of the remaining sound field. In this paper we also report two experiments that verify and demonstrate the algorithm. In one experiment six speakers are operated independently. The other is a vortex shedding experiment. Their results show that the decomposition method is useful for identifying hidden sources and estimating the power of individual sources. © 2004 Acoustical Society of America.
Show PACS
43.20.Rz Steady-state radiation from sources, impedance, radiation patterns, boundary element methods
43.60.Cg Statistical properties of signals and noise
43.60.Sx Acoustic holography
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