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May 2012

Volume 131, Issue 5, pp. EL355-4232

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Number and location of zero-group-velocity modes

Eduardo Kausel

J. Acoust. Soc. Am. Volume 131, Issue 5, pp. 3601-3610 (2012); (10 pages) | Cited 1 time

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The frequency-wavenumber spectra of laminated media often exhibit anomalous modes with descending branches whose group velocity is negative, and these terminate at a minimum point at which the group velocity transitions from negative to positive. These minima are associated with resonant conditions in the medium, which have been clearly observed in experiments and in the nondestructive testing of laminated plates. Starting from first principles, this paper provides a theoretical analysis on the number and location of such zero-group-velocity (ZGV) modes for horizontally layered media bounded by any arbitrary combination of external boundaries. It is found that these ZGV points are few in number and show up mostly in low-order modes which are characterized by a negative second derivative at the cutoff frequencies, a condition that can readily be tested. It is also shown that the effective number of ZGVs is small even when the ratio of the dilatational and shear wave velocity is a rational number and there exist coincidences in cutoff frequencies, a condition that at first would suggest that the number of ZGVs is infinite. Finally, it is shown that the number of ZGVs decreases with the Poisson’s ratio.
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43.20.Bi Mathematical theory of wave propagation
43.40.Dx Vibrations of membranes and plates

A unified optical theorem for scalar and vectorial wave fields

Kees Wapenaar and Huub Douma

J. Acoust. Soc. Am. Volume 131, Issue 5, pp. 3611-3626 (2012); (16 pages)

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The generalized optical theorem is an integral relation for the angle-dependent scattering amplitude of an inhomogeneous scattering object embedded in a homogeneous background. It has been derived separately for several scalar and vectorial wave phenomena. Here a unified optical theorem is derived that encompasses the separate versions for scalar and vectorial waves. Moreover, this unified theorem also holds for scattering by anisotropic elastic and piezoelectric scatterers as well as bianisotropic (non-reciprocal) EM scatterers.
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43.20.Fn Scattering of acoustic waves
43.20.Gp Reflection, refraction, diffraction, interference, and scattering of elastic and poroelastic waves

Acoustic particle manipulation in a 40 kHz quarter-wavelength standing wave with an air boundary

Giuliana Trippa, Stéphanie Trine, Yiannis Ventikos, and Constantin-C. Coussios

J. Acoust. Soc. Am. Volume 131, Issue 5, pp. 3627-3637 (2012); (11 pages)

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An implementation of a quarter-wavelength standing wave separator that exploits an air drum to achieve the pressure node is presented and characterized experimentally. The air drum configuration was implemented and tested in a set-up with a 40 kHz transducer immersed in a water tank with the quarter-wavelength gap being approximately 9 mm wide. Injection of suspensions of 5 μm and 45 μm diameter polystyrene particles at flow rates of 30 ml/h and 60 ml/h was studied and particle deflection towards the pressure node at the air drum surface was observed for a range of acoustic pressures. Computational results on single particle trajectories show good agreement with the experimental findings for the 45 μm particles, but not for the 5 μm particles. These were considered to behave as aggregates of higher effective dimension, due to their much higher number density relative to the 45 μm particles in the suspensions used. The set-up developed in this study includes a robust method for achieving a pressure node in a quarter-wavelength system and can represent the first step toward the development of an alternative separator configuration in respect to small channel MHz range operated systems for the manipulation of particles streams.
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43.20.Ks Standing waves, resonance, normal modes
43.25.Gf Standing waves; resonance
43.35.Ty Other physical effects of sound

A hybrid finite element approach to modeling sound radiation from circular and rectangular ducts

Wenbo Duan and Ray Kirby

J. Acoust. Soc. Am. Volume 131, Issue 5, pp. 3638-3649 (2012); (12 pages)

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A numerical model based on a hybrid finite element method is developed that seeks to join sound pressure fields in interior and exterior regions. The hybrid method is applied to the analysis of sound radiation from open pipes, or ducts, and uses mode matching to couple a finite element discretization of the region surrounding the open end of the duct to wave based modal expansions for adjoining interior and exterior regions. The hybrid method facilitates the analysis of ducts of arbitrary but uniform cross section as well the study of conical flanges and here a modal expansion based on spherical harmonics is applied. Predictions are benchmarked against analytic solutions for the limiting cases of flanged and unflanged circular ducts and excellent agreement between the two methods is observed. Predictions are also presented for flanged and unflanged rectangular ducts, and because the hybrid method retains the sparse banded and symmetric matrices of the traditional finite element method, it is shown that predictions can be obtained within an acceptable time frame even for a three dimensional problem.
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43.20.Mv Waveguides, wave propagation in tubes and ducts
43.20.El Reflection, refraction, diffraction of acoustic waves
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