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Research Papers

# Incoherent Waves in Fluid-Saturated Sintered Granular Systems: Scattering Phenomena

[+] Author and Article Information
Ibrahim Güven

Institute of Mechanics,
Ruhr-University Bochum,
Universitätsstr. 150,
Bochum D-44 801, Germany;
Multi-Scale Mechanics/MESA+, ET,
University of Twente,
Drienerlolaan 5,
Enschede 7522 NB, The Netherlands
e-mail: ibrahim.gueven@gmx.de

Stefan Luding

Multi-Scale Mechanics/MESA+, ET,
University of Twente,
Drienerlolaan 5,
Enschede 7522 NB, The Netherlands
e-mail: s.luding@utwente.nl

Holger Steeb

Institute of Applied Mechanics (CE),
University of Stuttgart,
Pfaffenwaldring 7,
Stuttgart D-70 569, Germany;
Stuttgart Research Center for Simulation Technology,
Pfaffenwaldring 5a,
Stuttgart D-70569, Germany
e-mail: steeb@ist.uni-stuttgart.de

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 28, 2016; final manuscript received August 5, 2017; published online October 4, 2017. Assoc. Editor: Matthew Brake.

J. Vib. Acoust 140(1), 011018 (Oct 04, 2017) (7 pages) Paper No: VIB-16-1611; doi: 10.1115/1.4037701 History: Received December 28, 2016; Revised August 05, 2017

## Abstract

The incoherent transport of ultrasound waves in water-saturated sintered glass bead packings is experimentally investigated. The spectral energy density of scattered high-frequency waves is explained by a diffusion wave equation. Immersion broadband transducers with central frequencies of 1 MHz are positioned at a distance of 73 mm to the porous sample. The diffusion coefficient and quality factor are predicted from a diffusion approximation of the time-dependent intensity curve to the ensemble-averaged measurement data. From the diffusion coefficient, we deduce a mean-free path for scattering events at $l*=0.87±0.03$ mm close to the range of particle diameters of the samples ($1.0 mm). Results are in good agreement with observations from Jia (2004, “Codalike Multiple Scattering of Elastic Waves in Dense Granular Media,” Phys. Rev. Lett., 93(15), p. 154303) observed for nonsintered and consolidated bead packings ($0.6 mm). The low-quality factor $Q=190±10$ indicates a high amount of intrinsic damping of the scattered waves although water was used as saturating and coupling fluid.

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## Figures

Fig. 1

Experimental setup according to the transmission method, where the square wave pulser of Olympus (model 5077PR) is used as pre-amplifier

Fig. 2

Simplified sketch of the measuring cell with length specifications used for ultrasound measurements

Fig. 3

Received time signal in raw state

Fig. 4

Probability distribution of equivalent particle diameter (solid line) and corresponding cumulative curve (dashed line) determined from XRCT scans after sintering

Fig. 5

Investigated subset from XRCT scan with 14,053 particles (voxel resolution 16 μm) used for the determination of the equivalent particle diameter distribution shown in Fig. 4. The bounding box indicates the entire scanned region. Thecuboid-shaped subset has the dimensions of 1940×1965×2200 voxel3 (31.04×31.44×35.20 mm3).

Fig. 6

Corresponding power spectra of the raw signal

Fig. 7

Received time signal after high-pass filtering. The cut-off frequency is chosen at 0.7 MHz.

Fig. 8

Corresponding power spectra of the high-pass-filtered high-frequency incoherent part. The vertical dotted line indicates the selected cutoff frequency at 0.7 MHz.

Fig. 9

Comparison of normalized intensities obtained from ultrasound measurements and the related diffusion model. The measured averaged intensity curve is determined from ten independent experimental measurements. The piezoelectric acoustic transmitter is excited with a ten-cycle-sinus burst at 0.9 MHz. The diffusion coefficient and the effective quality factor are determined fitting the diffusion model to the measured averaged intensity profile at D=0.83±0.03 m2/s and Q=190±10.

Fig. 10

Diffusion model for different parameters of the diffusion coefficient and quality factor. The best fit for the normalized intensity curve from the ultrasound measurement, shown in Fig. 9, is represented by the solid line. The remaining intensity curves refer to different D and Q values with deviations of ±20% from the best-fit intensity curve.

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