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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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doi:10.5194/npg-2016-83
© Author(s) 2017. This work is distributed
under the Creative Commons Attribution 3.0 License.
Research article
11 Jan 2017
Review status
This discussion paper is under review for the journal Nonlinear Processes in Geophysics (NPG).
Effect of Disorder on Bulk SoundWave Speed : A Multiscale Spectral Analysis
Rohit Kumar Shrivastava and Stefan Luding Multiscale Mechanics (MSM), MESA+, Faculty of Engineering Technology (CTW), P.O. Box 217, 7500 AE Enschede, Netherlands
Abstract. Disorder of size (polydispersity) and mass of discrete elements/particles in randomly structured media (e.g. granular matter like soil) has numerous effects on the materials' sound propagation characteristics [Mouraille and Luding, Ultrasonics, 48, 498–505 (2008); Lawney and Luding, Acta Mechanica, 225, 2385–2407 (2014)]. The influence of disorder on the sound wave speed and its low pass frequency filtering characteristics is the subject of this study. Goal is understanding the connection between the particle-micro-scale disorder and dynamics and the system-macro-scale wave propagation which can be applied to non-destructive testing, seismic exploration of buried objects (oil, mineral, etc.) or to study the internal structure of earth. To isolate the longitudinal P-wave mode from shear and rotational modes, a one-dimensional system of elements/particles is used to study the effect of mass disorder alone via ensemble averaged real time signals, signals in Fourier space and dispersion curves. Increase in polydispersity can decrease the sound wave speed because of a decrease in the number of contacts between particles [Mouraille and Luding, Ultrasonics, 48, 498–505 (2008)]. Also, increase in mass disorder (where disorder has been defined such that it is independent of the shape of the probability distribution of masses) decreases the sound wave speed along a particular granular chain. Energies associated with the eigenmodes are constant, independent of time and have been used to derive dispersion relations for disordered chains, these dispersion relations show a decrease in cut-off frequency and thus wave speed with increasing disorder.

Citation: Shrivastava, R. K. and Luding, S.: Effect of Disorder on Bulk SoundWave Speed : A Multiscale Spectral Analysis, Nonlin. Processes Geophys. Discuss., doi:10.5194/npg-2016-83, in review, 2017.
Rohit Kumar Shrivastava and Stefan Luding
Rohit Kumar Shrivastava and Stefan Luding
Rohit Kumar Shrivastava and Stefan Luding

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Short summary
The article aids in understanding propagation of vibration through a complex media (for e.g. soil). It presents various techniques to better interpret signals (recorded vibrations). The mathematical work done in the article can be utilized for various engineering applications like oil/mineral exploration, designing materials for shock protection or energy trapping applications. The conclusion section of the article also mentions some of the ongoing as well as future work related to the research.
The article aids in understanding propagation of vibration through a complex media (for e.g....
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