Articles | Volume 24, issue 3
Nonlin. Processes Geophys., 24, 435–454, 2017

Special issue: Waves in media with pre-existing or emerging inhomogeneities...

Nonlin. Processes Geophys., 24, 435–454, 2017

Research article 09 Aug 2017

Research article | 09 Aug 2017

Effect of disorder on bulk sound wave speed: a multiscale spectral analysis

Rohit Kumar Shrivastava and Stefan Luding Rohit Kumar Shrivastava and Stefan Luding
  • Multiscale Mechanics (MSM), MESA+, Engineering Technology (ET), P.O. Box 217, 7500 AE Enschede, the Netherlands

Abstract. Disorder of size (polydispersity) and mass of discrete elements or particles in randomly structured media (e.g., granular matter such as soil) has numerous effects on the materials' sound propagation characteristics. The influence of disorder on energy and momentum transport, the sound wave speed and its low-pass frequency-filtering characteristics is the subject of this study. The goal is understanding the connection between the particle-microscale disorder and dynamics and the system-macroscale wave propagation, which can be applied to nondestructive testing, seismic exploration of buried objects (oil, mineral, etc.) or to study the internal structure of the Earth. To isolate the longitudinal P-wave mode from shear and rotational modes, a one-dimensional system of equally sized elements or particles is used to study the effect of mass disorder alone via (direct and/or ensemble averaged) real time signals, signals in Fourier space, energy and dispersion curves. 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 granular chain. Energies associated with the eigenmodes can be used to obtain better quality dispersion relations for disordered chains; these dispersion relations confirm the decrease in pass frequency and wave speed with increasing disorder acting opposite to the wave acceleration close to the source.

Short summary
The article aids the understanding of the propagation of vibration through complex media (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 such as oil or mineral exploration, designing materials for shock protection or energy-trapping. The conclusion of the article also mentions some of the ongoing as well as future work related to the research.