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

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