Abstract
A mechanical wave is propagation of vibration with transfer of energy and momentum. Understanding the spectral energy characteristics of a propagating wave through disordered granular media can assist in understanding the overall properties of wave propagation through inhomogeneous materials like soil. The study of these properties is aimed at modeling wave propagation for oil, mineral or gas exploration (seismic prospecting) or non-destructive testing of the internal structure of solids. The focus is on the total energy content of a pulse propagating through an idealized one-dimensional discrete particle system like a mass disordered granular chain, which allows understanding the energy attenuation due to disorder since it isolates the longitudinal P-wave from shear or rotational modes. It is observed from the signal that stronger disorder leads to faster attenuation of the signal. An ordered granular chain exhibits ballistic propagation of energy whereas, a disordered granular chain exhibits more diffusive like propagation, which eventually becomes localized at long time periods. For obtaining mean-field macroscopic/continuum properties, ensemble averaging has been used, however, such an ensemble averaged spectral energy response does not resolve multiple scattering, leading to loss of information, indicating the need for a different framework for micro-macro averaging.
Highlights
Disorder in granular materials can manifest in many ways from grain level to system level
All may have an effect on the mechanical wave transmission through the granular material in it’s own unique way
There is a need to study the effects of disorder individually and the focus in this article will only be on mass disorder, for which 1D granular chain has been chosen so that the P-wave mode is isolated from shear or rotational modes
Summary
Disorder in granular materials (like soil) can manifest in many ways (contact disorder, geometrical disorder, asphericity, layering, etc.) from grain level to system level. All may have an effect on the mechanical wave transmission through the granular material in it’s own unique way (for instance, contact disorder due to tiny polydispersity can reduce the mechanical wave speed [9]). Knowing this effect can aid us in numerous ways for subsurface exploration or for non-destructive testing. There is a need to study the effects of disorder individually and the focus in this article will only be on mass disorder, for which 1D granular chain has been chosen so that the P-wave mode is isolated from shear or rotational modes. A mechanical wave propagating through this 1D granular chain is bound to suffer from multiple scattering. All the more reason to study energy content and spectral energy response of the propagating wave
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