45 research outputs found
Wave propagation of spectral energy content in a granular chain
Get PDFA 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
Towards Stochastic and Deterministic Modeling of Mechanical Waves in Disordered Media
Get PDF{What?} 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 materials’ sound propagation characteristics. The influence of disorder on energy and momentum transport during vibration propagation (mechanical/sound wave), the sound wave speed and its low-pass frequency-filtering characteristics is the subject of this study. {Why?} 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. {How?} The mechanical wave/vibration propagating through granular media exhibits a specific signature in time; a coherent pulse or wavefront arrives first with multiply scattered waves (coda) arriving later. The coherent pulse is of low frequency nature and micro-structure independent i.e. it depends only on the bulk properties of the disordered granular sample, the sound wave velocity and hence, bulk and shear moduli. The coda or the multiply scattered waves are of high frequency nature and are micro-structure dependent. Numerical and stochastic techniques for 1-D, 2-D discrete element systems and experiments with 1-D photoelastic particles constituting a granular chain have been employed to isolate and study different modes of the propagating waves (namely, P and S waves), disorder dependent dispersion relations, sound wave velocity and diffusive transport of spectral energy. {Results} 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. Averaging over energies associated with the eigenmodes can be used to obtain better quality dispersion relations and can be formulated in a way to give a Master Equation of energy in terms of wavenumber or frequency which identifies the switching and cross-talk of energy between different frequency bands; 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. Also, it is observed that 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
Effect of disorder on bulk sound wave speed: a multiscale spectral analysis
Get PDFDisorder 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
Wave propagation of spectral energy content in a granular chain
No full textA 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
Backscattering Spectral Analysis for 1-D Granular Chain. IV International Conference on Particle-based Methods: Fundamentals and Applications -PARTICLES 2015
Get PDFBayesian modelling for determining material properties
Get PDFSound wave propagation in materials has been used extensively for nondestructive testing of materials, studying the internal structure of Earth or for oil/gas/mineral exploration. The propagation characteristics have been exploited and studied using signal processing tools for analyzing the material properties or for examining the sub-surface features. The signal processing tools can be innovated in accordance with the characteristics of the sound wave propagation in the media for improvement of the signal to noise ratio. A synthetic model of one dimensional chain of spherical particles is used to generate space time responses when impulse moves along the chain, it gives information about the longitudinal wave propagation (P-wave). The space time responses obtained from the synthetic model are used by the Bayesian inference technique to obtain the properties of the media (particle size/mass distribution of the chain). Finally, the importance of Bayesian inference technique as a signal processing tool is discussed upon
Dwell motion from spatial linkages
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Stochastic model for energy propagation in disordered granular chains
Get PDFEnergy transfer is one of the essentials of mechanical wave propagation (along with momentum transport). Here, it is studied in disordered one-dimensional model systems mimicking force-chains in real systems. The pre-stressed random masses (other types of disorder lead to qualitatively similar behavior) interact through (linearized) Hertzian repulsive forces, which allows solving the deterministic problem analytically. The main goal, a simpler, faster stochastic model for energy propagation, is presented in the second part, after the basic equations are re-visited and the phenomenology of pulse propagation in disordered granular chains is reviewed. First, the propagation of energy in space is studied. With increasing disorder (quantified by the standard deviation of the random mass distribution), the attenuation of pulsed signals increases, transiting from ballistic propagation (in ordered systems) towards diffusive-like characteristics, due to energy localization at the source. Second, the evolution of energy in time by transfer across wavenumbers is examined, using the standing wave initial conditions of all wavenumbers. Again, the decay of energy (both the rate and amount) increases with disorder, as well as with the wavenumber. The dispersive ballistic transport in ordered systems transits to low-pass filtering, due to disorder, where localization of energy occurs at the lowest masses in the chain. Instead of dealing with the too many degrees of freedom or only with the lowest of all the many eigenmodes of the system, we propose a stochastic master equation approach with reduced complexity, where all frequencies/energies are grouped into bands. The mean field stochastic model, the matrix of energy-transfer probabilities between bands, is calibrated from the deterministic analytical solutions by ensemble averaging various band-to-band transfer situations for short times, as well as considering the basis energy levels (decaying with the wavenumber increasing) that are not transferred. Finally, the propagation of energy in the wavenumber space at transient times validates the stochastic model, suggesting applications in wave analysis for non-destructive testing, underground resource exploration, etc
