Longitudinal and transverse elastic waves in 1D granular materials modeled as micromorphic continua

Misra, Anil; Nejadsadeghi, Nima

doi:10.1016/j.wavemoti.2019.05.005

Cited by 33 publications

(22 citation statements)

References 32 publications

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“…At last, it is strongly suggested that the modified nano-TiO 2 doped with Fe 3+ may be further fused with other granular metamaterial components in concrete, to explore potential enhancement in both mechanical and chemical properties in further studies on the basis of the dispersive behavior of granular materials [37,38].…”

Section: Resultsmentioning

confidence: 99%

Preparation and Evaluation of Exhaust-Purifying Cement Concrete Employing Titanium Dioxide

Huang

Zhang

et al. 2019

Materials

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To address the increasing air pollution caused by vehicle exhaust, environment-friendly pavement materials that possesses exhaust-purifying properties were prepared using common cement concrete and porous cement concrete as the base of photocatalyst nano-titanium dioxide (TiO2), respectively. Firstly, Fe3+-doped TiO2 powder was prepared by applying planetary high-energy ball milling in order to improve the efficiency of the semiconductor photocatalyst for degrading vehicle exhausts. Two nano-TiO2, namely the original and modified nanomaterials, were adopted to produce the photocatalytic cement concretes subsequently. The physicochemical properties of the modified powder, as well as the mechanical and photocatalytic properties of TiO2-modified concrete, were characterized using a suite of complementary techniques, including X-ray diffraction (XRD), scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), compressive strength and degradation efficiency tests. The results show that the ball milling method not only successfully doped Fe3+ into catalysts but also caused significant changes in: (1) decreased particle sizes, (2) more amorphous morphology, (3) decreased percentage of the most thermodynamically stable crystal facet, and (4) increased percentage of other high gas sensing crystal facets. Both the original and modified nano-TiO2 can improve the concrete strength while the strengthening effect of modified nanomaterials is superior. It is pronounced that the photocatalytic property of the modified nano-TiO2 is much better than that of the original nano particles, and the degradation rate of porous concrete is also better than common concrete when exposed to the same photocatalyst content. In a comprehensive consideration of both mechanical performance and degradation efficiency, the recommended optimum dosage of TiO2 is 3% to 4% for exhaust-purifying concrete.

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Section: Resultsmentioning

confidence: 99%

Preparation and Evaluation of Exhaust-Purifying Cement Concrete Employing Titanium Dioxide

Huang

Zhang

et al. 2019

Materials

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“…We use the small amplitude and the long wave length limit approximation, as previously reported [25][26][27], then we obtain the equation of motion of an arbitrary bead i by multifarious mathematical derivation as follows where N indicates the numbers of the beads which interact with bead i, i.e., the distances between bead i and these N beads are less than the bead diameter.…”

Section: Equation Of Motionmentioning

confidence: 99%

“…0 is its equilibrium value of d and d = -R d 2 ij 0 0 . We have assumed that the initial prestress (d ij 0 ) is much less than the bead radius (R), while the displacements of s s s , , ix iy iz are much less than the initial prestress [25][26][27]…”

Section: Introductionmentioning

confidence: 99%

Localization of the small amplitude wave in three dimensional granular material

et al. 2020

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A general small amplitude wave equations are proposed for the granular material. It is shown that the wave is localized in a certain region which is in agreement with that found in both the analytical and the simulation results. The localization region depends on the wave frequency and the parameters of the granular material such as the bead radius, the magnitude of the initial prestress, the Young's modulus and the bead mass. Several examples are given which indicate that the attenuation rate of the wave depend on the permutation of the bead. It also depends on whether the wave is longitudinal or tangential.

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“…Including disorder, e.g., adding inclusions with different properties or size, will lead to enhanced absorption in typical frequency ranges/bands, relative to the basis material. Thus, there is a need to study the effects of disorder individually, and hence, the focus of this article will only be on mass disorder, for which a 1D granular chain was chosen so that the P-wave mode is isolated from the shear or rotational mode [ 23 , 24 ]. A mechanical wave propagating through this simplified model 1D granular medium is bound to suffer from multiple scattering [ 25 , 26 , 27 , 28 ].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Model for Energy Propagation in Disordered Granular Chains

2021

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Energy 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.

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Longitudinal and transverse elastic waves in 1D granular materials modeled as micromorphic continua

Cited by 33 publications

References 32 publications

Preparation and Evaluation of Exhaust-Purifying Cement Concrete Employing Titanium Dioxide

Preparation and Evaluation of Exhaust-Purifying Cement Concrete Employing Titanium Dioxide

Localization of the small amplitude wave in three dimensional granular material

Stochastic Model for Energy Propagation in Disordered Granular Chains

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