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In the present work, we numerically and experimentally investigate the propagation of nonlinear waves in a hexagonally packed granular channel. Specifically, we assemble a simple 1-2-1 granular chain, which triggers not only normal but also tangential interactions of particles up on a striker impact. We experimentally measure the transmission of nonlinear waves propagating along the channel direction using an embedded piezoelectric sensor particle. For numerical simulations, we introduce a discrete element model that accounts for both elastic and damping effects in axial and rotational directions. As a result, we find that the wave propagation in this 1-2-1 hexagonal architecture is governed strongly by the rotational dynamics of particles. We also verify that the effect of rotational damping is crucial for the accurate description of the particle’s dynamics. The findings in this study hints the significance of particles’ rotational dynamics when stress waves propagate along hexagonally packed particle channels even in highly ordered 2D/3D granular architectures. [ABSTRACT FROM AUTHOR]

We report the numerical and experimental study of elastic Wannier-Stark ladders and Bloch oscillations in a tunable one-dimensional granular chain consisting of cylindrical particles. The Wannier-Stark ladders are obtained by tuning the contact angles to introduce a gradient in the contact stiffness along the granular chain. These ladders manifest as resonant modes localized in the space. When excited at the corresponding resonant frequencies, we demonstrate the existence of time-resolved Bloch oscillations. The direct velocity measurements using laser Doppler vibrometry agree well with the numerical simulation results. We also show the possibility of further tailoring these Bloch oscillations by numerical simulations. Such tunable systems could be useful for applications involving the spatial localization of elastic energy. [ABSTRACT FROM AUTHOR]

We assemble granular chains composed of spheres of uniform diameter in different curved configurations. We study the properties of highly nonlinear solitary waves traveling in the curved channels as a function of the curve angle and of the radius of curvature, using experiments and numerical simulations. We observe that solitary waves propagate robustly even under drastic deflection, such as $$90^{\circ }$$ and $$180^{\circ }$$ turns. When the solitary waves encounter a sharp turn with a radius of curvature as small as one spherical particle's diameter, we report the formation of secondary solitary waves resulting from the interaction with the guiding rail. We compare experimental results with numerical simulations based on a discrete element model that accounts for nonlinear and dissipative interactions between particles. This study demonstrates that granular chains are efficient wave-guides, even in complex geometrical configurations. Moreover, the findings in this study suggest that solitary waves could be used as novel information and/or energy carriers. [ABSTRACT FROM AUTHOR]

Abstract: We investigate the reflection of highly nonlinear solitary waves in one-dimensional granular crystals interacting with large plates. We observe significant changes in the reflected waves’ properties in terms of wave amplitude and time of flight in association with the intrinsic inelasticity of large plates, which are governed by the plate thickness and the size of the granular constituents. We also study the effects of fixed plate boundaries in the formation of reflected waves, and find the existence of a critical distance, within which the interaction between the granular chain and plate is strongly modified. We explain the effects of intrinsic inelasticity and of boundaries in the large plates by using plate theory and the contact mechanics between a plate and a spherical striker. We find that experimental results are in excellent agreement with the analytical predictions and numerical simulations based on the combined discrete element and spectral element models. The findings in this study can be useful for the nondestructive evaluation of plate structures using granular crystals, which can improve the resolution of in-situ, portable measurement instruments leveraging high acoustic energy and sensitivity of solitary waves. [Copyright &y& Elsevier]

We study the wave propagation in a curved chain of spherical particles constrained by elastic guides under the axial impact of a falling mass. We characterize the force transmission properties of the chain by varying the striker's mass and the chain's curvature. Experimental tests demonstrate amplitude-dependent attenuation of compressive waves propagating through the curved chain. In particular, we observe that the curved systems present an improved transmission of small dynamic disturbances relative to that of strong excitations, resulting from the close interplay between the granular particles and the softer elastic medium. We also find that the transmission of the compressive waves through the chains is dependent on the initial curvature imposed to the system. Numerical simulations, based on an approach that combines discrete element and finite element methods, corroborate the experimental results. The findings suggest that hybrid structures composed of granular particles and linear elastic media can be employed as new passive acoustic filtering materials that selectively transmit or mitigate excitations in a desired range of pressure amplitudes. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we present a nondestructive evaluation technique based on the propagation of highly nonlinear solitary waves (HNSWs) to monitor the hydration of cement. HNSWs are mechanical waves that can form and travel in highly nonlinear systems, such as one-dimensional chains of contacting spherical particles (i.e., granular crystals). In the present study, we use a granular crystal-based actuator/sensor to observe the solitary waves propagating to and from the mechanical interface between the transducer and a fresh gypsum cement sample. We hypothesize that the reflected HNSWs traveling along the crystal-based transducer are affected by the hydration process of the cement, and we assess the elastic modulus of the specimen in the localized region of the granular crystal contact. To verify the experimental results, we perform numerical simulations based on a simplified finite element model. The elastic properties of the cement specimen measured by the granular crystal transducer are compared with the compressive strength and the elastic modulus measurements obtained from destructive tests, conducted according to the ASTM C109. We observe good agreement between experiments and numerical simulations. [Copyright &y& Elsevier]