Time-of-flight of solitary waves in dry and wet chains of beads: experimental results and theoretical models (original) (raw)
Related papers
Journal of the Mechanics and Physics of Solids, 2014
Elastic solitary waves resulting from Hertzian contact in one-dimensional (1-D) granular chains have demonstrated promising properties for wave tailoring such as amplitudedependent wave speed and acoustic band gap zones. However, as load increases, plasticity or other material nonlinearities significantly affect the contact behavior between particles and hence alter the elastic solitary wave formation. This restricts the possible exploitation of solitary wave properties to relatively low load levels (up to a few hundred Newtons). In this work, a method, which we term preconditioning, based on contact pre-yielding is implemented to increase the contact force elastic limit of metallic beads in contact and consequently enhance the ability of 1-D granular chains to sustain high-amplitude elastic solitary waves. Theoretical analyses of single particle deformation and of wave propagation in a 1-D chain under different preconditioning levels are presented, while a complementary experimental setup was developed to demonstrate such behavior in practice. The experimental results show that 1-D granular chains with preconditioned beads can sustain high amplitude (up to several kN peak force) solitary waves. The solitary wave speed is affected by both the wave amplitude and the preconditioning level, while the wave spatial wavelength is still close to 5 times the preconditioned bead size. Comparison between the theoretical and experimental results shows that the current theory can capture the effect of preconditioning level on the solitary wave speed.
Characterization of wave propagation in elastic and elastoplastic granular chains
Physical Review E, 2014
For short duration impulse loadings, elastic granular chains are known to support solitary waves, while elastoplastic chains have recently been shown to exhibit two force decay regimes [Pal, Awasthi, and Geubelle, Granular Matter 15, 747 (2013).]. In this work, the dynamics of monodisperse elastic and elastoplastic granular chains under a wide range of loading conditions is studied, and two distinct response regimes are identified in each of them. In elastic chains, a short loading duration leads to a single solitary wave propagating down the chain, while a long loading duration leads to the formation of a train of solitary waves. A simple model is developed to predict the peak force and wave velocity for any loading duration and amplitude. In elastoplastic chains, wave trains form even for short loading times due to a mechanism distinct from that in elastic chains. A model based on energy balance predicts the decay rate and transition point between the two decay regimes. For long loading durations, loading and unloading waves propagate along the chain, and a model is developed to predict the contact force and particle velocity.
Highly nonlinear solitary waves in chains of cylindrical particles
Granular Matter, 2011
We study the dynamic response of uniform granular chains composed of short cylindrical particles excited by an impulse. The particles in the chains are arranged with their axes orthogonal to the chain's axis, and the particles maintain a constant relative orientation angle. We study the formation and propagation of solitary waves in the chains varying the orientation angle (α) between particles, and show tunability of the stress transfer as a function of α. We use the general Hertzian contact theory to model the interaction between particles. We compare experimental findings with theoretical predictions based on the long wavelength approximation, and with numerical predictions based on a one-dimensional discrete particle model, and on a three-dimensional finite element approach, finding good agreement.
Solitary wave trains in granular chains: experiments, theory and simulations
Granular Matter, 2007
The features of solitary waves observed in horizontal monodisperse chain of barely touching beads not only depend on geometrical and material properties of the beads but also on the initial perturbation provided at the edge of the chain. An impact of a large striker on a monodisperse chain, and similarly a sharp decrease of bead radius in a stepped chain, generates a solitary wave train containing many single solitary waves ordered by decreasing amplitudes. We find, by simple analytical arguments, that the unloading of compression force at the chain edge has a nearly exponential decrease. The characteristic time is mainly a function involving the grains' masses and the striker mass. Numerical calculations and experiments corroborate these findings.
Solitary waves in the granular chain
Physics Reports, 2008
Solitary waves are lumps of energy. We consider the study of dynamical solitary waves, meaning cases where the energy lumps are moving, as opposed to topological solitary waves where the lumps may be static. Solitary waves have been studied in some form or the other for nearly 450 years. Subsequently, there have been many authoritative works on solitary waves. Nevertheless, some of the most recent studies reveal that these peculiar objects are far more complex than what we might have given them credit for. In this review, we introduce the physics of solitary waves in alignments of elastic beads, such as glass beads or stainless steel beads. We show that any impulse propagates as a new kind of highly interactive solitary wave through such an alignment and that the existence of these waves seems to present a need to reexamine the very definition of the concept of equilibrium. We further discuss the possibility of exploiting nonlinear properties of granular alignments to develop exciting technological applications.
Delayed scattering of solitary waves from interfaces in a granular container
Physical Review E, 2006
In granular media, the characterization of the behavior of solitary waves around interfaces is of importance in order to look for more applications of these systems. We study the behavior of solitary waves at both interfaces of a symmetric granular container, a class of systems that has received recent attention because it posses the feature of energy trapping. Hertzian contact is assumed. We have found that the scattering process is elastic at one interface, while at the other interface it is observed that the transmitted solitary wave has stopped its movement during a time that gets longer when the ratio between masses at the interfaces increases. The origin of this effect can be traced back to the phenomenon of gaps opening, recently observed experimentally. PACS numbers: 46.40.Cd; 45.70.-n; 47.20.Ky
Crossing of identical solitary waves in a chain of elastic beads
Physical Review E, 2000
We consider a chain of elastic beads subjected to vanishingly weak loading conditions, i.e., the beads are barely in contact. The grains repel upon contact via the Hertz-type potential, Vϰ␦ n , nϾ2, where ␦у0, ␦ being the grain-grain overlap. Our dynamical simulations build on several earlier studies by Nesterenko, Coste, and Sen and co-workers that have shown that an impulse propagates as a solitary wave of fixed spatial extent ͑dependent only upon n͒ through a chain of Hertzian beads and demonstrate, to our knowledge for the first time, that colliding solitary waves in the chain spawn a well-defined hierarchy of multiple secondary solitary waves, which is ϳ 0.5% of the energy of the original solitary waves. Our findings have interesting parallels with earlier observations by Rosenau and colleagues ͓P.
Experimental evidence of solitary wave interaction in Hertzian chains
Physical Review E, 2011
We study experimentally the interaction between two solitary waves that approach one to another in a linear chain of spheres interacting via the Hertz potential. When these counter propagating waves collide, they cross each other and a phase shift respect to the noninteracting waves is introduced, as a result of the nonlinear interaction potential. This observation is well reproduced by our numerical simulations and it is shown to be independent of viscoelastic dissipation at the beads contact. In addition, when the collision of equal amplitude and synchronized counter propagating waves takes place, we observe that two secondary solitary waves emerge from the interacting region. The amplitude of secondary solitary waves is proportional to the amplitude of incident waves. However, secondary solitary waves are stronger when the collision occurs at the middle contact in chains with even number of beads. Although numerical simulations correctly predict the existence of these waves, experiments show that their respective amplitude are significantly larger than predicted. We attribute this discrepancy to the rolling friction at the beads contacts during solitary wave propagation. PACS numbers: 43.25.+y 45.70.-n
Physical Review E, 2019
A granular chain of elastic spheres via Hertzian contact incorporates a classical nonlinear force model describing dynamical elastic solitary wave propagation. In this paper, the multiple solitary waves and their dynamic behaviors and stability in such a system are considered. An approximate KdV equation with the standard form is derived under the long-wavelength approximation and small deformation. The closed-form analytical single-and multiple-soliton solutions are obtained. The construction of the multiple-soliton solutions is analyzed by using the functional analysis. It is found that the multiple-soliton solution can be excited by the single-soliton solutions. This result is confirmed by the numerical analysis. Based on the soliton solutions of the KdV equation, the analytic solutions of multiple dark solitary waves are obtained from the original dynamic equation of the granular chain in the long-wavelength approximation. The stability of the single and multiple dark solitary wave solutions are numerically analyzed by using both split-step Fourier transform method and Runge-Kutta method. The results show that the single dark solitary wave solution is stable, and the multiple dark solitary waves are unstable.