Nonlinear Coherent Structures in Granular Crystals

In this work, we study the wave propagation in a recently proposed acoustic structure, the locally resonant granular crystal. This structure is composed of a one-dimensional granular crystal of hollow spherical particles in contact, containing linear resonators. The relevant model is presented and examined through a combination of analytical approximations (based on ODE and nonlinear map analysis) and of numerical results. The generic dynamics of the system involves a degrada...

We study the interaction of highly nonlinear solitary waves in granular crystals, with an adjacent linear elastic medium. We investigate the effects of interface dynamics on the reflection of incident waves and on the formation of primary and secondary reflected waves. Experimental tests are performed to correlate the linear medium geometry, materials, and mass with the formation and propagation of the reflected waves. We compare the experimental results with theoretical anal...

We report the experimental observation of discrete breathers in a one-dimensional diatomic granular crystal composed of compressed elastic beads that interact via Hertzian contact. We first characterize their effective linear spectrum both theoretically and experimentally. We then illustrate theoretically and numerically the modulational instability of the lower edge of the optical band. This leads to the dynamical formation of long-lived breather structures, whose families o...

We computationally investigate the wave propagation characteristics of nanoscopic granular crystals composed of one-dimensionally arrayed gold nanoparticles using molecular dynamics simulation. We examine two basic configurations, i.e. homogeneous lattices and diatomic lattices with mass-mismatch. We discover that homogeneous lattices of gold nanospheres support weakly dissipative and highly localized solitary wave at 300 K, while diatomic lattices have a good tuning ability ...

We use experiments, numerical simulations, and theoretical analysis to investigate the propagation of highly nonlinear solitary waves in periodic arrangements of dimer (two-mass) and trimer (three-mass) cell structures in one-dimensional granular lattices. To vary the composition of the fundamental periodic units in the granular chains, we utilize beads of different materials (stainless steel, bronze, glass, nylon, polytetrafluoroethylene, and rubber). This selection allows u...

We present a gradient-index crystal that offers extreme tunability in terms of manipulating the propagation of elastic waves. For small-amplitude excitations, we achieve control over wave transmission depth into the crystal. We numerically and experimentally demonstrate a boomerang-like motion of wave packet injected into the crystal. For large-amplitude excitations on the same crystal, we invoke nonlinear effects. We numerically and experimentally demonstrate asymmetric wave...

We report the design and testing of a tunable and nonlinear mechanical metamaterial, called locally resonant granular chain. It consists of a one-dimensional array of hollow spherical particles in contact, containing local resonators. The resonant particles are made of an aluminium outer spherical shell and a steel inner mass connected by a polymeric plastic structure acting as a spring. We characterize the linear spectra of the individual particles and of one-dimensional arr...

By applying an out-of-phase actuation at the boundaries of a uniform chain of granular particles, we demonstrate experimentally that time-periodic and spatially localized structures with a nonzero background (so-called dark breathers) emerge for a wide range of parameter values and initial conditions. Importantly, the number of ensuing breathers within the multibreather pattern produced can be "dialed in" by varying the frequency or amplitude of the actuation. The values of t...

There is growing interest in engineering unconventional computing devices that leverage the intrinsic dynamics of physical substrates to perform fast and energy-efficient computations. Granular metamaterials are one such substrate that has emerged as a promising platform for building wave-based information processing devices with the potential to integrate sensing, actuation, and computation. Their high-dimensional and nonlinear dynamics result in nontrivial and sometimes cou...

In the present work, we attempt a brief summary of various areas where nonlinear waves have been emerging in the phenomenology of lattice dynamical systems. These areas include nonlinear optics, atomic physics, mechanical systems, electrical lattices, nonlinear metamaterials, plasma dynamics and granular crystals. We give some of the recent developments in each one of these areas and speculate on some of the potentially interesting directions for future study.