Nonlinear Coherent Structures in Granular Crystals

Breathing solitons consist of a fast beating wave within a compact envelope of stable shape and velocity. They manifest themselves in a variety of contexts such as plasmas, optical fibers and cold atoms, but have remained elusive when energy conservation is broken. Here, we report on the observation of breathing, unidirectional, arbitrarily long-lived solitons in non-reciprocal, non-conservative active metamaterials. Combining precision desktop experiments, numerical simulati...

A model is presented for the characterization of dissipative effects on highly nonlinear waves in one-dimensional dry granular media. The model includes three terms: Hertzian, viscoelastic, and a term proportional to the square of the relative velocity of particles. The model outcomes are confronted with different experiments where the granular system is subject to several constraints for different materials. Excellent qualitative and quantitative agreement between theory and...

We study the vibrational spectra of one-dimensional statically compressed granular crystals (arrays of elastic particles in contact) containing defects. We focus on the prototypical settings of one or two spherical defects (particles of smaller radii) interspersed in a chain of larger uniform spherical particles. We measure the near-linear frequency spectrum within the spatial vicinity of the defects, and identify the frequencies of the localized defect modes. We compare the ...

We present numerical simulations of acoustic wave propagation in confined granular systems consisting of particles interacting with the three-dimensional Hertz-Mindlin force law. The response to a short mechanical excitation on one side of the system is found to be a propagating coherent wavefront followed by random oscillations made of multiply scattered waves. We find that the coherent wavefront is insensitive to details of the packing: force chains do not play an important...

We investigate the tunable vibration filtering properties of one-dimensional diatomic granular crystals composed of arrays of stainless steel spheres and cylinders interacting via Hertzian contact. The arrays consist of periodically repeated three-particle unit cells (steel-cylinder-sphere) in which the length of the cylinder is varied systematically. We apply static compression to linearize the dynamic response of the crystals and characterize their linear frequency spectrum...

We investigate the propagation and scattering of highly nonlinear waves in disordered granular chains composed of diatomic (two-mass) units of spheres that interact via Hertzian contact. Using ideas from statistical mechanics, we consider each diatomic unit to be a "spin", so that a granular chain can be viewed as a spin chain composed of units that are each oriented in one of two possible ways. Experiments and numerical simulations both reveal the existence of two different ...

The interaction of a solitary wave front with an interface formed by two strongly-nonlinear non-cohesive granular lattices displays rich behaviour, characterized by the breakdown of continuum equations of motion in the vicinity of the interface. By treating the solitary wave as a quasiparticle with an effective mass, we construct an intuitive (energy and linear momentum conserving) discrete model to predict the amplitudes of the transmitted solitary waves generated when an in...

Granular materials demonstrate a strongly nonlinear behavior influencing the wave propagation in the medium. We report the first experimental observation of impulse energy confinement and the resultant disintegration of shock and solitary waves. The medium consists of alternating ensambles of high-modulus vs orders of magnitude lower modulus chains of different masses. The trapped energy is contained within the "softer" portions of the composite chain and is slowly released i...

We present here a detailed numerical study of the dynamical behaviour of `soft' uncompressed grains in a granular chain where the grains interact via the intrinsically nonlinear Hertz force. It is well known that such a chain supports the formation of solitary waves (SWs). Here, however, the system response to the material properties of the grains and boundaries is further explored. In particular, we examine the details of the transition of the system from a SW phase to an eq...

Solitary waves (SWs) are generated in monoatomic (homogeneous) lightly contacting spherical granules by an applied input force of any time-variation and intensity. We consider finite duration shock loads and focus on the transition regime that leads to the formation of SWs. Based on geometrical and material properties of the granules and the properties of the input shock, we provide explicit analytic expressions to calculate the peak value of the compressive contact force at ...