Stress Wave Anisotropy in Centered Square Highly Nonlinear Granular Systems

Highly ordered, close packed granular systems present a nonlinear dynamic behavior stemming from the Hertzian contact interaction between particles. We investigated the propagation of elastic stress waves in an uncompressed, centered square array of spherical and cylindrical particles. We show, via experiments and numerical simulations, that systematic variations of the mass and stiffness ratios of the spherical and cylindrical particles lead to large variations in the characteristics of the propagating stress wave fronts traveling through the system. The ability to control the stress wave front properties in these granular systems may allow for the development of new wave-tailoring materials including systems capable of redirecting impact energy

Strongly nonlinear wave dynamics in a chain of polymer coated beads

Strongly nonlinear phononic crystals were assembled from a chain of Parylene-C coated steel spheres in a polytetrafluoroethylene holder. This system exhibits strongly nonlinear properties and extends the range of materials supporting sonic-vacuum-type behavior. The combination of a high density core and a soft (low elastic modulus) coating ensures a relatively low velocity of wave propagation. The bead contact interaction caused by the deformation of the Parylene coating can be described by classical nonlinear elastic Hertz theory with an effective value of the elastic modulus equal to 15 GPa for the contact interaction. Strongly nonlinear solitary waves excited by impacts were investigated experimentally and compared to chains composed of uniform steel beads. Fracture of the polymer coating was detected under relatively large pulse amplitude

Strongly Nonlinear Waves in 3D Phononic Crystals

Three dimensional phononic crystal ("sonic vacuum" without prestress) was assembled from 137 vertical cavities arranged in hexagonal pattern in Silicone matrix filled with stainless steel spheres. This system has unique strongly nonlinear properties with respect to wave propagation inherited from nonlinear Hertz type elastic contact interaction. Trains of strongly nonlinear solitary waves excited by short duration impact were investigated. Solitary wave with speed below sound speed in the air and reflection from the boundary of two "sonic vacuums" were detected

Influence of Controlled Viscous Dissipation on the Propagation of Strongly Nonlinear Waves in Stainless Steel Based Phononic Crystals

Strongly nonlinear phononic crystals were assembled from stainless steel spheres. Single solitary waves and splitting of an initial pulse into a train of solitary waves were investigated in different viscous media using motor oil and non-aqueous glycerol to introduce a controlled viscous dissipation. Experimental results indicate that the presence of a viscous fluid dramatically altered the splitting of the initial pulse into a train of solitary waves. Numerical simulations qualitatively describe the observed phenomena only when a dissipative term based on the relative velocity between particles is introduced.Comment: 4 pages, 3 figures, conference pape

Nonlinear phononic crystals based on chains of disks alternating with toroidal structures

We study experimentally the acoustic response of a load-bearing, phononic crystal composed of alternating steel disks, and polytetrafluoroethylene o-rings under precompression. The crystal allows for axial, rocking, and shear-polarized wavemodes when excited by a broad-band signal applied off-axis. Finite element analysis is employed to determine the system’s wave modes. The nonlinear interaction between disks and o-rings supports a dynamic response that is tunable with variations in static precompression, leading to controllable frequency shifts in a large band gap. A modal analysis reveals that four of the six principal wave modes are susceptible to external precompression while two modes are not

Multiscale mass-spring models of carbon nanotube foams

This article is concerned with the mechanical properties of dense, vertically aligned CNT foams subject to one-dimensional compressive loading. We develop a discrete model directly inspired by the micromechanical response reported experimentally for CNT foams, where infinitesimal portions of the tubes are represented by collections of uniform bi-stable springs. Under cyclic loading, the given model predicts an initial elastic deformation, a non-homogeneous buckling regime, and a densification response, accompanied by a hysteretic unloading path. We compute the dynamic dissipation of such a model through an analytic approach. The continuum limit of the microscopic spring chain defines a mesoscopic dissipative element (micro-meso transition) which represents a finite portion of the foam thickness. An upper-scale model formed by a chain of non-uniform mesoscopic springs is employed to describe the entire CNT foam. A numerical approximation illustrates the main features of the proposed multiscale approach. Available experimental results on the compressive response of CNT foams are fitted with excellent agreement

Strongly nonlinear waves in a chain of Teflon beads

One dimensional "sonic vacuum" type phononic crystals were assembled from a chain of Teflon spheres with different diameters in a Teflon holder. It was demonstrated for the first time that this polymer-based "sonic vacuum", with exceptionally low elastic modulus of particles, supports propagation of strongly nonlinear solitary waves with a very low speed.Comment: 33 pages, 6 figure

Highly nonlinear pulse splitting and recombination in a two-dimensional granular network

The propagation of highly nonlinear signals in a branched two-dimensional granular system was investigated experimentally and numerically for a system composed of chains of spherical beads of different materials. The system studied consists of a double Y-shaped guide in which high- and low-modulus/mass chains of spheres are arranged in various geometries. We observed the transformation of a single or a train of solitary pulses crossing the interface between branches. We report fast splitting of the initial pulse, rapid chaotization of the signal and impulse redirection and bending. Pulse and energy trapping was also observed in the branches. Numerical analysis based on Hertzian interaction between the particles and the side walls of the guide was found in agreement with the experimental data, except for nonsymmetric arrangements of particles excited by a large mass striker

Dark Breathers in Granular Crystals

We present a study of the existence, stability and bifurcation structure of families of dark breathers in a one-dimensional uniform chain of spherical beads under static load. A defocus- ing nonlinear Schrodinger equation (NLS) is derived for frequencies that are close to the edge of the phonon band and is used to construct targeted initial conditions for numerical computations. Salient features of the system include the existence of large amplitude solutions that bifurcate with the small amplitude solutions described by the NLS equation, and the presence of a nonlinear instability that, to the best of the authors knowledge, has not been observed in classical Fermi- Pasta-Ulam lattices. Finally, it is also demonstrated that these dark breathers can be detected in a physically realistic way by merely actuating the ends of an initially at rest chain of beads and inducing destructive interference between their signals

Strongly Nonlinear Waves in Polymer Based Phononic Crystals

One dimensional "sonic vacuum"-type phononic crystals were assembled from chains of polytetrafluoroethylene (PTFE) beads and Parylene coated spheres with different diameters. It was demonstrated for the first time that these polymer-based granular system, with exceptionally low elastic modulus of particles, support the propagation of strongly nonlinear solitary waves with a very low speed. They can be described using classical nonlinear Hertz law despite the viscoelastic nature of the polymers and the high strain rate deformation of the contact area. Trains of strongly nonlinear solitary waves excited by an impact were investigated experimentally and were found to be in reasonable agreement with numerical calculations. Tunability of the signal shape and velocity was achieved through a non-contact magnetically induced precompression of the chains. This applied prestress allowed an increase of up to two times the solitary waves speed and significant delayed the signal splitting. Anomalous reflection at the interface of two "sonic vacua"-type systems was reported