Highly nonlinear solitary waves in heterogeneous periodic granular media

Abstract

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 us to tailor the response of the system based on the masses, Poisson ratios, and elastic moduli of the components. For example, we examine dimer configurations with two types of heavy particles, two types of light particles, and alternating light and heavy particles. Employing a model with Hertzian interactions between adjacent beads, we find very good agreement between experiments and numerical simulations. We find equally good agreement between these results and a theoretical analysis of the model in the long-wavelength regime that we derive for heterogeneous environments (dimer chains) and general bead interactions. Our analysis encompasses previously-studied examples as special cases and also provides key insights on the influence of heterogeneous lattices on the properties (width and propagation speed) of the nonlinear wave solutions of this system.

Highly nonlinear solitary waves in chains of ellipsoidal particles

“…The particles were cut along their major diameter direction and carved to accommodate wires. The final assembly of the sensor particles was achieved following a procedure similar to the one described in [15,16] for spherical particles. All the sensors were precalibrated to obtain the relation between voltage output from the oscilloscope and the corresponding force on the particle assuming conservation of linear momentum.…”

“…Following previous investigations [9,13,15,16], we modeled a chain composed of N uniform ellipsoidal particles as a onedimensional system, where the ellipsoidal particles are treated as point masses connected by nonlinear springs according to the elliptical contact law in Eq. (1).…”

“…One-dimensional chains of spherical particles have been extensively studied in the literature and are known to present highly nonlinear dynamic properties [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. When the chains are uncompressed, they support the formation and propagation of compact solitary waves that have been predicted theoretically [1], and observed numerically [1,6] and experimentally [4,5].…”

“…These systems derive their unique characteristics from a double nonlinearity in the particles interaction: a powerlaw-type contact potential in compression and a zero tensile strength. One of the fundamental characteristics of such systems is their high degree of tunability in terms of control over the traveling pulse width, speed, and the number of separated pulses that can be generated in the chain [2,3,9,[13][14][15][16]. The tunability of these systems is evident when the addition of static precompression on the chain of particles enables the system to change from the highly nonlinear, to the weakly nonlinear, to the linear dynamic regime [2,3,5,13].…”

“…Changing the type and duration of the initial excitation applied to the system, it is possible to generate a single or train of pulses with variable amplitudes [2,14]. Changing the particle diameters, the particle material properties, and/or their periodicity, it is also possible to change the solitary waves' amplitude and traveling speed [9,13,15,16]. This ability to control the wave properties in such chains has been proposed for a variety of practical engineering applications; for example, it could be employed for shock absorbing materials [7,12,19,21], vibration damping [20], sound scramblers [9,10], and sound focusing [22].…”