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

Solitary and shock waves in discrete double power-law materials

A novel strongly nonlinear laminar metamaterial supporting new types of solitary and shock waves with impact energy mitigating capabilities is presented. It consists of steel plates with intermittent polymer toroidal rings acting as strongly nonlinear springs with large allowable strain. Their force-displacement relationship is described by the addition of two power-law relationships resulting in a solitary wave speed and width depending on the amplitude. This double nonlinearity allows splitting of an initial impulse into two separate strongly nonlinear solitary wave trains. Solitary and shock waves are observed experimentally and analyzed numerically in an assembly with Teflon o-rings.Comment: 14 pages, 6 figure

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

Pulse propagation in a linear and nonlinear diatomic periodic chain: effects of acoustic frequency band-gap

One-dimensional nonlinear phononic crystals have been assembled from periodic diatomic chains of stainless steel cylinders alternated with Polytetrafluoroethylene spheres. This system allows dramatic changes of behavior (from linear to strongly nonlinear) by application of compressive forces practically without changes of geometry of the system. The relevance of classical acoustic band-gap, characteristic for chain with linear interaction forces and derived from the dispersion relation of the linearized system, on the transformation of single and multiple pulses in linear, nonlinear and strongly nonlinear regimes are investigated with numerical calculations and experiments. The limiting frequencies of the acoustic band-gap for investigated system with given precompression force are within the audible frequency range (20–20,000 Hz) and can be tuned by varying the particle’s material properties, mass and initial compression. In the linear elastic chain the presence of the acoustic band-gap was apparent through fast transformation of incoming pulses within very short distances from the chain entrance. It is interesting that pulses with relatively large amplitude (nonlinear elastic chain) exhibit qualitatively similar behavior indicating relevance of the acoustic band gap also for transformation of nonlinear signals. The effects of an in situ band-gap created by a mean dynamic compression are observed in the strongly nonlinear wave regime

Pulse mitigation by a composite discrete medium

The strongly nonlinear interaction between elements in discrete materials (e.g., grains in granular media) is responsible for their unique wave propagation properties. The paper will present an experimental observation of impulse energy confinement and the resultant disintegration of shock and solitary waves by discrete materials with strongly nonlinear interaction between elements. Experiments and numerical calculations will be presented for alternating ensembles of high-modulus vs orders of magnitude lower-modulus chains of spheres of different masses. The trapped energy is contained within the “softer” portions of the composite chain and is slowly released in the form of weak, separated pulses over an extended period of time. This effect is enhanced by using a specific group assembly and a superimposed force

Propagation of rarefaction pulses in particulate materials with strain-softening behavior

We investigate rarefaction waves in nonlinear periodic systems with a 'softening' power-law relationship between force and displacement to understand the dynamic behavior of this class of materials. A closed form expression describing the shape of the strongly nonlinear rarefaction wave is exact for n = 1/2 and agrees well with the shape and width of the pulses resulting from discrete simulations. A chain of particles under impact was shown to propagate a rarefaction pulse as the leading pulse in initially compressive impulsive loading in the absence of dissipation. Compression pulses generated by impact quickly disintegrated into a leading rarefaction solitary wave followed by an oscillatory train. Such behavior is favorable for metamaterials design of shock absorption layers as well as tunable information transmission lines for scrambling of acoustic information

Experimental evidence of solitary wave interaction in Hertzian chains

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

Observation of two-wave structure in strongly nonlinear dissipative granular chains

In a strongly nonlinear viscous granular chain under conditions of loading that exclude stationary waves (e.g., impact by a single grain) we observe a pulse that consists of two interconnected but distinct parts. One is a leading narrow "primary pulse" with properties similar to a solitary wave in a "sonic vacuum." It arises from strong nonlinearity and discreteness in the absence of dissipation, but now decays due to viscosity. The other is a broad, much more persistent shock-like "secondary pulse" trailing the primary pulse and caused by viscous dissipation. The medium behind the primary pulse is transformed from a "sonic vacuum" to a medium with finite sound speed. When the rapidly decaying primary pulse dies, the secondary pulse continues to propagate in the "sonic vacuum," with an oscillatory front if the viscosity is relatively small, until its eventual (but very slow) disintegration. Beyond a critical viscosity there is no separation of the two pulses, and the dissipation and nonlinearity dominate the shock-like attenuating pulse which now exhibits a nonoscillatory front

Evolution of the Primary Pulse in 1D Granular Crystals Subject to On-Site Perturbations: Analytical Study

Propagation of primary pulse through an un-compressed granular chain subject to external on-site perturbation is studied. Analytical procedure predicting the evolution of the primary pulse is devised for the general form of the on-site perturbation applied on the chain. The validity of the analytical model is confirmed with several specific granular setups such as, chains mounted on the nonlinear elastic foundation, chains perturbed by the dissipative forces as well as randomly perturbed chains. Additional interesting finding made in the present study corresponds to the chains subject to a special type of perturbations including the terms leading to dissipation and those acting as an energy source. It is shown in the study that application of such perturbation may lead to formation of stable stationary shocks acting as attractors for the initially unperturbed, propagating Nesterenko solitary waves. Interestingly enough the developed analytical procedure provides an extremely close estimations for the amplitudes of these stationary shocks as well as predicts zones of their stability. In conclusion we would like to stress that the developed analytical model have demonstrated spectacular correspondence to the results of direct numerical simulations for all the setups considered in the study