Anomalous Wave Reflection at the Interface of Two Strongly Nonlinear Granular Media

Abstract

Granular materials exhibit a strongly nonlinear behavior affecting the propagation of energy and information. Dynamically self-organized strongly nonlinear solitary waves are the main information carriers in granular chains. We report the first experimental observation of the dramatic change of solitary wave reflectivity from the interface of two granular media triggered by a magnetically induced precompression. It may be appropriate to name this phenomenon the ''acoustic diode'' effect. We explain this effect by the high gradient of particle velocity near the interface. DOI: 10.1103/PhysRevLett.95.158702 PACS numbers: 05.65.+b, 43.25.+y, 45.70.2n, 46.40.Cd Strongly nonlinear granular chains are ''sonic vacuum'' (SV) type systems that support a new type of solitary wave with parameters determined by the interaction force [1][2][3]. These solitary waves are qualitatively different from the well known weakly nonlinear solitary waves of the Korteweg-de Vries equation [4,5] which were first discovered experimentally by Russel [6] in 1834. The concept of a SV was proposed to emphasize the uniqueness of the types of materials that do not support sound waves without initial prestress [3,7]. The unique property of these materials is that a single parameter (initial prestress) is able to tune the response from a linear to a strongly nonlinear regime. One of the main features of strongly nonlinear solitary waves is that the speed is strongly influenced by interrelated potential and kinetic energies [3]. A granular chain with particles interacting according to Hertz law [8] is just one example of strongly nonlinear behavior which can support the new type of solitary wave [3]. Different groups investigated numerically and experimentally the properties of these waves [1,2,9-20] and found a good agreement with the theoretical predictions based upon a long wave approximation. Nonlinear dynamic properties can be extended to other metamaterials including the propagation of electrical or other types of signals. Interesting applications of this new area of wave dynamics have been proposed, e.g., for the creation of nanodroplets [21].Another intriguing property of these materials is the reflection of the solitary waves at the interface of two SV materials [3,7,20,22], from imperfections [11] or from a wall [19]. Based on the former, the novel concept of impulse trapping inside a protecting granular laminar layer has been proposed [23,24].In this Letter we present the first experimental and numerical observation of strongly nonlinear wave interaction with the interface of two SV-type systems resulting in anomalous reflected compression and transmitted rarefaction waves when the magnetically induced prestress is applied.We propose a new method of noncontact precompression based on the magnetic interaction of the first magnetic particle in the chain with a Nd-Fe-B ring magnet [25]. The magnetic force (2.38 N) is practically independent of the motion of the magnetic particle.In experiments we placed a chain of 20 nonmagnetic stain...

Interaction of highly nonlinear solitary waves with linear elastic media

“…Previous work to understand the interaction of solitary waves with linear elastic interfaces has been reported in the literature [15][16][17][18][19]. Job et al investigated the collision of a single solitary wave with elastic media of various hardness (herein referred to as the "wall"), and reported different force profiles originating from the interactions with such walls [15].…”

“…Falcon et al studied the impact of a column of beads on a fixed wall focusing on the bouncing behaviors of the chain [16]. The decomposition of incident solitary waves has been reported under the influence of large-mass granular impurities [17,18] and heterogeneous granular chains [19]. * Corresponding author: daraio@caltech.edu…”

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