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.

[1]  V. Nesterenko,et al.  Observation of a new type of solitary waves in a one-dimensional granular medium , 1985 .

[2]  Adam Sokolow,et al.  Solitary wave trains in granular chains: experiments, theory and simulations , 2007, 0712.0006.

[3]  C. Daraio,et al.  Pulse propagation in a linear and nonlinear diatomic periodic chain: effects of acoustic frequency band-gap , 2009 .

[4]  C Daraio,et al.  Anomalous wave reflection at the interface of two strongly nonlinear granular media. , 2005, Physical review letters.

[5]  V. Nesterenko.  Solitary waves in discrete media with anomalous compressibility and similar to sonic vacuum , 1994 .

[6]  C. Daraio,et al.  Tunability of solitary wave properties in one-dimensional strongly nonlinear phononic crystals. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Mason A Porter,et al.  Dissipative solitary waves in granular crystals. , 2008, Physical review letters.

[8]  V. Nesterenko,et al.  Dynamics of Heterogeneous Materials , 2001 .

[9]  H. C. Corben,et al.  Classical Mechanics (2nd ed.) , 1961 .

[10]  Thomas P. Russell,et al.  Shock Compression of Condensed Matter , 2006 .

[11]  Surajit Sen,et al.  Solitonlike pulses in perturbed and driven Hertzian chains and their possible applications in detecting buried impurities , 1998 .

[12]  Jongbae Hong,et al.  Universal power-law decay of the impulse energy in granular protectors. , 2005, Physical review letters.

[13]  C. Daraio,et al.  Energy trapping and shock disintegration in a composite granular medium. , 2006, Physical review letters.

[14]  C. Daraio,et al.  Strongly nonlinear waves in a chain of Teflon beads. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Bruno Gilles,et al.  On the validity of Hertz contact law for granular material acoustics , 1999 .

[16]  V. Nesterenko,et al.  Propagation of nonlinear compression pulses in granular media , 1984 .

[17]  C Daraio,et al.  Strongly nonlinear wave dynamics in a chain of polymer coated beads. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  M. Porter,et al.  Discrete breathers in one-dimensional diatomic granular crystals. , 2009, Physical review letters.

[19]  I. Goldhirsch,et al.  Friction enhances elasticity in granular solids , 2005, Nature.

[20]  Joseph C. Foster,et al.  Dynamic stress chain formation in a two-dimensional particle bed , 2002 .

[21]  A. Shukla,et al.  Angular dependence of dynamic load transfer due to explosive loading in granular aggregate chains , 1988 .

[22]  Eric Falcon,et al.  Solitary waves in a chain of beads under Hertz contact , 1997 .

[23]  T. Majmudar,et al.  Contact force measurements and stress-induced anisotropy in granular materials , 2005, Nature.

[24]  Adam Sokolow,et al.  How hertzian solitary waves interact with boundaries in a 1D granular medium. , 2005, Physical review letters.

[25]  Mason A Porter,et al.  Highly nonlinear solitary waves in periodic dimer granular chains. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  H. Jaeger,et al.  Structural signature of jamming in granular media , 2005, Nature.

[27]  V. Nesterenko,et al.  The decay of soliton at the contact of two “acoustic vacuums” , 1995 .

[28]  Fernando Fraternali,et al.  Optimal Design of Composite Granular Protectors , 2008, 0802.1451.