Discrete Hertzian chains and solitons

We consider elastic grains which repel upon contact according to the Hertz potential V=aδn,n>2, where δ is the overlap between adjacent grains and report numerical and analytical studies for the case of a 1-D chain of spherical grains to show that an impulse initiated at an end of a chain of Hertzian grains in contact, eventually propagates as a soliton for all n>2.

[1]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[2]  J. Banavar,et al.  Computer Simulation of Liquids , 1988 .

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

[4]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[5]  Sound propagation in impure granular columns. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  POWER LAWS IN NONLINEAR GRANULAR CHAIN UNDER GRAVITY , 1998, cond-mat/9812137.

[7]  D. A. Spence,et al.  Self similar solutions to adhesive contact problems with incremental loading , 1968, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[8]  B. M. Fulk.  MATH , 1992 .

[9]  Sen,et al.  Nonlinear Dynamics in Granular Columns. , 1995, Physical review letters.

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

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