Authors: Gerasymov O., Spivak A.
Year: 2012
Issue: 14
Pages: 217-223
Abstract
We perform the linearized equations governing the impulse propagation along a 1D weakly nonlinear inhomogeneous granular chain of identical beads. It has been sown that the rigorous solution which satisfy considered problem in every point (including boundaries) can be choose in form of linear combination of farmer basis which consist on Bessel function an integer order and valid in the internal points only. Obtained results thought to be useful practically for the more adequate parameterization of impulse transport in low dimensional granular chains.
Tags: dynamic systems; energy/impulse transport; granular materials; Hertzian contact; nonlinear chain
Bibliography
- Bhatnagar P.L. Nonlinear waves in one dimensional dispersive systems.-Oxford: Clarendon, 1979.-250p.
- Jackson E.A. Perspectives of nonlinear dynamics.-Cambridge, 1990.-350p.
- Nesterenko V. Dynamics of Heterogeneous materials.-New York: Springer, 2001.-350p.
- Coste C., Falcon E., Fauve S. Stationary states in vertical cradle excited from the bottom // Phys. Rev. E-1997.-Vol.56.- P.6104.
- Sen S., Hong J., Bang J., Avalos E., Doney R. Soliton-like waves in low-dimensional granular systems //Phys. Rep.-2008.-N462, P.21-66.
- E.Somfai, J-N.Roux, T.Snoeijer, M.van Hecke, W.van Saarlos. Dispersive waves in 1D granular chain //Phys. Rev. E-2005.-Vol.72.-P.021301.
- Герасимов О.І., Вандевалле Н., Співак А.Я., Худинцев М.М., Люмє Г., Дорболло С., Клименков О.А. Стаціонарні стани у 1D системі непружних частинок //Укр.фіз.журн. – 2008.- Т.53, № 11. – С.1129-1137.
- Герасимов О.І. Щодо двох точних розв’язків задачі про транспорт імпульсу в неоднорідному гранульованому ланцюжку //Доповіді НАН України. – 2012 (прийнято до друку).
- Landau L.D. Theory of elasticity, 3rd ed.- Heinemann: Butterworth, 1986.-200p.
- Pinney E. Ordinary Difference-differential equations.-Berkley and Los Angeles: University of California Press, 1955.-500p.