Simulation On Propagation Characteristics Of Solitary Waves In A One-Dimensional Charged Granular Chain

Granular matter is one of one of the widely existing types of substances in our production and life,and exhibits abundant rich mechanical properties including solid properties,liquid properties and even gas properties.It makes the propagation of solitary waves in discrete nonlinear systems have rich content and important significance.In recent years,more and more scientists began to pay attention to the propagation of nonlinear wave in one-dimensional(1D)granular chain,and studied it through experiment,numerical calculation and theoretical analysis.On the one hand,the study of the propagation characteristics of solitary waves in one-dimensional granular chain is beneficial to the further understanding of the nonlinear interactions between particles.On the other hand,it can provide a theoretical basis for the propagation of solitary waves in multi-dimensional granular systems.Firstly,the nonlinear dynamics model of one-dimensional charged granular chain is established in this paper,and the stable state of the system is obtained by using the difference method(leapfrog algorithm).In addition,the leapfrog algorithm is tested on the basis of energy conservation,and the results show that the numerical method can solve such nonlinear problems well.Finally,based on the one-dimensional charged granular chain model,the propagation characteristics of the solitary waves in the system are studied systematically with the influence of long-range interaction on the propagation of the solitary waves considered,that is,the coulomb force on the propagation of the solitary waves is considered in the numerical simulation.We find that not only single solitary but also multi-solitary wave can be excited in the granular system when the driven frequency varies.The effects of material physical parameters(such as Young’s Modulus Y,particle density ρ,damping coefficient β and charge quantity Q)on the propagation of solitary waves are numerically analyzed.As the existence of damping effect,the amplitude of solitary wave decays exponentially with time,and the general relation between the amplitude of solitary wave and time is given.Moreover,each physical parameter has a certain influence on the amplitude attenuation rate of the solitary wave.Specifically,Young’s Modulus and charge quantity have slightly effect on the amplitude attenuation rate.However,the damping coefficient and the density of particles have significantly effect.