Solitary Waves Propagating In A One-dimensional Damping Granular Chain

Granular matter can be seen everywhere around us,itself has a very rich physical properties.The granular system belongs to the macro system and is also a complex system.In recent years,research on granular systems has become a new field.Granular matter involves not only solid granular but also liquid granular and gas granular,which have become an important technological science in daily life.Since 1984,Nesterenko first discovered solitary waves in the granular chain and has already been confirmed.This kind of solitary wave is different from sonic wave,and it has many different properties.More and more researchers are interested in the nature of this solitary wave,and have done a lot of research in this area.In this paper,a one-dimensional damping granular chain is used as a model to study the solitary wave in the granular chain through numerical simulation.The numerical results shows that the solitary wave propagation is different from the undamped case when the damping effect is considered.As time goes by,the amplitude of the solitary wave decays exponentially as the solitary wave propagates.Meanwhile,the velocity of solitary wave also decayed with the increase of time.This result shows that for one-dimensional granular chains,the damping force has a great influence on the propagation of solitary waves,and the damping coefficient ? is an important parameter.In the one-dimensional damping granular chain,the influence of other parameters on the propagation of solitary waves,such as the particle radius R,Young's modulus Y,and Poisson's ratio ?,was also studied.For material selection,solitary waves in the model granular chain under different materials were studied.When the material is found to be different,solitary wave propagation is also different.For the theoretical analysis of solitary waves in a one-dimensional damping granular chain,a damped Kd V equation is obtained from the long-wave approximation and small-amplitude approximation theory by use the reductive perturbation method.It was found that the damped Kd V equation can be used to describe the propagation of solitary waves in one-dimensional damping granular chain.We give an analytical solution of the damped Kd V equation and compare it with the numerical solution,the results shows that the two solutions are in agreement.Finally,the granular chain of the model is extended and expanded,changed to one-dimensional charged and damping granular chain,and its characteristics are preliminary studied by numerical simulation.