Study On The Dynamics Of An Inelastic Bouncing Ball

Granular materials are ubiquitous in our daily lives; however, people do notclearly understand the law of motion about it. For example, we still cannottheoretically interpret the Brazil Nut Effect, Sandwich-like segregation, granularpatterns in vibrated granular materials bed, while all of these phenomenons oftenappear in the fields like agriculture, mine industry, pharmacy and so on, so theresearch of granular materials turns out to be very significant.In rare granular gas system, it would loss its kinetic energy due to inelasticcollisions among particles. For avoiding clustering, energy must be input into thesystem from outside, which is usually realized through boundary heating. Whateverthe force between particles and vibrator or the force between the particles of raregranular gas and container boundary, both cases can be approximately considered asbouncing ball model. Although the granular system is much more complex than this,the research of bouncing ball would be conducive to understand the granular system.In my thesis, on the basis of introducing some peculiar phenomenons of granularmaterials and commonly used simulation method, I would put the importance on theresearch of bouncing ball model. Different approaches are adopted. I also use themaximal Lyapunov Exponent and0-1test to detect the motion of inelastic bouncingball and find its very complex. It exhibits nonlinear phenomenon of period doublingbifurcation and chaos, etc. We also discuss the effect of air dumping, collisioncoefficient on the motion of bouncing ball, we find if the air dumping existing or thelarger collision coefficient, the ball will easily evolve into chaos. The research ofbouncing ball model show the complex character of granular materials from one sideand it also enlightens the research of granular segregation on the granular bed.