Effect Of Contact Duration On Period-Doubling Bifurcations In Vibrated Granular System

Granular matter generally refers to a discrete system composed of solids with a size greater than 1 ?m,which is widely used in industrial production and has important research value.Granular matter will exhibit nonlinear characteristics under external vibration,for example,when periodic vibration is applied in the vertical direction,as vibrating acceleration changes,the impact strength of the vibrated granular on the bottom of the container will in turn appear to be period-doubling,period-quadrupling,chaos,period-tripling,period-sextupling,etc.This phenomenon can be described by a completely inelastic bouncing ball model.Previous studies only considered the wall friction and air resistance during flight,and no detailed study was conducted on the collision process of granular and the bottom of the container.Therefore,in this dissertation,an experimental study on the period-doubling bifurcation process in the vibrated particle system is carried out,and a theoretical study on how the contact duration affects the period-doubling bifurcation process is carried out.First of all,this dissertation starts from the bouncing ball model and introduces the principle and process of the bouncing ball double period movement.Through experiment,the impact contact duration generated by the collision between the particles and the bottom of the container is in the range of 3 to 13 ms.As the value of the normalized vibration acceleration ? increases,there will be a period-doubling bifurcation phenomenon.At the same time,according to the characteristics of the pulse in the experiment,the impact contact duration is carefully divided to obtain the collision contact duration and the adhesion time.It is found that the collision contact duration also changes with the change of the ?,there will be a period-doubling bifurcation phenomenon.At the same time,the landing phase and exit phase corresponding to each impact pulse are obtained,which are in good agreement with the theoretical phase,and the bifurcation diagrams of landing speed and flight time are statistically organized.Then,based on the bouncing ball model,this dissertation theoretically analyzes how the contact duration affects the period-doubling bifurcation process.By adding a constant collision contact duration to the original theoretical model,the calculation shows that the cluster region will be widened after considering the collision contact duration.Although the bifurcation point obtained by this model is different from the bifurcation point in the experiment.The overall sport characteristics of the obtained bouncing ball are relatively in good agreement with the experiment.Finally,on the basis of the above model,this dissertation also considers the effect of drag on the movement of the particles.Since the drag on the particles during flight can be regarded as a constant friction,this dissertation improves the above model.The results show that the deviation between the theoretical value and the experimental value calculated by the new model will be significantly reduced,especially the cluster region will be further widened and overlap with the chaotic region in the experiment.