Numerical Simulation Of The Locomotion Of A Sphere Rotating And Vibrating In Granular Matter

We are interested by the capability of desert lizard(Phrynocephalus mystaceus)to sink into the sand or surface by vibrating the body.In this paper,we carry out the nu-merical simulation by LIGGGHTS of the locomotion of a sphere,with rotation of the sphere imitating rotaiton of the desert lizard’s body,and vibration of the sphere imitating vibration of the body.For the case of sphere rotating,the sphere almost always rise under given conditions.And with the increase in the friction coefficientμ between the sphere and the bed particles,the rising speed of the sphere increases too.If the sphere rotates on the axis of X or biaxial XZ,it will move in the Y direction.When the rotation speed ω is small,the sphere moves in the direction of Y+,and it moves in the direction of Y-with large ω.In the case of XZ biaxial rotation,the sphere moves in the direction of X-,and the increase in μ and ωwill lead to a larger locomotion speed.Three effects,repelling effect and friction effect and squeezing effect,are proposed to qualitatively explane the locomotion of the sphere in given cases.For the case where the vibration and rotation are compounded,if the moving direction of the vibration and the rotating direction change at the same time,the sphere will rise only or fall only.The specific moving direction is determined by the rotating direction during moving.The friction force plays a key role in the rising/falling of the sphere.With the increase of the rotation amplitude Ω,the rising/falling velocity Uz of the sphere increases at the beginning and then stabilizes.The relationship between Ω and Uz is Uz ∝(1-e-C1|Ω|).With the vibration amplitude A increases,the rising/falling velocity of the sphere increases linearly.With the vibration frequency f increases,the rising velocity increase first and decreases then in the rising case;in the falling case,the falling velocity of the sphere is increasing with f.The hole effect has played an important role in this process.Through the analysis of the results a fitting formula is given,with Ω and A and f as independent variables.The rising/falling velocity Uz of the sphere can be estimated via the fitting formula.