On the Vibrotransportation and Vibroseparation : Part I. On the Stability for the Periodic Motion of the Jumping Granular Solid

Abstract

Although theoretical analysis and experiments on this problem have been attempted by others, the stability analysis for the jumping granular solid has not been carried out. In this paper an exact solution for the periodic motion of the jumping granular solid is derived, and its stable regions are determined. The following conclusions can be drawn from this paper. (1) When the coefficient of restitution R&nedot;0, the stability boundaries K is given by [numerical formula] (2) When R=0 and the relative acceleration of the granular solid just after an impact y₀>0, K is given by [numerical formula] (3) When R=0 and y₀<0, K is given in the table, in which K=bω²/(gcosα), b : amplitude of the track surface. ω : angular frequency. g : acceleration of gravity. α : inclination of the track surface. n : 1, 2, 3, …….