Memory in random bouncing ball dynamics

Abstract

The bouncing of an inelastic ball on a vibrating plate is a popular model used in various fields, from granular gases to nanometer-sized mechanical contacts. For random plate motion, so far, the model has been studied using Poincaré maps in which the excitation by the plate at successive bounces is assumed to be a discrete Markovian (memoryless) process. Here, we investigate numerically the behaviour of the model for continuous random excitations with tunable correlation time. We show that the system dynamics are controlled by the ratio of the Markovian mean flight time of the ball and the mean time between successive peaks in the motion of the exciting plate. When this ratio, which depends on the bandwidth of the excitation signal, exceeds a certain value, the Markovian approach is appropriate; below, memory of preceding excitations arises, leading to a significant decrease of the jump duration; at the smallest values of the ratio, chattering occurs. Overall, our results open the way for uses of the model in the low excitation regime, which is still poorly understood.

Statistics of the separation between sliding rigid rough surfaces: Simulations and extreme value theory approach

“…[14][15] or semi-empirical expressions (Eqs. [16][17][18][19] are sufficient to evaluate most of the relevant statistical descriptors of the roughness-induced normal motion. Our results thus further extend the already large range of applicability of EVT to rough contact situations.…”

“…In the following, d 0 (u) is referred to as the normal motion. If the sliding velocity was high enough, the slider could loose contact with the track and enter a bouncing regime ( [15][16][17][18]). In the following, we only consider slow sliding, in which such inertia effects can be neglected.…”