Particle current on flexible surfaces excited by harmonic waves

Motion periodicity and bifurcation of a wave excited hopping ball

We consider the problem of a hopping ball excited by a travelling harmonic wave on an elastic surface. The ball, considered as a particle, is assumed to interact with the surface through inelastic collisions. The surface motion due to the wave induces a horizontal drift in the ball. The problem is treated analytically under certain approximations. The phase space of the hopping motion is captured by constructing a phase-velocity return map. The fixed points of the return map and its compositions represent periodic hopping solutions. The linear stability of the obtained periodic solution is studied in detail. The minimum frequency for the onset of periodic hops, and the subsequent loss of stability at the bifurcation frequency, have been determined analytically. Interestingly, for small values of wave amplitude, the analytical solutions reveal striking similarities with the results of the classical bouncing ball problem.

Creeping motion characteristics due to bulk wave excitation in an elastic half-space

In this work, the contact problem between a preloaded rigid surface against a restrained elastic half-space is considered under wave excitation. The half-space is assumed to be bonded imperfectly to the rigid surface, and subjected to external tractions and bulk waves. Under incident bulk wave excitation at the contact, we study the creeping motion of the preloaded rigid surface. Two possible local regions at the interface are considered, namely slip region, and region of separation, which are described by the corresponding boundary conditions and inequalities at the interface. With these considerations, creeping motion characteristics and interface conditions are obtained analytically and discussed. The effects of interface imperfection, wave parameters, and preload tractions are studied numerically. The creeping motion is found to be affected significantly by nature of the imperfection. In addition, creep motion is also analyzed considering friction at the interface. These aspects have potential applications in ultrasonic devices for micro-positioning and micro-motion control.