Abstract Summary
The dynamic behaviour of a freestanding block rocking on a rigid base when subjected to a horizontal ground excitation is a classical problem of nonlinear dynamics that has drawn considerable attention. Despite the apparent structural simplicity, rocking motion is characterised by various nonlinear and nonsmooth dynamics phenomena, which compose a complex and often chaotic behaviour. Chattering is a feature of nonlinear dynamics that might appear during the low amplitude forced oscillations of a rocking block. Chattering can be complete or incomplete. Complete chattering occurs when the block undergoes a theoretically infinite sequence of impacts in finite time, that eventually bring the block to the state of persistent (continuous) contact. On the contrary, incomplete chattering does not bring the block to rest after the theoretically infinite number of impacts. This paper analytically investigates the conditions under which a rigid rocking block undergoes complete chattering when subjected to low amplitude mathematical pulses. Specifically, the analysis proves the existence of a ground acceleration amplitude threshold below which the rocking block terminates its motion. Importantly, this work shows that the acceleration threshold mainly depends on the coefficient of restitution while it remains almost independent of the frequency of the ground excitation. Furthermore, the paper approximates the duration needed for the block to come to rest, namely chattering time. To this end, it adopts perturbation theory and proposes an iterative algorithm that accurately approximates chattering time. Finally, the analysis reveals how the acceleration amplitude of the ground excitation affects chattering time.
