Chattering: an overlooked peculiarity of rocking motion

Complete chattering occurs when a structure undergoes a theoretically infinite sequence of impacts in finite time, that eventually bring the structure to the state of persistent (continuous) contact. This study investigates the conditions under which a rigid rocking block undergoes complete chattering when subjected to sinusoidal ground excitation. The analysis explains how the acceleration amplitude of the ground excitation affects the chattering time. It also proves that there exists a (sinusoidal) ground acceleration amplitude, below which rocking motion terminates even under a nonzero ground excitation, almost independently of the frequency of the ground excitation. Furthermore, the study adopts perturbation theory and proposes an asymptotic approximation of the time needed for chattering to be completed, i.e. chattering time. It then verifies the asymptotic approximation using an independent semi-analytical approach. Overall, the results highlight the importance of complete chattering on the dynamic rocking response, a feature of nonlinear dynamics which is often overlooked in earthquake engineering.