Members of the S4H team have recently published a new paper in the journal of Nonlinear Dynamics.

The paper focuses on the chattering behaviour of a freestanding rocking block when subjected to a sinusoidal ground excitation of low amplitude. Chattering is a highly nonlinear phenomenon that can have a substantial influence on the dynamic response. Specifically, complete chattering refers to the phenomenon during which the block undergoes a theoretically infinite sequence of decaying impacts, in finite time, which eventually bring the block to rest even under nonzero ground excitation. This study investigates the conditions under which complete chattering occurs, and the corresponding (chattering) time needed for this to happen. In this context, the study adopts perturbation theory and conducts asymptotic analysis to treat the chattering phenomenon for rocking structures.

The main highlights of the paper are:

• It proves that there exists a (sinusoidal) ground acceleration amplitude, below which rocking motion terminates even under a nonzero ground excitation.
• It explains how the acceleration amplitude of the ground excitation affects chattering time.
• It shows that the ground acceleration amplitude that brings the block to rest depends mainly on the coefficient of restitution while it is marginally affected by the frequency of the ground excitation.
• It proposes an asymptotic approximation of the time needed for chattering to be completed, i.e. chattering time.
• It verifies the proposed asymptotic approximation using an independent semi-analytical approach.

Find more details here. You can also download the published version of the paper here.