Modeling and Simulation of Rocking Block Dynamics subjected to Base Motion using an Energetic Restitution Law

This work uses a nonsmooth dynamic model to study the motion of rocking-block structures with base excitation. In this study, the rocking blocks are modeled with respect to two contact points that represent the bottom face of the block. Each of these contact points can assume a state of either (a) free-flight, (b) contact, or (c) impact. Two of the key differences of this work from other studies of the rocking-block problem with base motion are (a) the collision model used here strictly enforces a rigidity property on the block, and (b) impacts are characterized using global energetic coefficients of restitution, which ensure energy consistency of the system. The proposed method also yields information on the history of impulses induced on the block due to the collisions, which has not been explored previously. This work can potentially lead to further insights into the rocking-block problem, which can be applied in earthquake and structural engineering.