Free Dynamics of Multi-Block Rocking Assemblies

Rocking systems are increasingly being investigated for use as base-isolators in structural engineering applications. Unfortunately these systems present complicated, piecewise defined, kinematic relationships between their generalized coordinates (usually the joint opening angles). This makes it difficult to obtain the governing equations, even for the dynamics between rocking/impact events. This paper seeks to address this through a systematic formulation of the governing equations of rocking post-tensioned assemblies with any number of blocks under base motion. The results are limited to the smooth dynamics between rocking events, and thus, although an important step, they do not give the complete description of rocking systems. The formulation utilizes the Euler-Lagrange equation to model the dynamics, with the constraint that all rocking occurs about the corners of the blocks.