Dynamics of Multi‐Block Rocking Assemblies

ABSTRACT This study presents a general numerical framework for simulating the seismic rocking response of multi‐block systems. The framework allows for user‐defined block counts, geometries, and restoring device configurations using arced rigid blocks characterized by double‐sided circular arcs. By employing curved surface contact and rolling constraints, the proposed model circumvents non‐smooth kinematics, such as impact, sliding, and bouncing, thereby mitigating the inherent nonlinearity of rocking behavior. To overcome the numerical instabilities and convergence issues typical of rectangular blocks due to centroidal discontinuities, a unified coordinate transfer formulation based on motion chains is developed to ensure continuous kinematic representation across arbitrary configurations. The governing equations of motion are derived via the Lagrangian method, incorporating generalized forces to construct a mathematical model that captures the dynamic equilibrium under seismic excitation and restoring actions. Numerical results demonstrate the framework's efficiency in capturing nonlinear rocking responses and inter‐block motion relationships during both free and forced vibrations. By establishing specific physical constraints and assumptions, this study develops a generalized numerical framework to reduce the analytical complexity of multi‐body rocking dynamics. Given the influence of multiple rocking interfaces on global structural response, potential application scenarios for multi‐segmented high‐rise rocking systems are outlined. Furthermore, the engineering relevance and limitations of the proposed model are discussed, considering factors such as the simplified equivalent representation of supplemental mechanical devices.