Research on Collision Restitution Coefficient Based on the Kinetic Energy Distribution Model of the Rocking Rigid Body within the System of Mass Points

Rocking structures exhibit significant collapse resistance during earthquakes. In studies of rocking rigid bodies, the collision restitution coefficient is typically determined based on the classical model of the rocking rigid bodies. However, during the rocking process, the collision restitution coefficient, influenced by the uncontrollable error in collision energy dissipation between the rigid body and the ground, indirectly impacts the final results of the equations of motion. Therefore, the rationality and reliability of the collision restitution coefficient are crucial for seismic analysis of rocking rigid bodies and self-centering members. This paper introduces a phasic energy dissipation and kinetic energy redistribution model specifically designed for the rocking rigid body within the system of mass point. This model divides the collision into three distinct stages, incorporating energy dissipation considerations in the first two stages to calculate the total kinetic energy of the rigid body. In the third stage, the remaining kinetic energy is redistributed to precisely determine the analytical solution for the collision restitution coefficient of an ideal, homogeneous rectangular rigid body during collision. Lastly, the validity and reliability of the proposed model are confirmed through comparisons with experimental data.