Dynamic behaviour of rocking two‐block assemblies

Abstract The dynamic behaviour of systems consisting of two blocks, one placed on the top of the other, and free to rock without sliding, is examined in this analysis. The equations of motion for each ‘mode’ of vibration are derived and criteria for the initiation of rocking and the transition between modes are given. During vibration, the system continuously changes from one mode to another and this makes the response non‐linear. This transition may be accompanied by impact, in which case dissipation of energy occurs, the amount of which depends on the relative velocities and the dimensions of the blocks. Also, redistribution of the kinetic energy of the system in the blocks happens. In most cases, the fractional contribution from the upper block to the system energy increases, which results in a larger and longer response of the top block, compared to the vibration of the lower one.