Toppling Dynamics of a Mass-Varying Domino System

This paper studies the toppling dynamics of a mass-varying domino system for which the mass of the domino changes at an exponential rate of its sequence number. By introducing geometrical constraints representing the interactions between the dominoes and the ground, we propose a simplified model which can describe their toppling dynamics as a one-degree-of-freedom structural-varying system. Principles of energy and generalized momentum conservation are used to investigate the free falling and the colliding phases of the system, and our proposed model is validated through a comprehensive numerical study. Furthermore, we develop an impact mapping for studying the evolution of the system by using the mathematical properties of their geometrical constraints and establish the occurrence conditions for solitary wave. According to these conditions, the system can exhibit four different propagation modes: non-solitary mode, uniform solitary mode, accelerating solitary mode and stopped mode. Based on the studies in this paper, we can reveal the dynamic characteristics of domino phenomenon and provide an insight into its energy evolution.