Multi‐Mode Tumbling Dynamics of Rigid Blocks Under Base Acceleration Excitations

ABSTRACT Research on the rocking response of rigid rectangular blocks has primarily concentrated on pre‐overturning dynamics, whereas post‐overturning kinematics and behavioral evolution remain underexplored. The overturning of rigid blocks can be conceptualized as a transformation between the rocking motions of two distinct blocks. Their slenderness ratios are reciprocals of one another, implying that a unified motion exists that integrates both rocking and overturning phases for blocks with distinct slenderness ratios, bridging these phenomena. This motion, defined as a tumbling motion, forms the core of this study. This article systematically investigates the tumbling motion of rigid blocks under pulse and sustained sinusoidal excitation. Six distinct tumbling motion modes are identified and characterized. The study further examines the distribution of tumbling motion modes across varying slenderness ratios and excitation types and summarizes the underlying evolution mechanisms among modes under differing conditions.