Analytical models for laterally flexible rocking bodies - Zhu, H (2023)
Rocking motion often arises due to dynamic excitations, such as earthquakes. To understand the rocking behaviour of non-rigid structures, specifically laterally flexible rocking bodies, this thesis develops analytical models of flexible rocking oscillators and validates them using experimental tests. With regards to the analytical models, an important contribution of this thesis relates to improving the modelling of impact during rocking motion. Based on the principle that spring and damper elements do not transfer impulses during an infinitesimal duration impact, a new impact model is developed. Numerical studies demonstrate this model’s ability to unify divergent modelling assumptions within a consistent framework. Another key area of research is the development of an analytical model capturing the sliding and free-flight phases of motion, which were overlooked in previous studies on laterally flexible rocking bodies. An impact model is formulated based on a hierarchical choice of post-impact phases for given impact parameters. Within this context, a new procedure is developed to choose new impact parameters if admissible solutions cannot be found for the original impact parameters. The inclusion of sliding behaviour allows the examination of how the overturning stability of flexible bodies is influenced by the coefficient of friction between the support medium and the structure. Additionally, failures of structures due to excessive sliding motion were also examined. The third area of focus in this thesis is an experimental investigation of the dynamic response of laterally flexible rocking bodies. An experimental setup is designed which allows examining bodies with variable lateral flexibility, slenderness, and coefficient of friction. Dynamic responses of the specimen under free rocking and pulse excitations were recorded using a 3D digital image correlation (DIC) system and accelerometers. Analysis of the data allows direct identification of the rigid body (including rocking and sliding motions) and flexible (lateral elastic deformation) components of the motion. Negligible impulse transfer to the flexible body during impact is experimentally validated, and key observations from the analytical models regarding overturning stability and sliding are confirmed experimentally.