Modelling the rocking dynamics of objects with irregular geometry

Free-standing objects are all around us. Computer monitors and towers, bottles, kitchen containers, museum artifacts, tables, chairs, and medical equipment are just a few of the objects which may be prone to rocking and toppling due to external forcing or support excitation. Many objects with irregular geometry are able to rock about their edges and vertices, twist, topple, and impact their support, and could thus pose hazards to the integrity of the object and also to surrounding structures, objects, and even human life. However, previous rocking models are not adequate to handle objects with irregular geometry due to their assumptions. Thus, this thesis aims to fill the knowledge gap of the dynamics of irregular objects by introducing new rocking models for planar and 3-D rocking which take into account the full irregular geometry of such objects. The planar rocking model assumes a rigid body and rigid support and fully considers sliding, free fight, and a variable location for the impulses at impact. The 3-D model similarly uses a rigid body and rigid support with a variable location for the impulses, but assumes no sliding or free fight, as it focuses on the pure rocking response of such systems and how this can lead to substantially more complicated responses of the body when taking into account the geometry. Examples of objects in both planar and 3-D rocking are provided and conclusions are drawn on the importance of irregular geometry, sliding, free fight, and a variable location for the impulse. Finally, the 3-D model is used to describe the rolling dynamics of various objects with curved geometry, offering a new dynamic model to describe these motions that is efficient and qualitatively similar to the experimental dynamic responses