On the dynamic response of rigid body assemblies

This paper examines dynamic response of a type of structural system that exhibits a significant degree of rigid body motion during earthquakes. An assembly of two‐dimensional rigid prisms subjected to self‐imposed kinematic constraints is chosen as a representative model for this type of structure. The corresponding equations of motion are non‐linear and have coefficients with step discontinuities; they are generally non‐autonomous and comprise, in effect, 2 N sets of N governing equations for an N degree‐of‐freedom model. Linearized time histories are presented for one and two degree‐of‐freedom systems. As expected, the response modes of the systems are poorly conditioned; small changes in input or geometry (or both) can create large changes in system response. By examining limiting cases of survival and failure for both analytical and probabilistic responses, some apparent trends in system behaviour have been discovered.