Non-linear dynamic model of a two-bodies vertical spanning wall elastically restrained at the top

Understanding the out-of-plane behavior of unreinforced masonry walls is crucial in seismic assessment of existing buildings. Here, the dynamic response of a vertical spanning strip wall, connected to a flexible diaphragm at the top, is investigated. Despite the simplicity of the model, two rocking rigid bodies elastically restrained at the top, the dynamic response is highly nonlinear. This behavior is due to different phenomena: when in motion the system may assume different configurations, with the transition between them due either to impacts or crack opening caused by ground acceleration. An analytical model capable to capture the complex dynamic response of the system is implemented. The equations of motion are first derived, using variational methods, then the events that the system can undergo during motion are studied. Finally, in order to show the potential of the model, some numerical exemplifications are presented applying an earthquake record and a sine pulse to the system.