Enhanced Modeling of the Rocking and Overturning of Objects on a Moving Base

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The rocking of objects and their overturning due to base motions such as earthquake excitations accounts for a substantial fraction of losses and in many cases functional disruption of facilities. While the rocking dynamics have been studied by several researchers since the 1960's surprisingly there are very large gaps in our ability to adequately simulate the response of the complex dynamics associated with the problem. This is a case where the combination of comparatively simple mechanical principles leads to highly complex nonlinear phenomena which are sensitive to parameter variations within the problem. The project will consider base deformability and damping properties, friction interactions at the base, uplift (when the body bounces during rocking), 3-dimensional analysis (which includes tri-axial base motion) with mass eccentricities of the object, non-rectangular base shapes, and more. The project plan focuses on the development of advanced computational simulations tools to model the complex nonlinear dynamics of rocking objects.In addition, an enhanced model would provide risk analysis of a wide variety of objects including everything from electrical transformers to masonry antiquities. Having such a model would greatly improve the ability to infer the historic earthquake record from the non-overturning or in some cases the overturning of ancient "precarious rocks" and structures. This improved understanding has the potential to better understand the historical events of earthquakes. In addition, features such as cart-like wheels (to simulate hospital medical equipment carts) will be added as extra degrees of freedom at the base, and also base restrainers (which may fail) at the beginning of the rocking response. In order to perform the inverse analysis, a probabilistic approach will be developed to determine what earthquakes (or sequence of earthquake) might have occurred over the history of a still standing ancient object. The research plan includes an experimental plan to be carried out on the PI's medium-scale shake table facility.