<p>The rolling isolation system (RIS) studied in this dissertation functions on the principle of a rolling pendulum; an isolated object rests on a steel frame that is supported at its corners by ball-bearings that roll between shallow steel bowls, dynamically decoupling the floor motion from the response of the object. The primary focus of this dissertation is to develop predictive models that can capture experimentally-observed phenomena and to advance the state-of-the-art by proposing new isolation technologies to surmount current performance limitations. To wit, a double RIS increases the system's displacement capacity, and semi-active and passive damped RISs suppress the system's displacement response.</p><p>This dissertation illustrates the performance of various high-performance isolation strategies using experimentally-validated predictive models. Effective modeling of RISs is complicated by the nonholonomic and chaotic nature of these systems which to date has not received much attention. Motivated by this observation, the first part of this dissertation addresses the high-fidelity modeling of a single, undamped RIS, and later this theory is augmented to account for the double (or stacked) configuration and the supplemental damping via rubber-coated bowl surfaces. The system's potential energy function (i.e. conical bowl shape) and energy dissipation model are calibrated to free-response experiments. Forced-response experiments successfully validate the models by comparing measured and predicted peak displacement and acceleration responses over a range of operating conditions.</p><p>Following the experimental analyses, numerical simulations demonstrate the potential benefits of the proposed technologies. This dissertation presents a method to optimize damping force trajectories subject to constraints imposed by the physical implementation of a particular controllable damper. Potential improvements in terms of acceleration response are shown to be achievable with the semi-active RIS. Finally, extensive time-history analyses establish how the undamped and damped RISs perform when located inside biaxial, hysteretic, multi-story structures under recorded earthquake ground motions. General design recommendations, supported by critical-disturbance spectra and peak-response distributions, are prescribed so as to ensure the uninterrupted operation of vital equipment.</p> / Dissertation