Analysis and Design of a Nonholonomic, Impact-Based, Dual-Mode Vibration Isolator/Absorber System

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The objective of this project is to insulate sensitive contents of a building from disruptions due to vibration, while also preventing severe damage to the structure of the building from large motions, such as from an earthquake. This will be achieved by advancing and combining the techniques of vibration isolation and vibration absorption, which have previously only been applied independently or in parallel. An effective method of protecting sensitive equipment from small amplitude building motion is a vibration isolation platform, supported by rollers. However, when the building motion is sufficiently large, as in an earthquake, the overriding concern becomes preventing the possible collapse of the structure. In this case a vibration absorber can be used to transfer mechanical energy out of the structure. This project uses the same system to act as a vibration isolator when the building motion is small, and as a vibration absorber when the building motion is large. The hybrid device is created using purely passive mechanical elements, each consisting of a ball rolling between two concave plates, with a restraining wall or similar structure at the boundary of the concave region. When the amplitude of motion is small, the ball remains near the center of the plates. As the motion becomes large, the ball will eventually impact the restraining structure, marking the transition from vibration isolator to vibration absorber. This project will relate parameters such as the curvature of the concave plates, the size of the concave region, and the materials of the plates and restraining boundary to the isolation and absorbing properties of the device. The results of this work will be used to minimize disruption to business operations, damage to structures, and injury to building occupants. Web-based demonstration of the concept will facilitate education and outreach to building owners, structural engineers, and future professionals. This project aims to answer the ongoing question: How can systems and their subsystems be designed to achieve synergistic interactions and enhanced system-level resilience? To answer this question, the research will: (a) develop a framework to model complex nonholonomic dynamical systems; (b) extend nonlinear vibration absorption theory; (c) optimize impact mechanisms for enhancing multi-level hazard mitigation; and (d) experimentally verify the predicted performance. Rolling isolation platforms are the primary means of equipment isolation. A new mathematical framework will be created to model the three-dimensional dynamics of these systems incorporating the nonholonomic constraints described by the kinematics of rolling balls, loss of contact, and impacts with displacement limits. At low-to-moderate disturbance levels, the platforms are to function primarily as isolators, and they will passively adapt under strong disturbances to function as essentially nonlinear (vibro-impact) dynamic vibration absorbers to protect the primary building system from collapse. In order to achieve the desired multi-functional dynamic behavior, this research will establish new algorithms for determining optimal control strategies satisfying inequality constraints on state and control trajectories. Ultimately, the methodologies developed in this project will help to understand the fundamental limitations and achievable performance of multi-functional isolation systems.