The project proposes to bring a radical new perspective and approach to two of the important and fundamental problems in dynamics, namely, hysteretic damping and hysteretic friction. This viewpoint is based on the principle of multistability, whereby the state of a system is attracted to input-dependent equilibria. For material damping, a postulated multistability mechanism for hysteretic damping is snap-through buckling, where the attractivity of multiple equilibrium shapes can transform viscous damping into hysteretic (asymptotically low frequency) energy dissipation. Likewise, in surface contact, the sudden-release mechanism provides a multistability foundation for hysteretic friction. The principle of multistability thus provides a novel paradigm for understanding how hysteresis arises from the constitutive relations of elastic and inelastic structural mechanics, while serving as a unifying principle for modeling and control of energy-dissipative hysteresis. This project will develop rheological models for hysteretic damping and friction based on the principle of multistability. We will develop and analyze multistable models for hysteretic damping and friction, experimentally verify these models through laboratory experiments, and develop and implement nonlinear control methods for mechanical systems with hysteresis.
Understanding the dynamics of mechanical systems can impact the physical infrastructure and economic health of our Country. Examples include buildings and bridges subject to earthquakes as well as precision devices in robotic systems used for manufacturing. At even smaller levels, nanometer-size mechanical devices provide the basis for innovative sensors for security applications. The dynamics of these systems depend on the way in which these systems dissipate energy. Energy is dissipated in two principal ways, namely, by damping and friction. Although the effects of damping and friction can be measured experimentally, these phenomena are notoriously difficult to analyze and predict. This project adopts a novel approach to understanding damping and friction by constructing models that capture hysteretic damping, which refers to damping that is able to dissipate energy under slow motion. This project is based on the concept of multistability, which means that the system can come to rest at multiple equilibria. The number and structure of these multiple equilibria provide insights into the physical mechanisms that give rise to hysteretic damping. By understanding these physical mechanisms, this project will provide engineers with the ability to model and predict the dynamics of mechanical systems in a wide range of applications.
