A Multistability Framework for Modeling and Control of Hysteretic Damping and Friction

该项目提出了一种全新的视角和方法来解决动力学中的两个重要而基本的问题，即滞回阻尼和滞回摩擦。这一观点基于多重稳定性原理，即系统的状态被吸引到依赖于投入的均衡。对于材料阻尼器，一种假定的滞回阻尼器的多稳定性机制是跳跃屈曲，其中多种平衡形状的吸力可以将粘性阻尼器转化为滞回(渐近低频)能量耗散。同样，在表面接触中，突然释放机制为滞后摩擦提供了多稳定性基础。因此，多重稳定性原理为理解由弹性和非弹性结构力学的本构关系引起的滞回现象提供了一种新的范式，同时也为耗能滞回的建模和控制提供了统一的原则。本项目将建立基于多稳定性原理的滞回阻尼器和摩擦力的流变模型。我们将开发和分析滞回阻尼和摩擦的多稳态模型，通过实验室实验对这些模型进行实验验证，并开发和实现具有迟滞的机械系统的非线性控制方法。了解机械系统的动力学可以影响我国的物理基础设施和经济健康。例子包括易受地震影响的建筑物和桥梁，以及用于制造的机器人系统中的精密设备。在更小的层面上，纳米尺寸的机械设备为安全应用的创新传感器提供了基础。这些系统的动态取决于这些系统耗散能量的方式。能量主要有两种消散方式，即通过阻尼力和摩擦力。虽然阻尼力和摩擦力的影响可以通过实验测量，但这些现象是出了名的难以分析和预测。这个项目采用了一种新的方法来理解阻尼和摩擦，通过构建模型来捕捉滞后阻尼，滞后阻尼指的是能够在慢动作下耗散能量的阻尼。这个项目是基于多重稳定性的概念，这意味着系统可以停留在多个均衡。这些多重均衡的数量和结构提供了对引起滞后阻尼的物理机制的洞察。通过了解这些物理机制，该项目将为工程师提供在广泛的应用中对机械系统的动力学进行建模和预测的能力。

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.