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

该项目的目标是使建筑物的敏感内容免受振动的破坏，同时防止建筑物的结构因大型运动(如地震)而严重损坏。这将通过推进和结合隔振和吸振技术来实现，这些技术以前只能独立或并行应用。保护敏感设备免受小幅建筑物运动影响的一种有效方法是由滚子支撑的隔振平台。然而，当建筑物的运动足够大时，如在地震中，最重要的问题是防止结构可能倒塌。在这种情况下，可以使用减振器将机械能转移到结构之外。该项目使用相同的系统，当建筑物运动较小时充当隔振器，而当建筑物运动较大时用作减振器。混合装置是使用纯被动机械元件创建的，每个元件由在两个凹形板之间滚动的球组成，在凹形区的边界处具有约束壁或类似的结构。当运动幅度较小时，球保持在板块中心附近。当运动变大时，球最终会撞击约束结构，标志着从隔振器到吸振器的转变。本项目将把凹板的曲率、凹区的大小、板的材料和约束边界等参数与装置的隔振和吸波性能联系起来。这项工作的结果将用于最大限度地减少对商业运营的干扰、对建筑物的损坏和对建筑物居住者的伤害。基于网络的概念演示将促进对建筑物业主、结构工程师和未来专业人员的教育和推广。该项目旨在回答正在进行的问题：如何设计系统及其子系统以实现协同互动和增强系统一级的复原力？为了回答这个问题，这项研究将：(A)开发一个框架来模拟复杂的非完整动力学系统；(B)扩展非线性减振理论；(C)优化冲击机制以增强多级减灾；以及(D)通过实验验证预测的性能。滚动隔震平台是设备隔震的主要手段。将创建一个新的数学框架来对这些系统的三维动力学进行建模，其中包括由滚珠运动学、接触损失和具有位移限制的碰撞所描述的非完整约束。在低至中等干扰水平下，平台的主要功能是隔离器，它们将在强干扰下被动适应，充当本质上是非线性(振动-冲击)的动态减振器，以保护主要建筑系统不会倒塌。为了达到期望的多功能动态行为，本研究将建立新的算法来确定满足状态和控制轨迹的不等式约束的最优控制策略。最终，本项目中开发的方法将有助于理解多功能隔离系统的基本限制和可实现的性能。

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.