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

该项目的目的是隔离建筑物的敏感内容，使其免受振动造成的破坏，同时防止建筑物结构因地震等大幅度运动而受到严重损坏。这将通过推进和结合振动隔离和振动吸收技术来实现，这些技术以前只能单独或并行应用。保护敏感设备免受小振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，首要的问题是防止结构的可能倒塌。在这种情况下，可以使用振动吸收器将机械能传递出结构。该项目使用相同的系统，当建筑物运动较小时作为隔振器，当建筑物运动较大时作为吸振器。混合装置使用纯被动机械元件来产生，每个被动机械元件包括在两个凹板之间滚动的球，在凹区域的边界处具有约束壁或类似结构。当运动幅度很小时，球保持在板块中心附近。当运动变大时，球最终将撞击约束结构，标志着从隔振器到吸振器的过渡。本计画将探讨凹板曲率、凹区大小、凹板材料及约束边界等参数对装置隔振及吸波特性的影响。这项工作的结果将用于最大限度地减少对业务运营的干扰、对结构的损坏和对建筑物占用者的伤害。基于网络的概念演示将促进教育和推广到建筑业主，结构工程师和未来的专业人士。该项目旨在回答持续存在的问题：如何设计系统及其子系统，以实现协同互动和增强系统层面的复原力？为了回答这个问题，研究将：（a）开发一个框架来模拟复杂的非完整动力系统;（B）扩展非线性振动吸收理论;（c）优化影响机制，以增强多级减灾;（d）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模拟这些系统的三维动力学，将非完整约束所描述的运动学的滚动球，接触损失，和位移限制的影响。在低至中等干扰水平下，平台主要起隔离器的作用，在强干扰下，它们将被动地适应，起到基本上非线性（振动冲击）的动力吸振器的作用，以保护主建筑系统免于倒塌。为了实现所需的多功能动态行为，本研究将建立新的算法来确定满足状态和控制轨迹不等式约束的最佳控制策略。最终，在这个项目中开发的方法将有助于了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.