DynSyst_Special_Topics: New Challenges in Non-Smooth Dynamical Systems - Experiments and Analysis

DynSyst_Special_Topics：非光滑动力系统的新挑战 - 实验与分析

• 批准号: 0927186
• 负责人: Lawrence Virgin
• 金额: $ 37.45万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-08-01 至 2013-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0927186&HistoricalAwards=false
• 关键词: DynSyst_Special_Topics; New; Challenges; Non; Smooth

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).This proposal puts forward closely coupled studies involving experiments, modeling, analysis, and numerical simulations of fundamental hybrid mechanical systems with piecewise smooth motion and discrete impact events. The investigators will use recent developments in the analysis of bifurcations in non-smooth dynamics as a starting point for the work. The approach taken in this project is to expand the understanding of the dynamics, stability and bifurcations of systems with impacts by detailed exploration of two prototype problems: (i) the driven motion of tethered particles and (ii) the impacting pendulum. These problems provide solid testbeds for the studies in response to recent interest in bifurcations due to non-smooth forcing and collisions in multi-element systems. These problems have significance as basic components in larger-scale mechanical and industrial systems. They are also very well suited to experimental studies, allowing for the validation of numerical simulations and simplified mathematical models. This project will advance the understanding of classes of mechanical systems ubiquitous in natural and industrial settings. Potential results on stability and bifurcations will allow for more efficient, productive and reliable operating conditions. Moreover, they fit into a long-term program for the study of the feasibility of damage detection via system response to impactive forcing. Namely, we seek to demonstrate that bifurcations and response to impactive forcing can be used to diagnose internal structural defects as a means of nondestructive testing and possible control and suppression of instabilities. The proposal builds a new collaboration between researchers in engineering and applied mathematics and will incorporate graduate and undergraduate student training in an interdisciplinary research program that will develop coordinated advanced skills in engineering and nonlinear dynamics. There are plans for ensuring the participation of under-represented groups, building on recent successes. Results from this project will be disseminated through journal publications in engineering and applied dynamical systems, presentations at research conferences and through a project web page and via connections with Duke University's Center for Nonlinear and Complex Systems. Research will be augmented by improvements in student training in the development of courses in engineering and applied mathematics.

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。该提案提出了密切耦合的研究，涉及实验，建模，分析和数值模拟的基本混合机械系统与分段平滑运动和离散的影响事件。研究人员将使用非光滑动力学中分叉分析的最新进展作为工作的起点。本项目所采取的方法是通过详细探讨两个原型问题来扩大对碰撞系统的动力学、稳定性和分叉的理解：（i）系留粒子的驱动运动和（ii）碰撞摆。这些问题提供了坚实的试验平台的研究，在响应最近的兴趣，由于非光滑的强迫和碰撞在多元素系统的分叉。这些问题作为大型机械和工业系统的基本组成部分具有重要意义。它们也非常适合实验研究，允许验证数值模拟和简化的数学模型。该项目将促进对自然和工业环境中普遍存在的机械系统类别的理解。关于稳定性和分叉的潜在结果将允许更有效、多产和可靠的操作条件。此外，他们适合于一个长期的计划，通过系统响应冲击力的损伤检测的可行性研究。也就是说，我们试图证明，分叉和响应冲击迫使可以用来诊断内部结构缺陷的无损检测和可能的控制和抑制不稳定性的一种手段。该提案建立了工程和应用数学研究人员之间的新合作，并将在跨学科研究计划中纳入研究生和本科生培训，该计划将发展协调的工程和非线性动力学高级技能。在最近取得的成功基础上，制定了确保代表性不足群体参与的计划。该项目的成果将通过工程和应用动力系统的期刊出版物、研究会议上的介绍、项目网页以及与杜克大学非线性和复杂系统中心的联系进行传播。将通过改进学生在工程和应用数学课程开发方面的培训来加强研究。