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。本提案提出了包括实验、建模、分析和数值模拟在内的具有分段光滑运动和离散碰撞事件的基本混合机械系统的紧密耦合研究。研究人员将利用非光滑动力学中分岔分析的最新进展作为工作的起点。本项目采用的方法是通过详细探索两个原型问题(i)系留粒子的驱动运动和（ii）冲击摆，来扩展对具有冲击的系统的动力学、稳定性和分岔的理解。这些问题为响应最近对多元素系统中非光滑强迫和碰撞引起的分支的研究提供了坚实的实验平台。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的理解。稳定性和分岔的潜在结果将使操作条件更加有效、高效和可靠。此外，它们适合通过系统对冲击力的响应来研究损伤检测可行性的长期计划。也就是说，我们试图证明分岔和对冲击力的响应可以用来诊断内部结构缺陷，作为无损检测和可能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，并将研究生和本科生的培训纳入跨学科研究计划，以开发工程和非线性动力学方面的协调先进技能。在最近成功的基础上，制定了确保代表性不足群体参与的计划。该项目的结果将通过工程和应用动力系统的期刊出版物、研究会议上的报告、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。通过改进学生在工程和应用数学课程开发方面的训练，研究将得到加强。