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

该奖项是根据2009年《美国复苏与再投资法案》(Public Law 111-5)资助的。这项建议提出了一项紧密耦合的研究，涉及具有分段平稳运动和离散冲击事件的基本混合机械系统的实验、建模、分析和数值模拟。研究人员将使用非光滑动力学中分叉分析的最新发展作为这项工作的起点。这个项目所采取的方法是通过对两个原型问题的详细探索来扩展对受影响系统的动力学、稳定性和分叉的理解：(I)系留粒子的驱动运动和(Ii)碰撞摆。这些问题为最近对多元素系统中由于非光滑强迫和碰撞引起的分叉的兴趣的研究提供了坚实的试验台。这些问题作为大型机械和工业系统的基础部件具有重要意义。它们也非常适合于实验研究，允许对数值模拟和简化的数学模型进行验证。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。在稳定性和分叉方面的潜在结果将允许更有效、更多产和更可靠的运行条件。此外，它们符合一个长期计划，用于研究通过系统对冲击强迫的反应进行损害检测的可行性。也就是说，我们试图证明，分叉和对冲击强迫的响应可以用来诊断内部结构缺陷，作为一种无损测试以及可能的控制和抑制不稳定性的手段。该提案在工程和应用数学领域的研究人员之间建立了一种新的合作，并将把研究生和本科生培训纳入一个跨学科研究项目，该项目将发展工程和非线性动力学方面的协调高级技能。在最近取得成功的基础上，制定了确保任职人数不足的群体参与的计划。该项目的成果将通过工程和应用动力系统的期刊出版物、在研究会议上的演讲、通过项目网页以及通过与杜克大学的非线性和复杂系统中心的联系来传播。将通过改进学生在开发工程和应用数学课程方面的培训来加强研究。

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.