Collaborative Research: Dynamics of Snapping of Tethers

这笔资金将用于研究降落伞、系缆绳、拖缆、安全带和能量收集装置中使用的柔性绳的性能、可靠性和安全性的准确设计，从而促进科学进步，促进国家繁荣。无论是自由端的还是系在有效载荷上的，工程应用中的柔性绳的行为只有考虑到潜在的导致损伤的折断类动力学才能被正确地理解，即松弛的物体突然被拉紧。由于动能集中在电缆另一端附近的一小块区域，即使是轻微的拉力也很容易放大电缆一端的加速度和张力几个数量级。抓拍过程的时间短促和相应的能量的强烈空间局部化可能会导致结构故障，但也可能是操纵有效载荷的一种方式。为了使研究人员和工程师能够量化、解释和预测一系列应用中的抓拍现象，该项目将建立理论和计算模型，这些模型由实验观察提供信息，并通过物理测试进行验证。为了鼓励学生参与STEM，内华达大学和奥斯汀得克萨斯大学将为高中生夏令营项目开发一个关于蹦极动力学的教学模块。本研究旨在开发一种建模方法，用于有效地从不可扩展的惯性运动到伸展运动的快速、非线性、松弛-拉紧的转变以及柔性对象的弹性波的产生，并将该方法转化为高效的模拟技术。它将通过得出新的边界层渐近性和尺度分析来实现这些结果，这些分析捕捉到张力和动能到弹性势能然后再回来的大空间梯度的突然爆发。然后，它在开发降阶模型和异步时间积分器的过程中建立了这样的技术，克服了与近乎奇异的捕捉动力学相关的独特的数值挑战。最后，将进行重力驱动抓拍的实验，以探索不同的行为模式，并获得与理论和模拟进行比较的数据。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This grant will fund research that enables accurate design for performance, reliability, and safety of flexible ropes used in parachutes, mooring lines, towing cables, safety harnesses, and energy harvesting devices, thereby promoting the progress of science, and advancing the national prosperity. Whether free-ended or tethered to payloads, the behavior of flexible ropes in engineering applications can be properly understood only by accounting for potentially damage-inducing snapping-like dynamics whereby a slack object is suddenly pulled taut. Even mild yanking at one end of a cable can easily amplify accelerations and tensions by several orders of magnitude, as kinetic energy is focused on a small region near the cable’s other end. The temporal brevity of the snapping process and the corresponding strong spatial localization of energy may lead to structural failures but can also be a way to manipulate a payload. To allow researchers and engineers to quantify, explain, and predict snapping phenomena across a range of applications, this project will build theoretical and computational models that are informed by experimental observations and validated against physical tests. To encourage participation in STEM, an educational module on bungee jump dynamics will be developed for summer camp programs for high school students at the University of Nevada and the University of Texas at Austin.This research aims to develop the foundations of a modeling method for rapid, nonlinear, slack-taut transitions between effectively inextensible inertial motion to stretching and elastic wave generation of flexible objects, and to translate this method into efficient simulation techniques. It will accomplish these outcomes by deriving new boundary-layer asymptotics and scaling analyses that capture a sudden onset of large spatial gradients in tension and rapid exchange of kinetic energy to elastic potential energy and back again. It then builds on such techniques in the development of reduced order models and asynchronous time integrators that overcome unique numerical challenges associated with the nearly singular snapping dynamics. Finally, experiments on gravity-driven snapping will be performed to explore different regimes of behavior and to obtain data for comparison with theory and simulation.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.