Quest for Mechanical Rogue Waves in One-dimensional Discrete Lattices

该奖项的研究目标是为机械结构中异常波的形成提供所需的知识。流氓波是一种异常的大振幅波，它突然出现，消失得无影无踪。海洋中的流氓浪，通常被称为？水之墙，？都被海员们见证过。然而，在很长一段时间里，这种吞噬海洋中大船的海浪的存在一直是神话。直到几十年前，它们的存在才被科学地证实。从那时起，在不同的媒体上，异常波就成为了深入研究的主题。尽管如此，迄今为止，在固体和结构中实现机械异常波仍然难以捉摸。在工程晶格中对这种机械异常波的探索构成了该项目的核心。机械异常波的成功形成将使科学家和工程师能够以有效和可控的方式集中机械能。因此，该项目的研究结果可以为引导高振幅机械波包、收集环境机械能和开发新型传感/驱动系统开辟新的途径。从工程的角度来看，这种新的机械能控制机制可以应用于航空航天、机械和民用工业，从而造福社会。从教育的角度来看，该项目将有助于培养科学和工程领域的年轻人，包括一些代表性不足的学生。操纵机械能流（即机械波）是具有挑战性的。特别是，机械能的可控局部化需要新的技术途径，而不是利用传统的线弹性波原理。本项目将引入异常波产生的概念，主要是在流体或光学介质中观察到的波的聚焦机制，到机械领域。作为一种分析准则，著名的非线性Schr？dinger方程将应用于一维力学晶格（即非线性弹簧质量系统，如Fermi-Pasta-Ulam-Tsingou晶格）。基于这一分析，动力格的计算模型将以一种促进机械异常波形成的形式建立起来。最后，将使用一维离散晶格制作一个原型系统。机械异常波的形成将通过对原型进行全场测量来验证。S波动力学使用基于动作相机的立体视觉技术。这些分析、计算和实验研究的所有组成部分将整合到参与的本科生和研究生的教育和培训中。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The research objective of this award is to provide the needed knowledge for the formation of rogue waves in mechanical structures. Rogue waves are abnormally large-amplitude waves that appear abruptly and disappear without the trace. Rogue waves in the ocean, often referred to as the ?wall of the water,? have been witnessed by seafarers. However, the existence of such waves that swallow big ships in the ocean has been mythical for a long time. It is only a couple of decades ago that their existence has been verified scientifically. Since then, rogue waves have been a subject of intense research in different media. Nonetheless, the realization of mechanical rogue waves in solids and structures remains elusive to date. The quest for such mechanical rogue waves in engineered lattices constitutes the core of this project. The successful formation of mechanical rogue waves will enable scientists and engineers to focus mechanical energy in an efficient and controllable manner. Thus, the findings from this project can open a new avenue to guiding high-amplitude mechanical wave packets, harvesting ambient mechanical energy, and developing novel sensing/actuation systems. From an engineering standpoint, this new mechanism of mechanical energy control can be applied to aerospace, mechanical, and civil industries, thereby benefiting society. From an educational standpoint, this project will help train young minds, including several underrepresented students, in the field of science and engineering.The manipulation of mechanical energy flow (i.e., mechanical waves) is challenging. Particularly, the controllable localization of mechanical energy demands new technical approaches beyond the utilization of conventional linear elastic wave principles. This project will introduce the concept of rogue wave generation, the focusing mechanism of waves mostly observed in fluidic or optical media, to the mechanical realm. As an analytical guideline, the celebrated nonlinear Schr?dinger equation will be applied to one-dimensional mechanical lattices (i.e., nonlinear spring mass systems like Fermi-Pasta-Ulam-Tsingou lattices). Based on this analysis, computational models of dynamic lattices will be established in a form that facilitate the formation of mechanical rogue waves. Lastly, a prototypical system will be fabricated using 1D discrete lattices. The formation of mechanical rogue waves will be verified by conducting full-field measurements of the prototype?s wave dynamics using action camera-based stereo vision techniques. All components of these analytical, computational, and experimental studies will be integrated into the education and training of participating undergraduate and graduate students.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.