EAGER/Collaborative Research: Switching Structures at the Intersection of Mechanics and Networks

这一探索性研究的早期概念补助金(AGER)将支持结构力学和网络理论的交叉研究。交换结构--由通过销钉连接的杆件组成的系统，其中一些杆件可以动态地开关--将被引入工程承载结构系统，模拟交换网络的复杂行为，其中连接节点的边进化、适应、切换和闪烁。众所周知，开关网络表现出奇异的动态；例如，在选定的开关频率下，在不稳定状态之间切换的网络可以获得稳定性。这一丰富的动态曲目为结构工程带来了有趣的机会。例如，由于开关元件的存在，人们能否创造出能够在即将崩溃时恢复稳定的结构系统？人们可以利用开关结构的时变特性来衰减振动吗？这些问题的答案需要发展关于开关结构的新的基本知识。这项研究将通过融合结构力学和网络理论的学科，并通过确定它们之间的共同建模工具来开发新的知识。反过来，这些知识将允许评估开关结构在结构工程和其他领域的潜在适用性。正如结构力学可以通过网络理论的进步来改变一样，网络理论也可以从创造可用于验证网络理论猜想的力学系统中受益匪浅。教育活动也处于网络和结构的交叉点，并利用所涉机构的不同身份(公立和私立、郊区和城市，但彼此之间只有50英里)来帮助扩大代表不足的群体对研究的参与，并有助于形成具有前瞻性的跨学科工程师。本项目的主要目标是建立一个研究交换结构的网络理论框架。这样的目标将通过制定交换结构的数学背景来实现，该背景认识到使它们在其他网络系统中独一无二的一些属性。这一数学背景，以及有限元模拟，将被用来绘制开关结构的稳定性及其对静态负载的响应。这些理论努力将使最近在交换网络中观察到的中间时间尺度的稳定行为孤岛的起源揭开面纱，但其物理基础尚未完全了解，最后，该项目将通过实现桌面规模的原型，向探索切换结构的可行性迈出重要的一步。该奖项反映了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 EArly-concept Grant for Exploratory Research (EAGER) will support research at the intersection of structural mechanics and network theory. Switching structures -- systems made of bars connected via pin-joints, where some of the bars can be dynamically switched ON and OFF -- will be introduced to engineer load-bearing structural systems that emulate the complex behavior of switching networks, where edges connecting the nodes evolve, adapt, switch, and blink. Switching networks are known to exhibit exotic dynamics; for example, at select switching frequencies, networks switching between unstable states can gain stability. This rich dynamic repertoire opens interesting opportunities in structural engineering. For example, can one create structural systems that, due to the presence of switching elements, can recover stability as they are about to collapse? Can one leverage the time-varying properties of switching structures for vibration attenuation? The answer to these questions requires the development of new fundamental knowledge about switching structures. The research will develop new knowledge by blending the disciplines of structural mechanics and network theory, and by identifying common modeling tools between them. In turn, this knowledge will allow to assess the potential applicability of switching structures in structural engineering and beyond. Just as structural mechanics can be transformed by network-theoretic advancements, network theory could immensely benefit from the creation of mechanical systems that can be used to validate network-theoretic conjectures. The educational activities are also at the intersection of networks and structures and leverage the contrasting identities of the institutions involved (public and private, suburban and urban, yet merely 50 miles away from each other) to help broaden participation of underrepresented groups in research and contribute to the formation of forward-thinking, interdisciplinary engineers. The primary objective of this project is to establish a network-theoretic framework to study switching structures. Such an objective will be achieved by formulating a mathematical backdrop of switching structures, which recognizes some of the attributes that make them unique among other network systems. This mathematical backdrop, together with finite-element simulations, will be used to chart the stability of switching structures, and their response to static loads. These theoretical endeavors will allow to unveil the origin of islands of stable behavior at intermediate time scales that have been recently observed in switching networks, but whose physical underpinnings are not yet fully understood, Finally, this project will provide significant steps towards exploring the feasibility of switching structures, by realizing tabletop-scale prototypes.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.