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

探索性研究早期概念基金（EAGER）将支持结构力学和网络理论交叉领域的研究。交换结构——由通过销钉连接的杆组成的系统，其中一些杆可以动态地开关开和关——将被引入工程承重结构系统，模拟交换网络的复杂行为，其中连接节点的边缘进化、适应、切换和眨眼。众所周知，交换网络表现出奇异的动态；例如，在选择的切换频率下，在不稳定状态之间切换的网络可以获得稳定性。这种丰富的动态曲目为结构工程提供了有趣的机会。例如，是否可以创建结构系统，由于开关元件的存在，可以在它们即将崩溃时恢复稳定性？能否利用开关结构的时变特性进行振动衰减？这些问题的答案需要发展有关开关结构的新基础知识。该研究将通过混合结构力学和网络理论的学科，并通过确定它们之间的通用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。正如结构力学可以被网络理论的进步所改变一样，网络理论也可以从可以用来验证网络理论猜想的机械系统的创造中获得巨大的好处。教育活动也在网络和结构的交叉点，并利用所涉及的机构（公共和私人，郊区和城市，但彼此仅相距50英里）的不同身份，帮助扩大代表性不足的群体参与研究，并有助于形成前瞻性思维，跨学科的工程师。本课题的主要目标是建立一个网络理论框架来研究交换结构。这样的目标将通过制定交换结构的数学背景来实现，它认识到使它们在其他网络系统中独特的一些属性。这个数学背景，连同有限元模拟，将用于绘制开关结构的稳定性，以及它们对静载荷的响应。这些理论上的努力将揭示最近在交换网络中观察到的中间时间尺度上稳定行为岛的起源，但其物理基础尚未完全理解。最后，该项目将通过实现桌面尺度原型，为探索交换结构的可行性提供重要步骤。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。

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.