Modern Approaches to Modeling and Predicting Bridge Instabilities

现代人行天桥、悬索桥和其他大型机械结构都是使用行业标准封装设计的，但仍会发生灾难性的共振，需要花费数百万美元进行维修。 该项目的主要研究目标是为实验验证的动力系统方法做出贡献，以了解桥梁和其他复杂机械结构与行人荷载相互作用的动力不稳定性机制。 研究人员开发预测方法和工程规模，但数学上易于处理，人类对桥梁运动和看台振动的反应的生物力学模型。 他实施了新的动态评估标准，为软件包的开发提供信息，这些软件包可以大大改善新桥梁和其他机械结构的设计以及现有结构的适用性评估。 这项研究的结果可能会提高安全性和经济效益。 研究生和本科生都参与了该项目的研究，该项目有助于对非光滑振子的集体动力学进行严格的高维研究。 目的是改进现有的行人对桥梁横向运动响应的倒立摆模型，并将联合收割机稳定性理论与多尺度渐近分析相结合，揭示行人引起桥梁失稳的真正原因。 它还针对建模和预测桥梁不稳定性的一个基本上未探索的领域，包括人类和振动机械结构之间的双向垂直相互作用。 在严格的数学和计算理论，结构工程和人类行为之间的接口，该项目提供了从严格的数学理论到实际工程分析的过渡，预测方法和行人模型可以用作“碰撞测试假人”来探测特定的桥梁设计。 研究生和本科生参与了该项目的研究。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

Modern pedestrian and suspension bridges and other large mechanical structures are designed using industry-standard packages, yet disastrous resonant vibrations are observed, necessitating multi-million dollar repairs. The main research objective of this project is to contribute to experimentally-validated dynamical systems approaches to understanding mechanisms of the dynamical instability of bridges and other complex mechanical structures interacting with pedestrian loads. The investigator develops predictive methods and engineering-scale, yet mathematically tractable, biomechanical models of humans' responses to bridge motion and vibrations of grandstands. He implements new dynamical assessment criteria to inform the development of software packages that can substantially improve both the design of new bridges and other mechanical structures and the assessment of serviceability of existing structures. Results from this research may lead to improved safety and economic benefits. Graduate and undergraduate students are engaged in the research of the project.This project contributes to a rigorous high-dimensional approach to the collective dynamics of non-smooth oscillators. It aims to improve existing inverted pendulum models of pedestrians' response to lateral bridge motion and to combine stability theory with multi-scale asymptotic analysis to reveal the true cause for the onset of pedestrian-induced bridge instabilities. It also targets a largely unexplored area in modeling and predicting bridge instabilities that includes bidirectional vertical interactions between humans and oscillating mechanical structures. At the interfaces between rigorous mathematical and computational theories, structural engineering, and human behavior, the project offers a transition from a rigorous mathematical theory to practical engineering analysis where predictive methods and pedestrian models can be used as "crash test dummies" to probe specific bridge designs. Graduate and undergraduate students are engaged in the research of the project.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.