Modern Approaches to Modeling and Predicting Bridge Instabilities

现代的人行桥、悬索桥和其他大型机械结构都是使用行业标准组件设计的，但观察到灾难性的共振振动，需要数百万美元的维修费用。本项目的主要研究目标是提供经过实验验证的动力学系统方法，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失稳机理。研究人员开发了预测方法和工程规模，但在数学上易于处理的人类对大桥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，以便为软件包的开发提供信息，这些软件包可以显著改进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带来更好的安全性和经济效益。研究生和本科生都在从事这个项目的研究。这个项目为非光滑振子的集体动力学提供了一种严谨的高维方法。它旨在改进现有的行人对桥梁横向运动响应的倒立摆模型，并将稳定性理论与多尺度渐近分析相结合，以揭示行人诱导桥梁失稳的真正原因。它还针对一个在很大程度上未被探索的领域进行建模和预测桥梁不稳定性，其中包括人类与振动机械结构之间的双向垂直相互作用。在严谨的数学和计算理论、结构工程和人类行为之间的界面上，该项目提供了从严格的数学理论到实际工程分析的过渡，其中预测方法和行人模型可以用作“碰撞试验假人”，以探索特定的桥梁设计。研究生和本科生从事该项目的研究。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.