Collective Dynamics of Mechanical Systems with Applications to Bridge Modeling

机械系统的集体动力学及其在桥梁建模中的应用

• 批准号: 1616345
• 负责人: Igor Belykh
• 金额: $ 27.12万
• 依托单位: Georgia State University Research Foundation, Inc.
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-07-01 至 2019-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1616345&HistoricalAwards=false
• 关键词: Collective; Dynamics; Mechanical; Systems; Applications

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 objective of this research project is to contribute to mathematical modeling of resonant vibrations caused by collective behavior of pedestrians or wind-induced coherent oscillations of load-bearing elements of bridges. This synergistic project aims to develop experimentally-validated nonlinear theory that will help engineers to estimate (i) the dynamical impact of pedestrian loads and (ii) a range of dangerous frequencies due to induced collective oscillations in a bridge's suspension/supporting systems. Such frequencies, which cannot be identified through the conventional linear calculations of natural frequencies, can lead to faulty, collapsing designs. Results from this research may lead to improved safety and economic benefits. This project focuses on an area of nonlinear science entailing mathematical analysis and modeling of mechanical networks, including bidirectional interactions between walking pedestrians and lively bridges and wind-induced oscillations of load-bearing elements of bridges. The first part of this project seeks to develop bio-mechanically inspired models of pedestrians' responses to bridge motion and detailed, yet analytically tractable, models of crowd dynamics and phase-locking. This project also seeks to verify a hypothesis that the balance control of pedestrians based on the lateral position of foot placement can initiate bridge wobbling, without crowd synchronization. The second part of this project aims at better understanding the cause of dangerous vibrations and bridges collapsing as a result of wind-induced oscillations at a frequency different from the natural frequencies of a bridge. The interdisciplinary research utilizes methods from applied mathematics and engineering, including stability and bifurcation theory, piecewise smooth and stochastic dynamical systems, graph theory, classical mechanics, and bio-mechanics.

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。本研究项目的主要目标是对行人集体行为引起的共振或桥梁承载元件的风致相干振荡进行数学建模。该协同项目旨在开发实验验证的非线性理论，以帮助工程师估计（i）行人荷载的动态影响和（ii）由于桥梁悬挂/支撑系统中诱导的集体振荡而引起的危险频率范围。这些频率无法通过传统的固有频率线性计算来识别，可能导致设计错误和崩溃。这项研究的结果可能会提高安全性和经济效益。该项目侧重于非线性科学领域，涉及机械网络的数学分析和建模，包括步行行人和活跃桥梁之间的双向相互作用以及桥梁承重元件的风致振动。该项目的第一部分旨在开发行人对桥梁运动的反应的生物机械模型，以及详细但易于分析的人群动力学和锁相模型。该项目还试图验证一个假设，即基于脚放置的横向位置的行人的平衡控制可以启动桥梁摆动，而无需人群同步。该项目的第二部分旨在更好地了解危险振动和桥梁倒塌的原因，这些振动和桥梁倒塌是由频率不同于桥梁自然频率的风引起的振动造成的。跨学科研究利用应用数学和工程方法，包括稳定性和分叉理论，分段光滑和随机动力系统，图论，经典力学和生物力学。