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.
