Resonance and excessive deflection in pedestrian bridges
Resonance and excessive deflection in pedestrian bridges
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Overview
Overview
This report was a case study of the London Millennium Bridge, a pedestrian bridge that exhibited lateral oscillations of up to 60mm, leading to its closure three days after opening. It was completed with a partner as part of the Dynamics 2 unit, which had a very strong focus on harmonic oscillations. I found it interesting and challenging to apply theory we had been learning in the context of machinery to a very different kind of vibration problem. It was an interesting angle on forced vibration: If the vibration forcing comes from hundreds of individual sources, then the relative phases of the forcing become the most important factor in the analysis.
This report was a case study of the London Millennium Bridge, a pedestrian bridge that exhibited lateral oscillations of up to 60mm, leading to its closure three days after opening. It was completed with a partner as part of the Dynamics 2 unit, which had a very strong focus on harmonic oscillations. I found it interesting and challenging to apply theory we had been learning in the context of machinery to a very different kind of vibration problem. It was an interesting angle on forced vibration: If the vibration forcing comes from hundreds of individual sources, then the relative phases of the forcing become the most important factor in the analysis.
As part of my analysis I modelled the vibration of the bridge with an equation of motion based on that of forced, damped spring mass oscillators. I wrote code and conducted simulations in python to analyse the effect of increasing phase locking.
As part of my analysis I modelled the vibration of the bridge with an equation of motion based on that of forced, damped spring mass oscillators. I wrote code and conducted simulations in python to analyse the effect of increasing phase locking.
Course: MEC3453: Mechanical Vibrations
Course: MEC3453: Mechanical Vibrations
Collaborators: Alexander Edmondson
Collaborators: Alexander Edmondson
Date: October 2025
Date: October 2025
Sections completed by me: 1, 2, 4 and 5
Sections completed by me: 1, 2, 4 and 5
Key skills: Dynamics, Python, Research, Report writing, Mathematical modelling
Key skills: Dynamics, Python, Research, Report writing, Mathematical modelling
Technical Essay - Resonance and excessive deflection on pedestrian bridges.pdfLessons Learned
Lessons Learned
Translating Theory to Complex Systems
Translating Theory to Complex Systems
I learned how to adapt the theoretical dynamics which we had primarily applied to standard machinery vibrations to more complicated real world human-structure interactions. Building the Python simulations taught me how to practically implement equations of motion to test hypotheses and visualize the impact of varying degrees of phase locking.
I learned how to adapt the theoretical dynamics which we had primarily applied to standard machinery vibrations to more complicated real world human-structure interactions. Building the Python simulations taught me how to practically implement equations of motion to test hypotheses and visualize the impact of varying degrees of phase locking.
The Importance of Designing for Edge Cases
The Importance of Designing for Edge Cases
This project completely shifted my perspective on failure modes. I realised that assuming standard operating conditions (like pedestrians walking out of step) is insufficient. It reinforced the necessity of modeling worst case, compounding scenarios when evaluating the stability of a design, and highlighted the risks of only considering the most likely modes of failure.
This project completely shifted my perspective on failure modes. I realised that assuming standard operating conditions (like pedestrians walking out of step) is insufficient. It reinforced the necessity of modeling worst case, compounding scenarios when evaluating the stability of a design, and highlighted the risks of only considering the most likely modes of failure.
Broadening Engineering Solutions
Broadening Engineering Solutions
While researching mitigation strategies, I learned to look beyond traditional mechanical fixes. Exploring human centric solutions, like gamification to prevent phase alignment, showed me that an effective engineering solution can sometimes involve altering the system's inputs rather than just reinforcing the physical structure.
While researching mitigation strategies, I learned to look beyond traditional mechanical fixes. Exploring human centric solutions, like gamification to prevent phase alignment, showed me that an effective engineering solution can sometimes involve altering the system's inputs rather than just reinforcing the physical structure.
Targeted Technical Communication
Targeted Technical Communication
Taking ownership of the core problem definition and engineering solutions refined my ability to synthesize complex, multi-variable dynamic problems. It improved my capacity to clearly explain my mathematical modeling and coordinate technical research effectively alongside a partner.
Taking ownership of the core problem definition and engineering solutions refined my ability to synthesize complex, multi-variable dynamic problems. It improved my capacity to clearly explain my mathematical modeling and coordinate technical research effectively alongside a partner.
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