This paper surveys an area of nonlinear functional analysis and its applications. The main application is to the existence and multiplicity of periodic solutions of a possible mathematical models of nonlinearly supported bending beams, and their possible application to nonlinear behavior as observed in large-amplitude flexings in suspension bridges. A second area, periodic flexings in a floating beam, also nonlinearly supported, is covered at the end of the paper.

Large-amplitude periodic oscillations in suspension bridges: some new connections with nonlinear analysis

The action of flexible bridges under wind, I: Flutter theory†

Damping in structures: its evaluation and treatment of uncertainty

The action of flexible bridges under wind, II: Buffeting theory

A time-resolved particle image velocimetry (PIV) system has been developed at the University of Western Ontario, London, ON, Canada, with long-recording-time capabilities This system is uniquely suited to the study of unsteady aerodynamics and hydrodynamics, such as avian aerodynamics or bluff-body oscillations Measurements have been made on an elongated bluff body through the initial build-up phase of flutter The possibilities to study this instability, which was responsible for the collapse of the Tacoma Narrows Bridge, are significantly broadened by the use of this system The long-time recording capability of the system allows for novel results since it yields data that are spatially and temporally resolved over a long record length The buildup of flutter is shown to exhibit complex dynamics that are heavily influenced by the flow-induced motion of the body Features of the wake turbulence as a function of time are presented and shown to substantially vary

Long-Duration Time-Resolved PIV to Study Unsteady Aerodynamics

The writers compare the flutter phenomena of the suspension bridge and the airfoil and employ a free-oscillation experimental method to measure model bridge flutter coefficients analogous to airfoil flutter coefficients. They employ the airfoil as a check on the experimental method, both as a theoretical backdrop and to test out the nature of aerodynamic oscillatory forces under exponentially modified motion. A short catalogue of bridge deck flutter coefficients is then experimentally obtained and presented covering a range of bridge deck forms. Detailed results are described to account for a number of phenomena observed in the wind tunnel and in the field.

John J. Tomko

Papers

Airfoil and Bridge Deck Flutter Derivatives