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Mathematical Analysis of Flow-Induced Oscillations
of Spring-Mounted Body in a Navier–Stokes Liquid

by Giovanni Paolo Galdi
University of Pittsburgh

Abstract

The flow of viscous fluid around structures is a fundamental problem that lies at the heart of the broad research area of Fluid-Solid
Interaction. A main feature of this problem regards the study of the oscillations (vibrations) produced by the fluid on the structure.
In fact, they may lead either to useful and pleasant effects, like ringing wind chimes or Aeolian harps, or else destructive
consequences, such as damage or even collapse of the structure. Regarding the latter, of particular significance is the
phenomenon of forced oscillation of suspension bridges, induced by the vortex shedding of the fluid (air), which reflects into an
oscillatory regime of the wake. When the frequency of the wake approaches the natural structural frequency of the bridge, a
resonant phenomenon may occur that could culminate into structural failure. A very well-known and infamous example of this
phenomenon is the collapse of the Tacoma Narrows bridge. In this presentation we will provide a rigorous, and to an extent rather
complete, mathematical analysis of flow-induced oscillations on classical models proposed by the current engineering literature.
Among other things, this analysis shows that, at least for the commonly adopted models, a dramatic structural failure cannot just
be ascribed to resonance effects.

Organizacijski odbor: Dražen Adamović, Vjekoslav Kovač, Boris Muha