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Plate Models

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Mathematical Models for Suspension Bridges

Part of the book series: MS&A ((MS&A,volume 15))

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Abstract

The most natural way to describe the bridge roadway is to view it as a rectangular elastic plate. Rocard (Dynamic instability: automobiles, aircraft, suspension bridges. Crosby Lockwood, London, 1957, p. 150) writes:

The plate as a model is perfectly correct and corresponds mechanically to a vibrating suspension bridge.

In this chapter we make some attempts to model suspension bridges with nonlinear plate equations. We discuss both material nonlinearities, such as the behavior of the restoring force due to the hangers and the sustaining cables, and geometric nonlinearities due to possible wide oscillations which bring the plate (roadway) far away from its equilibrium position. The results in the present chapter should be seen as a prelude of more detailed studies aiming to increase the knowledge of the qualitative behavior of suspension bridges through plate models. Still, these results are sufficient to highlight a torsional instability and the existence of a flutter energy similar to those described in the previous chapters for different models.

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  1. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Filippo Gazzola

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Gazzola, F. (2015). Plate Models. In: Mathematical Models for Suspension Bridges. MS&A, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-319-15434-3_5

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