The collapse of the Tacoma Narrows suspension bridge in the state of Washington in 1940 is one of most spectacular failures of a large engineering structure due to an (aeroelastic) instability () in a steady wind flow. This example shows that for the practical use of many technical systems stability properties can be a decisive design criterium. Some other examples, where stability properties are important, are slender structures consisting of rods, plates and shells under pressure loading or under loading by flowing fluids, like the liquid flow in a pipe. For vehicles moving at high speed, like truck-trailer combinations or railway trains (, ), severe operating restrictions can result from stability limits. An important class of stability problems concerns the field of hydrodynamic stability. Here the stability of certain flow states of viscous fluids is studied. Two important examples are the convective motion in a horizontal layer heated from below (Bénard problem) and the flow in the gap between two coaxial cylinders rotating at different angular velocities (Couette problem) (, ). Here not only the stability of certain states is of interest but also the qualitative change in the flow pattern under variation of external parameters. Such parameters would be in these two flow examples the temperature difference for the Bénard flow and the angular velocities for the Couette flow. As a final example consider the following question: how should the shape of the hull of a ship be designed in order to guarantee static stability (safety against capsizing) over a wide range of loading conditions (, ch. 10)?
KeywordsStability Problem Nonlinear Stability Center Manifold Negative Real Part Small Aspect Ratio
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