# I³MS - Schewe Seminar

## Dr. Günter Schewe - Flow-Induced Vibrations and the Landau Equation

Institute for Aeroelasticity, DLR Göttingen

### Abstract

Flow induced vibrations are a prime example of a nonlinear phenomenon, in which limit-cycle-oscillations occur beyond a critical value. Even in its simplest form, the Landau equation describes universal properties of nonlinear systems, which can be of physical or more natural types. Thus the question arises: to which extent can self-excited, flow-induced vibrations be described by the Landau Equation?

Three different cases were studied experimentally, each using bodies with generic shapes. The first case was a bluff body that resembles a simplified section of the Tacoma Bridge and has a single torsional degree of freedom. The second case was a two-dimensional airfoil in a transonic flow having one heave and one torsional degree of freedom. The third case was an elastic half-wing model, also investigated in a transonic flow.

It is shown that in all three cases, beyond a critical point and at small initial amplitude, the build up of the oscillations and the transition to the limit-cycle, i.e. the envelope of the measured time functions, agreed with the solutions of the Landau equation. For the Tacoma section and the airfoil, the agreement was also demonstrated for initial amplitudes much larger than that of the limit-cycle. In addition for the first two cases, the bifurcation behaviour was investigated and the Landau constants were determined. The latter can be seen as a measure for the degree of nonlinearity. Apart from the experimental demonstration, a physical explanation for the nonlinear phenomena is given.