Identification of Parametric Resonances in a Geometrically Exact Model of a Rotating Blade

Much research has been done in the past couple of decades on the vibrations of rotating structures, such as helicopter and wind turbine blades. This is the consequence of ever increasing standards towards dynamic performance of these systems. Previous investigations have primarily dealt with constant rotational velocity, with a focus on the determination of the linear dynamic response. The rotational speed cannot always be considered constant due to fluctuating external loads or due to specific ramp-up regimes. This non-constant angular velocity brings about terms with time dependent coefficients in the equations of motion which can result in the existence of so-called parametric resonances. These resonance phenomena are quite unknown in this field of application. Nevertheless, they are of major concern to mechanical engineers because it can lead to structural damage due to large amplitude oscillations as a result of parametric resonances. In this thesis a fully geometrically nonlinear beam model is set up to study the fundamental behavior that causes parametric resonances in rotating blades. These equations are solved by means of two numerical approaches, the finite element method and the Galerkin method. The first one is used to obtain the linear modal properties. The Galerkin discretized equations are adopted to examine the linear and non-linear dynamics in time. The linear response is investigated to obtain the regions in which the unstable motions occurs due to parametric excitation. The non-linear response is obtained to show the stable post-critical behavior in these instability regions. Furthermore, it is shown that for specific values of the rotational speed and the parametric excitation frequency, instability occurs in each principal direction.

Subject

parametric resonances
non-linear
geometrically exact
rotating blades

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master thesis

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