Geometric nonlinear vibrations of rotating variable thickness plates induced by periodic incoming wakes

Incoming wakes significantly affect vibration characteristics of rotating blades in turbomachines. This paper develops a periodic incoming wake mathematical model to consider the influence of pressure variations. Considering thickness variations along both the chord to reduce vibrations and the span to decrease centrifugal stress, a wake-induced vibration model based on rotating large deformation cantilever plates is established. Natural frequencies calculated by different methods show that the present method has a high degree of accuracy. And analysis of incoming wake-induced vibrations indicates the incoming wake model can analyze effects of important parameters of such wakes on vibration characteristics. With the aggravation of wakes induced-vibrations, geometric nonlinear vibrations become more remarkable, which indicates the necessity of large deflection analysis. Discussions on variable thickness demonstrate that increasing thickness on the fixed end or maximum thickness along the chord not only reduces vibrations caused by incoming wakes, but also decreases the centrifugal stress, which are two better ways to reduce this kind of vibrations.