Abstract
The general vibration of a rotating blade with time-dependent angular speed is investigated in this paper. A simple plate model is used to represent the blade, and its angular speed is characterized as a small periodic perturbation superimposed on a constant speed. Due to this non-constant rotational speed, terms with time-dependent coefficients appear in the equation of motion, which results in parametric instability. The method of multiple scales is used to derive approximate solutions and expressions for the boundaries of the unstable regions. All cases of possible resonant combinations up to the second order are studied, and the effects of system parameters, such as the damping coefficient, aspect ratio, rotating speed and setting angle, on the boundaries of the unstable regions are also investigated.
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