Dynamic analysis of asymmetric bladed-rotors supported by anisotropic stator

For the mathematical convenience of conventional rotor dynamic analysis, the components of the entire rotor system are often classified into two parts: the stationary parts and the rotating parts, depending upon whether or not the corresponding components rotate with respect to their axes of rotation. Even for bladed-rotors, the rotor blades have been treated along the same lines as the ordinary rotating components such as the rotor disk and the shaft. The distinct dynamic nature of the blades, therefore, has not been thoroughly taken into account in the conventional rotor dynamic analysis. In this paper, the rotating parts of a bladed-rotor system are further subdivided into the rotor blade-group and the other rotating components. The equation-of-motion for the bladed-rotor system is then developed, by modifying the conventional general rotor system equation to adopt the blade-group dynamics without loss of generality. Complex modal solutions to the bladed-rotor system are investigated based on a new modulated coordinate transformation approach, yielding newly defined directional frequency response functions that characterize the nature of asymmetry present in the rotating blade-array. Finally, the effects of the blade-group asymmetry on the rotor system dynamics are demonstrated with a pertinent numerical example.