Resonant vibration control of rotating beams

Rotating structures, like e.g. wind turbine blades, may be prone to vibrations associated with particular modes of vibration. It is demonstrated, how this type of vibrations can be reduced by using a collocated sensor-actuator system, governed by a resonant controller. The theory is here demonstrated by an active strut, connecting two cross-sections of a rotating beam. The structure is modeled by beam elements in a rotating frame of reference following the beam. The geometric stiffness is derived in a compact form from an initial stress formulation in terms of section forces and moments. The stiffness, and thereby the natural frequencies, of the beam depend on the rotation speed and the controller is tuned to current rotation speed to match the resonance frequency of the selected mode. It is demonstrated that resonant control leads to introduction of the intended level of damping in the selected mode and, with good modal connectivity, only very limited modal spill-over is generated. The controller acts by resonance and therefore has only a moderate energy consumption, and successfully reduces modal vibrations at the resonance frequency.