Vibration reduction of turbomachinery bladed disks with changing dynamics using piezoelectric materials

Piezoelectric-based vibration reduction can alleviate the unwanted vibration levels of tur-bomachinery, thus reducing the dangers of high-cycle fatigue while also decreasing the blade weight, drag, and jet noise. Most passive approaches provide limited benefit in turbomachinery due to the changing blade dynamics and excitation conditions that make optimally tuning a shunt circuit difficult. Active control typically provides large vibration reduction but requires a power source in the rotating frame. Semi-active approaches seek to balance the advantages of passive and active systems, outperforming the passive approaches while significantly reducing the power required. This research presents a semi-active approach that applies to excitations with swept frequencies. It involves detuning the structural resonance frequency from the excitation frequency by altering the structural stiffness (here by switching the electrical boundary conditions of a piezoelectric element), thus limiting the structural dynamic response. Including a switch back to the original stiffness state, detuning requires two switches per resonance / excitation frequency crossing, orders of magnitude fewer than other state switching approaches that require four switches per cycle of vibration. The detuning method applies to any mode of vibration with a positive electromechanical coupling coefficient and provides the greatest normalized vibration reduction for slow sweeps, low damping, and high coupling coefficient. Yet even for a moderate sweep rate α = 10^-4 and modal damping ζ = 0.1%, detuning a structure with a coupling coefficient k² = 10% provides the same vibration reduction as increasing either the sweep rate or modal damping by an order of magnitude.