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This paper extends the resonance frequency detuning (RFD) vibration reduction approach to cases of turbomachinery blade mistuning. Using a lumped parameter mistuned blade model with included piezoelectric elements, this paper presents an analytical solution of the blade vibration in response to frequency sweep excitation; direct numerical integration confirms the accuracy of this solution. A Monte Carlo statistical analysis provides insight regarding vibration reduction performance over a range of parameters of interest such as the degree of blade mistuning, linear excitation sweep rate, inherent damping ratio, and the difference between the open-circuit (OC) and short-circuit (SC) stiffness states. RFD reduces vibration across all degrees of blade mistuning as well as the entire range of sweep rates tested. Detuning also maximizes vibration reduction performance when applied to systems with low inherent damping and large electromechanical coupling. [ABSTRACT FROM AUTHOR]

Piezoelectric-based resonance frequency detuning can alleviate unwanted vibration of turbomachinery blades, thus reducing the dangers of high-cycle fatigue while also decreasing the blade weight. This semiactive approach applies to structures that are subjected to frequency-sweep excitation and involves altering the structural stiffness (here, by switching the piezoelectric electrical boundary conditions) to avoid a resonant condition, thus limiting the blade response. Detuning requires two switches per resonance/excitation frequency crossing, including a switch back to the original the original state, many fewer than other semiactive approaches that require four switches per cycle of vibration. Resonance frequency detuning applies to any mode of vibration with a positive electromechanical coupling coefficient, and it 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%, optimally detuning a structure with an electromechanical coupling coefficient k² = 10% provides the same vibration reduction as increasing either the sweep rate or modal damping by an order of magnitude. With a lower sweep rate α = 10-5 and modal damping ζ = 0.01%, detuning with a coupling coefficient of only k² = 3% provides equivalent vibration reduction as an order of magnitude increase in sweep rate or modal damping. [ABSTRACT FROM AUTHOR]