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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]

Resonance frequency detuning (RFD) reduces vibration of systems subjected to frequency sweep excitation by altering the structural stiffness state as the excitation frequency passes through resonance. This vibration reduction technique applies to turbomachinery experiencing changes in rotation speed, for example, on spool-up and spool-down, and can be achieved through the inclusion of piezoelectric material and manipulation of its electrical boundary conditions. Key system parameters--the excitation sweep rate, modal damping ratio, electromechanical coupling coefficient, and, most importantly, the switch trigger that initiates the stiffness state switch (represented here in terms of excitation frequency)--determine the peak response dynamics. This paper exploits an analytical solution to a nondimensional single degree-of-freedom equation of motion to provide this blade response and recasts the equation in scaled form to include the altered system dynamics following the stiffness state switch. An extensive study over a range of sweep rates, damping ratios, and electromechanical coupling coefficients reveals the optimal frequency switch trigger that minimizes the peak of the blade response envelope. This switch trigger is primarily a function of the electromechanical coupling coefficient and the phase of vibration at which the switch occurs. As the coupling coefficient increases, the frequency-based switch trigger decreases, approximately linearly with the square of the coupling coefficient. Furthermore, as with other state-switching techniques, the optimal stiffness switch occurs on peak strain energy; however, the degradation in vibration reduction performance associated with a switch occurring at a nonoptimal phase is negligible for slow sweep rates and low modal damping. [ABSTRACT FROM AUTHOR]

Component miniaturization and reduced power requirements in sensors have enabled growth in the field of low-power ambient vibration energy harvesting. This work aims to increase bandwidth and power output beyond current techniques by inducing chaotic nonlinear phenomena and applying a low-power controller based on the method of Ott, Grebogi, and Yorke (OGY) to stabilize a chosen periodic orbit. Previously, researchers used a nonlinear piezomagnetoelastic beam in search of a large amplitude broadband voltage response, but chaos was strictly avoided. These large amplitude responses candeteriorate over time into low energy chaotic oscillations. Including chaos as a desirable property allows small perturbations to alter the behavior of a system dramatically, improving the dynamic response for energy harvesting. The nonlinear piezomagnetoelastic beam element described by a Duffing oscillator is extended to embrace chaotic motion more actively. By driving motion along a chaotic attractor, even single frequency excitation results in a theoretically infinite number of unstable periodic orbits that can be stabilized using small control inputs. The chosen orbit will be accessible from a large range of excitation frequencies and can be dynamically changed in real-time, potentially expanding the bandwidth of operation. [ABSTRACT FROM AUTHOR]