Switch Triggers for Optimal Vibration Reduction Via Resonance Frequency Detuning

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.