Switch Triggers for Optimal Vibration Reduction via Resonance Frequency Detuning

For systems subjected to linear frequency sweep excitation, piezoelectric-based resonance frequency detuning provides vibration reduction by altering the stiffness state of the material as it passes through resonance. This vibration reduction technique applies to turbomachinery experiencing changes in rotation speed, for example on spool-up and spool-down. The peak response dynamics are determined by the system’s sweep rate, modal damping ratio, electromechanical coupling coefficient, and, most importantly, the frequency at which the stiffness state is altered. An analytical approach is employed to solve the nondimensional single degree of freedom equation of motion and is scaled to incorporate the altered system frequency following the stiffness state switch. This paper provides an extensive study over a range of sweep rates, damping ratios, and electromechanical coupling coefficients to determine the optimal frequency switch trigger that minimizes the 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 switch trigger decreases and is approximately linear with the square of this coupling coefficient. Furthermore, as with other state-switching techniques, the optimal frequency switch occurs when the phase of vibration is at the point of maximum displacement, or peak strain energy.