Piezoelectric-based semi-active vibration reduction techniques typically rely on rapid changes in the electrical boundary conditions or corresponding stiffness state. Approaches such as state switching and synchronized switch damping on a resistor or an inductor require four switching events per vibration cycle, with switch timing associated with displacement extrema. Any deviation from this switch timing affects the performance of these techniques. Typical harmonic forcing analyses focus on the energy dissipation and only evaluate the performance at resonance. This study evaluates displacement reduction for harmonic excitation, both at resonance and for frequencies near resonance. Furthermore, it examines the effect of sub-optimal switch timings. Numerical simulations of a non-dimensional model are performed, and an analytical solution is derived for any switch time. This analysis shows that the optimal switch timing depends on the forcing frequency relative to the natural frequency of the structure. Thus, the classical switch time at peak displacement is only optimal when the excitation is exactly at resonance. Even when the optimal switch timing is known, uncertainties in vibration sensing cannot guarantee that switches will occur at the desired moment. Therefore, this work characterizes the degradation in vibration reduction performance when switching away from the optimal switch time based on global, non-dimensional parameters.
Development status and application prospect of semi-active vibration reduction technology for down-hole drilling tools