Cantilever self-excited with a higher mode by a piezoelectric actuator

The sensitivity of vibration-type sensors can be improved using a higher resonating frequency of a cantilever resonator. Resonance in such systems can be achieved using a self-excited oscillation, which overcomes the difficulty of using an external excitation in viscous environments. To enhance the sensitivity of cantilever resonators, several groups have proposed ways to increase the natural frequency of the first mode by changing the cantilever geometry. However, the sensitivity can be further improved by using a self-excited oscillation with a higher mode in addition to the geometry-changing technique. In this study, we present a method to realize this goal. We perform a nonlinear analysis of the governing equation of a cantilever excited by a piezoelectric actuator. For each mode, we also clarify the dependence of the critical feedback gain on the location of a displacement sensor, the output of which is used for feedback control. With the aid of filters, we then devise a way to generate a self-excited oscillation with a higher mode associated with a desired higher natural frequency. Finally, we carry out experiments using a macro-cantilever and report the observation of a self-excited oscillation with the second natural frequency, which is higher than the first natural frequency.