Experimental amplitude and frequency control of a self-excited microcantilever by linear and nonlinear feedback

Abstract

It is well known that the micro scale deviations of mechanical properties of a sample can be detected by measurement methods that use microcantilever as resonators. Those methods use the natural frequency shift of a resonator, thus we need to recognize the frequency shift caused by the effects of a sample on a resonator with high sensitivity and accuracy. Experimental approaches based on self-excited oscillation enable the detection of these shifts even when the resonator is immersed in a high-viscosity environment. In the present study, we experimentally and theoretically investigate the nonlinear characteristics of a microcantilever resonator and their control by nonlinear feedback. We show that the steady-state response amplitude and the corresponding response frequency can be controlled by cubic nonlinear velocity feedback and cubic nonlinear displacement feedback, respectively. Furthermore, the amplitude and frequency of the steady-state self-excited oscillation can be controlled separately. These results will expand application of measurement methods that use self-excited resonators.