Experimental construction of force- and frequency-response curves of nonlinear resonators

We present an experimental technique to construct the response of nonlinear resonators under harmonic excitation as a control parameter is swept. Our technique can resolve nonlinear features in the resonator response, such as bifurcations and hysteresis. To validate it, we construct the frequency response of a MEMS resonator while the excitation frequency is swept. The response is measured optically and recorded in the time domain. The root-mean-square of the response is calculated over a variable-size time-window. The sweep time, window size, and frequency step size were found to be limited by the quality factor of the resonator under test. We examine and describe those limitations in terms of the slew rate and sampling frequency. Although we used optical measurements to validate the technique, the methods described herein are applicable to any measured response signal.

Automated summary

We propose an experimental technique for constructing nonlinear resonator response under sweeping control parameters. Our technique can accurately capture nonlinear features such as bifurcations and hysteresis. To validate the technique, we apply it to construct the frequency response of a MEMS resonator under sweep excitation. The response is optically measured and recorded in the time domain, with the root-mean-square calculated over variable-size time windows. The limitations in sweep time, window size, and frequency step are determined by the resonator's quality factor, and we analyze them in terms of slew rate and sampling frequency. Although optical measurements were used for validation, the described methods can be applied to any measured response signal.