Entrainment of Micromechanical Limit Cycle Oscillators in the Presence of Frequency Instability

The nonlinear dynamics of micromechanical oscillators are explored experimentally. Devices consist of singly and doubly supported Si beams, 200 nm thick and 35 μm long. When illuminated within a laser interference field, devices self-oscillate in their first bending mode due to feedback between laser heating and device displacement. Compressive prestress buckles doubly supported beams leading to a strong amplitude-frequency relationship. Significant frequency instability is seen in doubly supported devices. Self-resonant beams are also driven inertially with varying drive amplitude and frequency. Regions of primary, sub-, and superharmonic entrainment are measured. Statistics of primary entrainment are measured for low drive amplitudes, where the effects of frequency instability are measurable. Sub- and superharmonic entrainment are not seen in singly supported beams. A simple model is built to explain why high-order entrainment is seen only in doubly supported beams. Its analysis suggests that the strong amplitude-frequency relationship in doubly supported beams enables hysteresis, wide regions of primary entrainment, and high orders of sub- and superharmonic entrainment.