Mutual 3:1 subharmonic synchronization in a micromachined silicon disk resonator

Abstract

We demonstrate synchronization between two intrinsically coupled oscillators that are created from two distinct vibration modes of a single micromachined disk resonator. The modes have a 3:1 subharmonic frequency relationship and cubic, non-dissipative electromechanical coupling between the modes enables their two frequencies to synchronize. Our experimental implementation allows the frequency of the lower frequency oscillator to be independently controlled from that of the higher frequency oscillator, enabling study of the synchronization dynamics. We find close quantitative agreement between the experimental behavior and an analytical coupled-oscillator model as a function of the energy in the two oscillators. We demonstrate that the synchronization range increases when the lower frequency oscillator is strongly driven and when the higher frequency oscillator is weakly driven. This result suggests that synchronization can be applied to the frequency-selective detection of weak signals and other mechanical signal processing functions.

Nonlinear polarization coupling in freestanding nanowire/nanotube resonators

“…5(c) (black dashed lines) the evolution of ω x,eff versus the amplitude R y and the backbone curve of the unperturbed y polarization [Eqs. (11) and (12)]. We see that the transition occurs when the two effective frequencies are crossing each other.…”

“…A huge amount of literature has been dedicated to internal resonances in the nonlinear dynamics community over the past 50 years, since they are commonly observed in macrostructures, for instance, in the case of nonlinear musical instruments. 8,9 For micro/nano resonators, internal resonance received increasing attention [10][11][12] over the past few years. In the special case of a resonator with two vibration modes of almost identical eigenfrequencies, a so-called one to one (1:1) internal resonance can be observed.…”

Nonlinear couplings and energy transfers in micro- and nano-mechanical resonators: intermodal coupling, internal resonance and synchronization

“…Synchronization has also been suggested to improve the performance of gyroscopes [70,88]. Experiments were performed on a silicon disc oscillator and its phase synchronization was demonstrated.…”

“…Different ranges of entrainment are shown in devil's staircase plot. (b) Phase synchronization in a micro disc having a 3 : 1 subharmonic frequency relationship[88]. Synchronization range measured for upwards and downwards frequency sweeps.…”

Limit cycles and bifurcations in a nonlinear MEMS resonator with a 1:3 internal resonance

“…Internal resonance mediated through cubic nonlinearity has been observed in a variety of electromechanical systems including quartz crystals [12] and MEMS oscillators [13][14][15]. This behavior can be of practical value, since the finger print of internal resonance, usually seen as a plateau feature in the nonlinear response of the lower frequency mode, was suggested as a means to fix the oscillator's frequency and improve its stability [14].…”