Demonstration of Multiple Internal Resonances in a Microelectromechanical Self-Sustained Oscillator

Abstract

We investigate the dynamics of a microelectromechanical (MEMS) self-sustained oscillator supporting multiple resonating and interacting modes. In particular, the interaction of the first four flexural modes along with the first torsional mode are studied, whereby 1:2, 1:3, and 2:1 internal resonances occur. Even and odd modes are induced to couple by breaking the longitudinal symmetry of the structure. Self-oscillations are induced in the second flexural mode via a gain-feedback loop, thereafter its frequency is pulled into a commensurate frequency ratio with the other modes, enabling the oscillator to act as a driver/pump for four modes simultaneously. Thus, by leveraging multiple internal resonances, a five modes frequency-locked comb is generated.

The Librator: A new dynamical regime for nonlinear microelectromechanical devices

“…Furthermore, that a librator maybe synchronized by the application of a weak external forcing, in a manner similar to the way oscillators can be synchronized, is worth investigating. And the formation of a librator network, potentially within a single multi-mode device [69] could be of great practical importance.…”

A Kuramoto Network in a Single Nonlinear Microelectromechanical Device

“…An undesirable effect is equally visible in Fig. 3(b), which is due to the fact that the resonance frequency ratio of modes 1 and 3 is ω 3 /ω 1 ≈ 3, thus a region of resonant energy transfer, or internal resonance, can be accessed [29,32]. In this work, such effect is undesirable, as it changes drastically the nature of the coupling, and the region where this resonant energy transfer takes place is avoided.…”

“…Therefore, by relying on mode-coupling it is possible to reduce the essential elements of a network to the creation of the limit cycles only, and allow the mode-coupling to generate the necessary connections in a single physical device. * samer.houri.dg@hco.ntt.co.jp However, a straightforward implementation of a network in a multi-mode device with self-sustained oscillating modes is not possible without resorting to resonant four-wave mixing, i.e., internal resonance [27][28][29]. Internal resonance requires special frequency ratios that are difficult to scale to a large number of modes, and at the same time could result in strong coupling between the oscillating elements [30][31][32], which is undesirable for an oscillator network.…”

“…The device in question possesses two electrodes on each end of the structure length, see representation in Fig. 1(a), by equally actuating both electrodes (not shown in schematic) only odd modes are efficiently excited [29]. Three odd modes are accessible these are the first, third, and fifth out-of-plane flexural modes, respectively, with the following modal frequencies ω 01 = 2π × 321 kHz, ω 03 = 2π × 954 kHz, ω 05 = 2π × 2.325 MHz.…”

Limits to Thermal-Piezoresistive Cooling in Silicon Micromechanical Resonators

“…The quality factor (Q), or inverse damping of a resonator, is perhaps the most important property of these systems since it determines the dynamic response and thermomechanical signal-to-noise ratio (SNR). A wide range of phenomena are under investigation for tuning the effective quality factor (Q eff ) and inducing oscillations in micro-and and nano-scale resonators [5]- [12]. Feedback-based schemes can suppress Q eff , improving the resonator bandwidth [13]- [16], or enhance Q eff to the onset of self-sustained oscillations.…”