Dynamic Behavior of T-beam Resonator With Repulsive Actuation

We introduce a MEMS resonator that uses a "T"-shape beam driven by repulsive force, of which the first advantage is to avoid pull-in instability; thus, high enough voltages can be applied to the MEMS system to tune the center frequency. A T-beam model is derived from the beam-paddle hypothesis, and theoretical analysis regarding both static and dynamic behaviors, including primary resonance and secondary resonance, is conducted. This study shows an electrostatic T-beam resonator's feasibility based on repulsive force and outlines its advantages over a traditional cantilever beam resonator. Additional micro-paddle to the micro-beam means larger surface for absorption of targeted analytes and lower natural frequency, but higher resonant responses. We present a thorough analysis of primary and parametric resonances, which can enhance the system signal-to noise ratio and response time. This design enables potential applications in MEMS mass-sensors, where a large area for attachment and a high resolution are often vital.

Phase-delay Induced Variation of Synchronization Bandwidth and Frequency Stability in a Micromechanical Oscillator

Phase feedback is commonly utilized to set up a synchronized MEMS oscillator for high performance sensor applications. It's a consensus that the synchronization region varies with phase delay with a `Anti-U' mode within 0 to pi and phase delay is typically fixed on pi/2 to achieve maximum synchronization range and best frequency stability. In this paper, phase-delay induced variation of synchronization bandwidth and frequency stability in a micromechanical oscillator is investigated analytically and experimentally. A self-sustained oscillator is built by applying phase feedback to an electrostatically actuated micro-beam resonator and synchronization phenomenon is observed after coupling it to a weak external periodic excitation. The analytical expression for predicting the synchronization bandwidth with phase delay is derived based on the dynamic model, from which three different types (`U', `Anti-U' and `M') of variation pattern of synchronization bandwidth are observed as feedback tuning. The variation of frequency stability along phase delay is also studied. The synchronization bandwidth and the frequency stability have exactly opposite variation pattern with phase delay in linear oscillators while they are totally consistent in nonlinear oscillators. Experimental tests in vacuum environment are carried out to validate the analytical observations. Our work presented here provides a precise way for achieving best performance of a synchronized MEMS oscillator in the sensor application.

Strong internal resonance in a nonlinear, asymmetric microbeam resonator

Exploiting nonlinear characteristics in micro/nanosystems has been a subject of increasing interest in the last decade. Among others, vigorous intermodal coupling through internal resonance (IR) has drawn much attention because it can suggest new strategies to steer energy within a micro/nanomechanical resonator. However, a challenge in utilizing IR in practical applications is imposing the required frequency commensurability between vibrational modes of a nonlinear micro/nanoresonator. Here, we experimentally and analytically investigate the 1:2 and 2:1 IR in a clamped–clamped beam resonator to provide insights into the detailed mechanism of IR. It is demonstrated that the intermodal coupling between the second and third flexural modes in an asymmetric structure (e.g., nonprismatic beam) provides an optimal condition to easily implement a strong IR with high energy transfer to the internally resonated mode. In this case, the quadratic coupling between these flexural modes, originating from the stretching effect, is the dominant nonlinear mechanism over other types of geometric nonlinearity. The design strategies proposed in this paper can be integrated into a typical micro/nanoelectromechanical system (M/NEMS) via a simple modification of the geometric parameters of resonators, and thus, we expect this study to stimulate further research and boost paradigm-shifting applications exploring the various benefits of IR in micro/nanosystems.

Parameters optimization method for the time-delayed reservoir computing with a nonlinear duffing mechanical oscillator

Reservoir computing (RC) is a recently introduced bio-inspired computational framework capable of excellent performances in the temporal data processing, owing to its derivation from the recurrent neural network (RNN). It is well-known for the fast and effective training scheme, as well as the ease of the hardware implementation, but also the problematic sensitivity of its performance to the optimizable architecture parameters. In this article, a particular time-delayed RC with a single clamped–clamped silicon beam resonator that exhibits a classical Duffing nonlinearity is presented and its optimization problem is studied. Specifically, we numerically analyze the nonlinear response of the resonator and find a quasi-linear bifurcation point shift of the driving voltage with the driving frequency sweeping, which is called Bifurcation Point Frequency Modulation (BPFM). Furthermore, we first proposed that this method can be used to find the optimal driving frequency of RC with a Duffing mechanical resonator for a given task, and then put forward a comprehensive optimization process. The high performance of RC presented on four typical tasks proves the feasibility of this optimization method. Finally, we envision the potential application of the method based on the BPFM in our future work to implement the RC with other mechanical oscillators.