Micro and nanoelectromechanical systems M/NEMS have been extensively investigated and exploited in the past few decades for various applications and for probing fundamental physical phenomena. Understanding the linear and nonlinear dynamical behaviors of the movable structures in these systems is crucial for their successful implementation in various novel technologies and to meet the long list of new sophisticated requirements. This paper presents a review for some of the recent topics pertaining to the dynamical behaviors, linear and nonlinear, of M/NEMS resonating structures. First, an overview is presented of the various used dynamical approaches to enhance the sensitivity of resonators for sensing applications. Then a summary is presented of the recent works on the linear and nonlinear mode coupling in M/NEMS resonator. Next, recent research is reviewed on coupled M/NEMS resonators, mechanically and electrically, leading to collective behaviors like mode localization. The final part of the paper discusses analytical approaches that have been developed to better understand and investigate the dynamical behavior of M/NEMS resonators focusing on the perturbation method the multiple time scales.

Micromachined shallow arch resonant beams have attracted significant attention thanks to their rich dynamical behavior, inherent nonlinearities, and the potential to excite various internal resonances. Currently, there is a lack of comprehensive experimental studies for the various types of internal resonances in arches and particularly at the micro and nano scales. Here, we aim to investigate and identify different types of internal resonances of an initially curved beam, electrothermally actuated and electrostatically driven, by electrical characterization techniques. Upon changing the electrothermal voltage of silicon micromachined arches, the second symmetric natural frequency of an arch is adjusted to near twice, three times, and four times the fundamental natural frequency, which gives rise to 2:1, 3:1, and 4:1 autoparametric resonances between the two modes. These resonances are demonstrated experimentally. We show various frequency-response curves of the total response around the excitation frequency and highlight the contribution of each mode before, during, and after the internal resonances. Allandeviation results are also shown indicating enhanced frequency stabilization of the arch oscillation when experiencing internal resonances. These studies motivate further research in this direction to exploit internal resonances of micromachined resonators for practical applications, such as sensors and mechanical amplifier.

Quartz crystal microbalance (QCM) coated with poly-4-vinylpyridine (PVP) and metal organic framework HKUST-1 are investigated and compared for humidity sensing. Drop casting method is employed to coat the PVP and HKUST-1 solutions onto the surface of a quartz crystal microbalance. The resonance frequencies of these sensors with varying relative humidity (RH) from 22% RH to 69% RH are measured using impedance analysis method. The sensitivity, humidity hysteresis, response, and recovery times of these sensors are studied. The sensitivities of uncoated, PVP, and HKUST-1 coated QCM sensors are 7 Hz, 48 Hz, and 720 Hz, respectively, in the range of 22% RH-69% RH. The extraction of desorption rate and adsorption energy associated with the adsorption and desorption of water molecules on these surfaces reveals that HKUST-1 has better sensing properties than PVP and uncoated QCM sensors. In this work, the HKUST-1 coated QCM is shown to be a promising material for moisture detection.

There is an increasing interest to realize smarter sensors and actuators that can deliver a multitude of sophisticated functionalities while being compact in size and of low cost. We report here combining both sensing and actuation on the same device based on a single microstructure. Specifically, we demonstrate a smart resonant gas (mass) sensor, which in addition to being capable of quantifying the amount of absorbed gas, can be autonomously triggered as an electrical switch upon exceeding a preset threshold of absorbed gas. Toward this, an electrostatically actuated polymer microbeam is fabricated and is then functionalized with a metal-organic framework, namely, HKUST-1. The microbeam is demonstrated to absorb vapors up to a certain threshold, after which is shown to collapse through the dynamic pull-in instability. Upon pull-in, the microstructure can be made to act as an electrical switch to achieve desirable actions, such as alarming.

In this study, we demonstrate analytically and experimentally the excitations of the higher order modes of vibrations in electrostatically actuated clamped–clamped microbeam resonators. The concept is based on using partial electrodes with shapes that induce strong excitation of the mode of interest. The devices are fabricated using polyimide as a structural layer coated with nickel from the top and chrome and gold layers from the bottom. Experimentally, frequency sweeps with different electro-dynamical loading conditions are shown to demonstrate the excitation of the higher order modes of vibration. Using a half electrode, the second mode is excited with high amplitude of vibration compared with almost zero response using the full electrode. Also, using a two-third electrode configuration is shown to amplify the third mode resonance amplitude compared with the full electrode under the same electrical loading conditions. An analytical model is developed based on the Euler–Bernollui beam model and the Galerkin method to simulate the device response. Good agreement between the simulation results and the experimental data is reported.

We report a new gas sensing technique based on the simultaneous tracking of multiple modes of vibration of an electrothermally heated bridge resonator operated near the buckling point. The proposed technique maximizes the sensitivity of the sensor to changes in gases concentrations. We demonstrate a 200% frequency shift in contrast to 0.5% resistance change using the conventional resistive technique. The method also demonstrates selective identification for some gases without the need for surface functionalization of the microstructure. The proposed method is simple in principle and design and is promising for achieving practical low-cost gas sensors.

Using partial electrodes and a multifrequency electrical source, we present a large-bandwidth, large-amplitude clamped-clamped microbeam resonator excited near the higher order modes of vibration. We analytically and experimentally investigate the nonlinear dynamics of the microbeam under a two-source harmonic excitation. The first-frequency source is swept around the first three modes of vibration, whereas the second source frequency remains fixed. New additive and subtractive resonances are demonstrated. We illustrated that by properly tuning the frequency and amplitude of the excitation force, the frequency bandwidth of the resonator is controlled. The microbeam is fabricated using polyimide as a structural layer coated with nickel from the top and chromium and gold layers from the bottom. Using the Galerkin method, a reduced order model is derived to simulate the static and dynamic response of the device. A good agreement between the theoretical and experimental data are reported.

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