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.

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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.