We experimentally demonstrate an exploitation of the nonlinear softening, hardening, and veering phenomena (near crossing), where the frequencies of two vibration modes get close to each other, to realize a bandpass filter of sharp roll off from the passband to the stopband. The concept is demonstrated based on an electrothermally tuned and electrostatically driven MEMS arch resonator operated in air. The in-plane resonator is fabricated from a silicon-on-insulator wafer with a deliberate curvature to form an arch shape. A DC current is applied through the resonator to induce heat and modulate its stiffness, and hence its resonance frequencies. We show that the first resonance frequency increases up to twice of the initial value while the third resonance frequency decreases until getting very close to the first resonance frequency. This leads to the phenomenon of veering, where both modes get coupled and exchange energy. We demonstrate that by driving both modes nonlinearly and electrostatically near the veering regime, such that the first and third modes exhibit softening and hardening behavior, respectively, sharp roll off from the passband to the stopband is achievable. We show a flat, wide, and tunable bandwidth and center frequency by controlling the electrothermal actuation voltage.

We investigate experimentally and analytically the effect of initial shapes, arc and cosine wave, on the static and dynamic behavior of microelectromechanical systems (MEMS) arch resonators. We show that by carefully choosing the geometrical parameters and the initial shape of the arch, the veering phenomenon (avoided-crossing) among the first two symmetric modes can be strongly activated. To demonstrate this, we study electrothermally tuned and electrostatically driven initially curved MEMS resonators. Upon changing the electrothermal voltage, we demonstrate high frequency tunability of arc resonators compared to the cosine-configuration resonators for the first and third resonance frequencies. For arc beams, we show that the first resonance frequency increases up to twice its fundamental value and the third resonance frequency decreases until getting very close to the first resonance frequency triggering the veering phenomenon. Around the veering regime, we study experimentally and analytically the dynamic behavior of the arc beam for different electrostatic loads. The analytical study is based on a reduced order model of a nonlinear Euler-Bernoulli shallow arch beam model. The veering phenomenon is also confirmed through a finite-element multi-physics and nonlinear model.

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.