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.

Understanding the various mechanisms of nonlinear mode coupling in micro and nano resonators has become an imminent necessity for their successful implementation in practical applications. However, consistent, repeatable, and flexible experimental procedures to produce nonlinear mode coupling are lacking, and hence research into well-controlled experimental conditions is crucial. Here, we demonstrate well-controlled and repeatable experiments to study nonlinear mode coupling among micro and nano beam resonators. Such experimental approach can be applied to other micro and nano structures to help study their nonlinear interactions and exploit them for higher sensitive and less noisy responses. Using electrothermal tuning and electrostatic excitation, we demonstrate three different kinds of nonlinear interactions among the first and third bending modes of vibrations of slightly curved beams (arches): two-one internal resonance, three-one internal resonance, and mode veering (near crossing). The experimental procedure is repeatable, highly flexible, do not require special or precise fabrication, and is conducted in air and at room temperature. This approach can be applied to other micro and nano structures, which come naturally curved due to fabrication imperfections, such as CNTs, and hence lays the foundation to deeply investigate the nonlinear mode coupling in these structures in a consistent way.

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