Effect of Initial Curvature on the Static and Dynamic Behavior of MEMS Resonators

In this paper, we investigate experimentally and analytically the effect of the initial shape, arc and cosine wave, on the static and dynamic behavior of microelectromechanical (MEMS) resonators. We show that by carefully choosing the geometrical parameters and the shape of curvature, the veering phenomenon (avoided-crossing) between the first two symmetric modes can be activated. To demonstrate this concept, we study electrothermally tuned and electrostatically driven MEMS initially curved resonators. Applying electrothermal voltage heats up the beams and then increases their curvature (stiffness) and controls their resonance frequencies. While 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, using a reduced order model based on a nonlinear Euler-Bernoulli shallow arch beam model, the dynamic behavior of the arc beam for different electrostatic forcing.