Experimental and Theoretical Study of Two-to-One Internal Resonance of MEMS Resonators

In this paper, we investigate experimentally and theoretically the two-to-one (2:1) internal resonance between the first two symmetric vibrational modes of microelectromechanical (MEMS) arch resonator electrothermally tuned and electrostatically driven. Applying electrothermal voltage across the beam anchors controls its stiffness and then its resonance frequencies. Hence the ratio between the two frequencies can be tuned to a ratio of two. Then, we study the dynamic response of the arch beam during internal resonance. In the studied case, the presence of high AC bias excitation leads to the direct simultaneous excitation of the 1st and 3rd frequencies in addition to the activation of the internal resonance. A reduced order model and perturbation techniques are presented to analyze the nonlinear response of the structure. In the perturbation technique, the direct excitation of the 3rd resonance frequency is taken into consideration. Results show the presence of Hopf bifurcations, which can lead to chaotic motion at higher excitation. A good agreement among the theoretical and experimental results is shown.