Internal resonance between the extensional and flexural modes in micromechanical resonators

Abstract

Internal resonance between different vibration modes in micromechanical devices has been widely studied due to its promising application prospects in microelectromechanical systems (MEMS) resonators and oscillators. In this paper, we investigated the 2:1 internal resonance between the extensional and flexural modes in a micromechanical cantilever beam resonator using open and closed loop testing methods. In the open loop test, energy transfer from the extensional mode to the flexural mode induced by internal resonance is directly observed. Amplitude saturation and internal resonance bandwidth change in the extensional mode are experimentally studied and theoretically verified with numerical simulation. In the closed loop system, internal resonance produces a bistable self-oscillation frequency. The oscillation frequency of the extensional mode will be locked to one of the two peaks induced by internal resonance. In addition, obvious improvement in short-term frequency stability of the closed loop system is observed with the help of internal resonance. The dynamic characteristics studied in this research can be potentially used to enhance the performance of MEMS vibration devices by internal resonance.