Investigations into the linear coupling between symmetric and anti-symmetric modes of v-shaped mems resonators under electrostatic perturbation

In this paper, we investigate experimentally and theoretically the linear coupling between the first two symmetric and anti-symmetric modes of an electrothermally and electrostatically actuated in-plane V-shaped micro-beam. The micro-beam is fabricated from highly doped silicon and is sandwiched between four electrodes to electrostatically activate both modes of vibrations. When tuning the electrothermal voltage, the natural frequencies of the two modes approach each other until they cross. Under electrostatic actuation, it is shown experimentally that the system undergoes a transition between modes crossing to veering. In addition, an analytical study is presented based on a Galerkin-based reduced-order model of a nonlinear Euler–Bernoulli shallow arch beam equation. The analytical results are compared to experimental data showing excellent agreement.