Nonlinear dynamic analysis of electrostatically actuated dual-axis micromirrors

Dual-axis micromirrors are considered as the crucial components used for light deflection and control, which can be employed for arbitrary-direction optical beam steering with a low operating voltage. In order to achieve large scanning angles with a low driving voltage and presenting high resolution and scanning speeds, micromirrors are excited at their corresponding resonance frequencies. In addition, a bias DC voltage is also provided in order to scan around a desired nonzero tilt angle. Therefore, a comprehensive understanding of the mirror’s response to a DC-shifted primary resonance excitations is crucial. In this study, various design conditions including the primary resonances and the feasibility of modal interaction in an electrostatically excitation are investigated, and also a parametric study is carried out in each case. We utilized the method of multiple scales to achieve a second-order nonlinear approximate analytical solution of the dual-axis micromirror steady-state response. We demonstrated that the response of the dual-axis micromirror shows a softening-type behavior that increases by increasing DC voltage and decreasing damping coefficient. Therefore, the effects of external damping and input voltages on the frequency response curves are also examined. The results showed that for a specific range of bias voltage and micromirror dimensions, one-to-one internal resonance occurs between the two torsional modes. Consequently, the energy fed to the first torsional mode may be channeled to the second mode, which leads to undesirable steady-state response. Therefore, internal resonance in the system leads to considerable degradation in the micromirror performance; accordingly, the designer needs to identify and control this phenomenon.