Supplementary materials for "Fourier Series based Analytic Model of a Resonant MEMS Mirror for General Voltage Inputs"

Description:

1. Movie "movie_S1.avi" demonstrates the normalized absolute element values of dynamic influence matrices and its scaled matrices by comb drive torque along the amplitude. The dynamic influence matrices are plotted according to the comb drive frequency component, index n, and the input frequency component, index m. The absolute values of the elements of the matrix are normalized by its maximum element. The maximum element is drawn in white and the normalized elements less than 10e−6 of the maximum element are depicted in black.

2. Movie "movie_S2.avi" illustrates the evolution of phase portraits with 60 V peak input voltage and 0.5 duty cycle by sweeping up actuation frequencies. The stationary solutions are drawn by the amplitude-phase plot (thick light blue colored lines). Frequency-amplitude response and frequency-phase response at the right side provide a link to stationary solutions at the operational frequency. From initial conditions (circles) the slow flow dynamics lead to the stable equilibria (blue squares) while the unstable equilibria are given by blue x marks. The color of the trajectory represents its final steady state value, i.e. if it arrives at the solution of the top response curve (red), of the bottom response curve (light blue), or the trivial solution of no oscillation (light gray).
The initial conditions of amplitudes and phases are defined by amplitude of 0.001 and 0.708 and phases kπ/6, k in (0, 1, · · · , 5) where the initial amplitude of 0.001 approximates the mirror with zero amplitude.