Stability analysis of two coupled pre-shaped beams in parallel

Parallel bistable mechanism rather than single bistable beam is preferred in micro devices like relays and resonators due to its higher stability in insensitive axis and higher robustness to fabrication errors. Its stability characteristics including nonlinearity and bistability or snap-through, however, rarely appear in current publications. The coupled mechanism constructed by two pre-shaped beams in parallel is investigated analytically and numerically in this paper. Based on the quasi-linearization of the problem and analytical equation of force and displacement, the dimension combinations of coupled beams are categorized into three types according to the apex amplitudes of cosine-shaped beams. It is concluded that the appearance of snap-through behaviors in parallel coupled mechanism is sustained by both arranging two bistable beams and making the apex difference meet condition of F_min < 0. The smallest values of minimum force only appears when the apexes are equal to each other, and any efforts to increase or decrease the apex of single beam will lead the nonlinear phenomenon from snap-through to constrained-snap-through and further to no snap-through. The numerical method is also introduced to observe the stability of coupled mechanism and shows a good agreement with analytical methods proposed by this paper.