The Stability Analysis For The Cosine Beams Coupled In Parallel

Bistable mechanisms are key components of many devices, such as micro-switches, micro-relays, micro-actuators, and so on. One advantage of such mechanisms is that they can apply a contact force without the need for continued actuation power. A cosine curved clamped-clamped beam without prestress as a typical bistable mechanism is more easily to manufacture than a compressed bistable beam. Based on energy method and finite element method(FEM), this thesis researches the snap-through behavior of the cosine curved clamped-clamped beam and structure of two cosine beams coupled in parallel. Constraining the asymmetric mode will impact the bistable behavior of the cosine curved clamped-clamped beam. For the mechanism of two cosine shaped beams coupled in parallel, the variation of the beams’ initial apex heights and the thicknesses would affect the bistable behavior of the structure. The main contents are: 1. The methods of stability analysis for the micro-structure are summarized. Based principle of minimum potential energy, the method of using force-displacement curve to analyze the stability of a mechanism is elucidated. 2. For a single cosine curved beam, theoretical and finite-element analyses are applied to obtain the force-displacement curve. According to the f-d curve, the influence of geometric parameters on the structural stability is discussed. Comparing with a cosine curved free of mode constrained, the cosine beam which of asymmetric mode is constrained is more likely to be bistable on the same condition of geometric parameters. In the meantime, the reason of bistable phenomenon is analyzed from the point of potential energy. 3. For the mechanism of two cosine shaped beams coupled in parallel, when the thickness of two beams is the same, the combinations of the structure can be divided into three kinds according to the height of arc. The bistable behavior of the structure in each case is analyzed. Under the same condition of the height of arc, how the variation of the beams’ thickness affect the displacement of the minimum transverse force is analyzed.