Abstract: Based on the generalized variation principles and the bi-stable characteristics of a post-buckling beam, the nonlinear relationship between the transversal force and displacement is deduced by considering the effects of axial compression on the beam length constraint. The analytical expression for the transverse force is obtained by using the meromorphic function method. The nonlinear coupled relations among the transverse critical force, the axial compression and the buckling modes are also analyzed by utilizing the assumed buckling mode method. With the deduction above, the transverse forces for different arc heights of the pre-stressed buckling beam are given while the second bifurcation buckling occurs during the snap-through process. Simulation results are in good agreement with those from experiments and numerical methods, and hence, it can find applications in designing the MEMS bistable device.

Key words: micro-electronic mechanic system, bistability, buckling mode, nonlinear snap-through, generalized variation principle