Description of snap-through instability in curved beams for millimeter scale actuation
In microelectromechanical systems (MEMS), engineers must accurately predict the nonlinear response of thin post-buckling beams, especially the nonlinear transverse stiffness. The bistability of post-buckling beams can significantly reduce the power required to run microdevices or microsystems. However, the intractable geometric nonlinear control equations for large deflection beams make it difficult to analyse post buckling and snap-through reactions. Improved dynamic behaviour can be produced by manipulating nonlinear interactions of suspended mechanical parts. This increases the dynamic range and control of snap-through. To actuate displacement, we show how curved, doubly clamped, bistable micromechanical beams interact with a zipping boundary condition. That affects both nonlinear electrostatic interactions and the effective stiffness of the curved beam. Better control can be achieved by actively adjusting the beam near the start of snap-through bistability. This method could be used in MEMS actuators and soft robots. In this project, the key steps involve defining the geometry, developing a mathematical model, assuming a basic form of solution and iterating the solutions in MATLAB®. Preliminary expectations of results from the study are to obtain the beam states, bifurcation diagram for varied control parameters and estimation of transient behaviour. However, the work needs to be further validated with experiments that could provide more insights to analytical results. The results of the numerical solutions of the mathematical model demonstrate that the curved beam will automatically snap to the opposite equilibrium position whenever the zipping length is greater than the critical value. The accurate configurations of the post-buckling curved beam with various zipping configurations are presented during the snap-through process. According to our analysis, it was discovered that the nonlinear stiffness decreases as the zipping length increases.