On a tunable bistable MEMS - Theory and experiment

A tunable micromechanical bistable system is presented in this paper, It consists of a long slender micromechanical beam attached to an actuator, The beam is subjected to a transverse force at the middle and a residual stress developed during fabrication. The actuator generates a force along the axial direction of the beam, and is shared by the beam and springs of the actuator, If the total axial load on the beam is compressive and exceeds a critical value, then the beam buckles along the transverse direction and it has two possible equilibrium states. Thus, the actuator and beam together become a bistable system. An analytical model is presented to characterize the system. The model is based on the first mode of buckling of the beam. The model accounts for the elastic axial shortening of the beam and the nonlinear coupling between the beam and actuator, The main result of this paper is a closed-form relation between the transverse force and corresponding equilibrium transverse displacement of the beam for a given actuator force. It shows that the transverse stiffness of the beam decreases linearly with the actuator force (when compressive) until it reaches zero at the critical buckling load. After buckling, the stiffness about the buckled state increases linearly with the axial force. The rate of increase is twice that of decrease. The potential energy of the system after buckling becomes quartic, and the system can be switched from one buckled state to the other by a threshold transverse force, which increases linearly with the cube of the buckled displacement. Depending on the level of tuning by the actuator and a prescribed transverse force, the threshold force can be on the order of pN (10(-12)N)s and the state change may involve a displacement on the order of 10 mu m, The time of flight during state change is also derived, An experimental micromechanical device is designed and fabricated to verify the theoretical model. Excellent correspondence is found between theory and experiment, as if the experimental device emulates the mathematical model, which is an important result of this paper, since now experimental studies, both quasi-static and dynamic, of bistable systems are possible, which are otherwise difficult to conduct with macrosystems. Several examples of possible applications of the bistable system are provided, including digital sensing of physical parameters. Bistable systems also show attractive potential to be used as data storage and memory elements, as well as optomechanical computing elements.