Analytical Modeling for Rapid Design of Bistable Buckled Beams

Wenzhong Yan, Yunchen Yu, Ankur Mehta

Double-clamped bistable buckled beams, as the most elegant bistable mechanisms, demonstrate great versatility in various fields, such as robotics, energy harvesting, and MEMS. However, their design is always hindered by time-consuming and expensive computations. In this work, we present a method to easily and rapidly design bistable buckled beams subjected to a transverse point force. Based on the Euler-Bernoulli beam theory, we establish a theoretical model of bistable buckled beams to characterize their snap-through properties. This model is verified against the results from an FEA model, with discrepancy less than 7 %. By analyzing and simplifying our theoretical model, we derive explicit analytical expressions for critical behavioral values on the force-displacement curve of the beam. These behavioral values include critical force, critical displacement, and travel, which are generally sufficient for characterizing the snap-through properties of a bistable buckled beam. Based on these analytical formulas, we investigate the influence of a bistable buckled beam's key design parameters, including its actuation position and precompression, on its critical behavioral values, with our results validated by FEA simulations. This way, our method enables fast and computationally inexpensive design of bistable buckled beams and can guide the design of complex systems that incorporate bistable mechanisms.

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