Stability Analysis of Initially Curved Beams Mechanically Coupled in a Parallel Arrangement

This paper investigates the stability behavior of a mechanically coupled bi-stable mechanism made of two parallel and initially curved microbeams with focus on the influence of the coupled beams' initial curvatures on the system. First, the nonlinear and coupled force-displacement equation is derived. Then, a parametric study of the coupled beams system is studied with the system categorized into different structural compartment types according to the initial curvature of the coupled beams. It is concluded that the snap-through of such a coupled bi-stable system is governed by the beams' initial curvatures difference. The simulation results showed that these two parameters (the beams' initial curvatures) essentially govern the structural behavior of the coupled system in satisfying the necessary structural stability condition. It is found that the smallest (critical) value of the minimum force amplitude occurs only when both initial beams' mid-point elevations are equal to each other. Furthermore, it is shown that any probability to increase or decrease the curvature of any beam will alter the nonlinear behavior of the coupled beam system from a simple regular snap-through to a constrained-snap-through, and even to the disappearance of the snap-through. Finally, a finite element method is conducted to investigate the stability of the coupled mechanism, of which the results show a good agreement with the analytical results of this paper.