Vibration and Snap-Through of Bent Elastica Strips Subjected to End Rotations

A flexible strip is rotated at its ends until it forms a deep circular arc above its ends. Then the ends are kept immovable and are rotated downward until the arch suddenly snaps into an inverted configuration. The strip is analyzed as an inextensible elastica. Two-dimensional equilibrium shapes, vibration modes and frequencies, and critical rotations for snap-through are determined using a shooting method. Experiments are also conducted and results are compared with those from the analysis. The agreement is good. In addition, a microelectromechanical systems (MEMS) example is analyzed, in which an electrostatic force below a buckled strip causes the strip to snap downward, and the critical force is obtained as a function of the vertical gap.