Snap-through of a bistable beam using piezoelectric actuators: modeling and optimization

In the study, we report the snap-through effect of a bistable beam by means of piezoelectric actuators. We first consider a bistable mechanism consisting of a buckled elastic thin beam. The latter is symmetrically equipped with two piezoelectric layers. The electric potential applied on the faces of the piezoelectric actuators is such as a moment at each end of the active layers is produced. The modeling of the elastic beam is based on the elastica theory. The main goal of the study is the investigation of the bistable response according to the applied electric voltage and the configurational parameters. A numerical study is proposed based on the equation of the beam model sandwiched by two piezoelectric layers, and a numerical validation of the model approach is performed using the finite element method. An optimization study is reported for the placement of the piezoelectric actuators as well as their dimensions (length and thickness). We look for the position of the piezoelectric actuators that minimizes the applied voltage to trigger the snap-through and maximize the beam deflection. The work is extended to the bistable actuation using two pairs of piezoelectric elements.