Piezoelectrically induced snap-through buckling in a buckled beam bonded with a segmented actuator

Abstract

In this article, a mathematical model is developed to analyze piezoelectrically induced deformations of bistable smart beams with various geometric configurations and boundary conditions. The model delineates a straight beam bonded with a segmented piezoelectric material. Three types of support conditions are considered, namely, simple, clamped–clamped, and clamped–pinned supports. The beam is buckled into two possible stable curved shapes by means of edge shortening compression. A sudden change in transverse deflection from one to the other stable shape, so-called snap-through action, can be stimulated by electrical activation given to the piezoelectric material. The minimum potential energy principle associated with the modified Ritz method is used to predict developing shapes of the smart beam and the snap-through voltage. Principal minors of bordered Hessian matrix are calculated to determine the stability of the shapes obtained. Experiments were also conducted to corroborate the computational results in the case of the simply-supported smart beam. Comparisons between the two approaches reveal very good agreements in both mid-span displacements of buckled shapes and snap-through voltages. Finally, size and location of the segmented piezoelectric actuator are varied to search for the minimum critical electrical field for each support condition.