Equilibrium of a shallow arch subjected to PZT actuators and a deadweight load

The geometrically nonlinear response of a shallow, circular, cylindrical panel under a midspan line load and induced strain actuation is presented. The panel is a laminate of piezoelectric material perfectly bonded to the convex and concave surfaces of a core of passive material. Since the curved edges are free and the straight edges are pinned a fixed distance apart, the response of the panel is independent of the axial coordinate. Hence, the governing ordinary differential equations are of the same form as for a shallow circular arch. Without induced strain actuation, the panel exhibits snap-through behavior under the midspan load. Induced strain distributions are determined at a constant midspan load to displace the panel to an inverted configuration in a stable manner. This adaptive structure may find application as an electromechanical, nonlinear spring with a digital-like, load-displacement response characteristic.