| A stacked structure consisting of two beam-plates, each being a different piezoelectric material, subject to a uniformly increasing electric field is analyzed. One beam-plate is perfectly adhered over the central portion of the other. We consider the limiting boundary conditions for the bottom layer, the baseplate: clamped-fixed and hinged-fixed boundaries. A quasi-static analysis is performed, in which a geometrically nonlinear strain-displacement relation is incorporated to account for infinitesimal strain, while allowing for moderate rotation of the structure. The strain energy of the stacked structure is formulated, and the governing equations, constitutive relations, and boundary and matching conditions are derived self-consistently after invoking the Theorem of Stationary Potential Energy. Stability is assessed through evaluation of the second variation of the PE under perturbation. A closed form analytical solution is obtained, and numerical simulations based on these solutions are presented. It is shown that, for certain combinations of piezoelectric materials and orientations of the applied increasing electric field, the structure will exhibit sling-shot buckling---an instability where the orientation of the deflection of the structure will dynamically change when a critical electric field and critical membrane force are reached. These critical values are identified from the analytical equations. A parameter study shows how the critical values depend on various geometric and material properties of the structure. |
