Cylindrical Bending of Laminated Plates with Distributed and Segmented Piezoelectric Actuators / Sensors

The generalized plane quasistatic deformations of linear piezoelectric laminated plates are analyzed by the Eshelby–Stroh formalism. The laminate consists of homogeneous elastic or piezoelectric laminae of arbitrary thickness and width. The three-dimensional differential equations of equilibrium for a piezoelectric body are exactly satisŽ ed at every point in the body. The analytical solution is in terms of an inŽ nite series; the continuity conditions at the interfaces between adjoining laminae and boundary conditions at the edges are satisŽ ed in the sense of Fourier series. The formulation admits different boundary conditions at the edges and is applicable to thick and thin laminated plates. Results are presented for laminated elastic plates with a distributed piezoelectric actuator on the upper surface and a sensor on the lower surface and subjected to different sets of boundary conditions at the edges. Results are also provided for a piezoelectric bimorph and an elastic plate with segmented piezoelectric actuators bonded to its upper and lower surfaces.