A note on the static behavior of simply-supported laminated piezoelectric cylinders

An exact three-dimensional solution of the equations of linear piezoelectricity is given for the static response of a finite laminated piezoelectric cylinder with its ends simply supported. The equilibrium equations and the conservation of charge equation are constructed in cylindrical coordinates. The three displacement components and the electrostatic potential are expressed in terms of Fourier series in the axial and circumferential directions, leading to a coupled system of four ordinary differential equations in the radial coordinate. The Frobenious method is used to obtain the elastic and electric fields for each layer of the laminate, which are a function of eight constants. Enforcing the boundary and continuity conditions across each interface yields the required number of equations to solve for these constants. Several examples are presented to study the fundamental behavior of these solids. (C) 1997 Elsevier Science Ltd.