Static analysis for multi-layered piezoelectric cantilevers

Taking the bonding layers and electrodes into account, the multi-layered piezoelectric cantilevers are studied based on the theory of elasticity. Different from the traditional investigations based on the elementary theory of elasticity, the Airy stress function method is used in the present paper. The stress function and induction function are proposed and determined, and then the exact solutions of the static governing equations are found. The material properties and thickness of different layers may be different in the present investigations. As two special cases, the exact static solutions for both unimorph and bimorph are directly obtained by using the present general solutions. The exact solutions obtained in the present paper are compared with the numerical results and others’ investigations, and good agreements are found. In addition, the effects of the properties of both bonding layers and electrodes are discussed. Moreover, the present solution can be used for function graded piezoelectric cantilever beams when the thickness of each bonding layer is taken as zero.