科研之友
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摘要
Functionally graded and laminated piezoelectric cantilever actuators are investigated. Each material parameter of the functionally graded actuator can be an arbitrary continuous function of the thickness coordinate of the beam, while the property of each layer in the laminated actuator is uniform. Piezoelectricity solutions for the two actuators subjected to a constant electric potential difference are presented. Firstly, the partial differential equations for the plane problem of functionally graded piezoelectric materials, which govern the stress function and electric displacement function, are derived. Secondly, the stress function is assumed to be an undetermined function of the thickness coordinate, and the electric displacement function is assumed as a linear function of the longitudinal coordinate. In such a case, the stress and electric displacement function can be acquired through successive integrations. The analytical expressions of axial force, bending moment, shear force, displacements, electric displacements and electric potential are then deduced. The analytical solutions are finally obtained, with the integral constants completely determined from the boundary conditions. Comparisons of the present analytical solutions with beam theory, finite element method and experiments indicate that the analytical solutions are effective and exact, while certain deviations of the beam theory can be found.
