General solution of a density functionally gradient piezoelectric cantilever and its applications

We have used the plane strain theory of transversely isotropic bodies to study a piezoelectric cantilever. In order to find the general solution of a density functionally gradient piezoelectric cantilever, we have used the inverse method (i.e. the Airy stress function method). We have obtained the stress and induction functions in the form of polynomials as well as the general solution of the beam. Based on this general solution, we have deduced the solutions of the cantilever under different loading conditions. Furthermore, as applications of this general solution in engineering, we have studied the tip deflection and blocking force of a piezoelectric cantilever actuator. Finally, we have addressed a method to determine the density distribution profile for a given piezoelectric material.