SEVERAL ANALYTICAL SOLUTIONS FOR A FUNCTIONALLY GRADIENT PIEZOELECTRIC CANTILEVER

A piezoelectric cantilever subjected to a uniform loading or a voltage on the upper surface of the beam is studied. The density of the beam is considered to be of functionally gradient properties. By use of the inverse method or semi-inverse method, the stress functions and induction functions in the form of polynomials for the problem are found. Based on these functions the analytical solutions of the FGM cantilever are obtained. The uniform loading is applied axially and laterally on the upper surface or is a voltage. Finally, as particular cases, the solutions of a piezoelectric cantilever with constant body force as well as without body force are obtained.