Axisymmetric Free Vibration of Functionally Graded Piezoelectric Circular Plates

An analytical solution is presented for axisymmetric free vibration analysis of a functionally graded piezoelectric circular plate on the basis of the three-dimensional elastic theory of piezoelectric materials. The material properties are assumed to follow an exponential law distribution through the thickness of the circular plate. The state space equations for the free vibration behavior of the functionally graded piezoelectric circular plate are developed based on the state space method. The finite Hankel transform is utilized to obtain an ordinary differential equation with variable coefficients. By virtue of the proposed exponential law model, we have ordinary differential equations with constant coefficients. Then, the free vibration behaviors of the functionally graded piezoelectric circular plate with two kinds of boundary conditions are investigated. Some numerical examples are given to validate the accuracy and stability of the present model. The influences of the exponential factor and thickness-to-span ratio on the natural frequency of the functionally graded piezoelectric circular plate, constrained by different boundary conditions, are discussed in detail.