Free axisymmetric vibration of transversely isotropic piezoelectric circular plates

Based on three!dimensional elastic theory of piezoelectric materials\ the axisymmetric state space for! mulation of piezoelectric laminated circular plates is derived[ Finite Hankel transforms are used and the boundary variables in free terms are replaced\ for two kinds of boundary conditions\ to obtain ordinary di}erential equations with constant coe.cients[ Regarding the axisymmetric free vibration problem\ two exact solutions for two di}erent boundary conditions are found[ Discarding piezoelectric e}ect\ the exact solutions for transversely isotropic circular laminates are also obtained through the same procedure[ Numeri! cal examples are given and compared with those of Finite Element Method "FEM