Axisymmetric boundary condition problems for transversely isotropic piezoelectric materials

This paper presents an exact analysis of deformation and stress field in a finite cylinder under axisymmetric boundary conditions. The problem is formulated based on the state space formulation for transversely isotropic piezoelectric media. Upon the separation of variables method, we get a set of general solutions spanning over the complete solution space to cover all axisymmetric boundary conditions. Furthermore, a rigorous solution which satisfies the end conditions is determined by using eigenfunction expansion. Numerical results show that the local effect is significant but confined to boundary layer near the fixed end where the displacement and stress are remarkably different from those of other regions.