Vibration of infinite piezoelectric cylinders with anisotropic properties using cylindrical finite elements

Natural frequencies for free vibration of infinite piezoelectric cylinders are computed using finite elements that are formulated in cylindrical coordinates. The finite-element method is used to model the cross-section of the cylinder in r, theta coordinates using circular sectors. Material constants that are functions of theta are allowed to vary in each circular sector and are computed using standard tensor transformations. The accuracy of the finite-element formulation is verified using previous results for isotropic cylinders and axisymmetric piezoelectric cylinders. New results are tabulated for frequencies of free vibration of solid and hollow piezoelectric cylinders of LiNbO(3) of crystal class 3m. Displacements for typical mode shapes are illustrated graphically.