Free vibrations of piezoceramic hollow cylinders with radial polarization

We consider an axisymmetric problem of free longitudinal vibrations of hollow piezoelectric cylinders for some types of boundary conditions on the end faces. The piezoceramic material is polarized in the radial direction. The side faces of a cylinder are covered with short-circuited thin electrodes. The method of solution of the problem is based on the combination of the spline collocation method along the longitudinal coordinate and the step-by-step search method along the radial coordinate. We present results of a numerical analysis of a cylinder of PZT 4 ceramic in a wide range of changes in the geometric parameters of the cylinder. © 2011 Springer Science+Business Media, Inc.