SOLUTION OF THE PROBLEM OF NONAXISYMMETRIC FREE VIBRATIONS OF PIEZOCERAMIC HOLLOW CYLINDERS WITH AXIAL POLARIZATION

摘要

We consider the nonaxisymmetric problem of free vibrations of hollow piezoceramic cylinders for some types of boundary conditions at their end faces. The piezoceramics is polarized in the axial direction. The cylinder lateral surfaces are free from external loads and covered with thin electrodes that are short-circuited. The initial three-dimensional problem is reduced to two-dimensional after separation of vari-ables and representation of the components of the displacement vector and electrostatic potential in the form of standing waves in the circumferential direction. The method of solution of the problem is based on the joint use of the spline-collocation method along the longitudinal coordinate and the method of discrete orthogonalization combined with step-by-step search by the radial coordinate. We also present some results of numerical analysis of the behavior of a cylinder made of PZT 4 piezoceramics over a wide range of changes in the geometrical characteristics of the cylinder.