A problem on natural non-axisymmetrical vibrations of hollow piezoceramic cylinders with radial polarization is considered. To solve this problem, the effective numerical-analytical method is proposed. The initial three-dimensional problem of the theory of udelectroelasticity is reduced to the twodimensional one by use of representation of vector uddisplacement components in the form of standing waves in the circumferential direction. Using the method of spline-collocations in the direction of axial coordinate, the two- dimensional problem in hand is reduced to the boundary value problem in direction of radial coordinate. The last problem is solved by the stable method of discrete orthogonalization together with the step-by-step method. The results of numerical analysis of frequencies of natural vibrations in the wide range of changing the geometrical characteristics of piezoceramic cylinders are given.
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