Abstract
The three-dimensional problem of free nonaxisymmetric vibrations of hollow piezoceramic cylinders with axial polarization is considered. An efficient numerical analytic method to solve boundary-value problems is proposed. The original three-dimensional problem of electroelasticity is reduced to a two-dimensional problem by representing the displacement components as standing circumferential waves. Spline collocation with respect to the axial coordinate is used to reduce this two-dimensional problem to an eigenvalue boundary-value problem with respect to the radial coordinate. This problem is solved by the stable discrete-orthogonalization and incremental-search methods. Numerical results are presented and the natural frequencies of the cylinders are analyzed in a wide range of their geometric characteristics
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