The problem of the free axisymmetric vibrations of longitudinally polarized piezoceramic hollow cylinders is solved by a numerical analytic method. The spline-collocation method with respect to the longitudinal coordinate is used to reduce the original problem of electroelasticity to an eigenvalue boundary-value problem for ordinary differential equations 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 for a wide range of their geometric characteristics
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Translated from Prikladnaya Mekhanika, Vol. 46, No. 6, pp. 17–26, June 2010.
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Grigorenko, A.Y., Efimova, T.L. & Loza, I.A. Free vibrations of axially polarized piezoceramic hollow cylinders of finite length. Int Appl Mech 46, 625–633 (2010). https://doi.org/10.1007/s10778-010-0350-0
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DOI: https://doi.org/10.1007/s10778-010-0350-0