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Determining the natural frequencies of an elastic parallelepiped by the advanced Kantorovich–Vlasov method

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International Applied Mechanics Aims and scope

An approach to calculate the natural frequencies of an elastic parallelepiped with different boundary conditions is proposed. The approach rationally combines the inverse-iteration method of successive approximations and the advanced Kantorovich–Vlasov method. The efficiency of the approach (the accuracy of the results and the number of approximating functions) is demonstrated against the Ritz method with different basis systems, including B-splines. The dependence of the lower frequencies of a three-dimensional cantilever beam on its cross-sectional dimensions is examined

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Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov St., Kyiv, Ukraine, 03057

    E. I. Bespalova

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  1. E. I. Bespalova
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Correspondence to E. I. Bespalova.

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Translated from Prikladnaya Mekhanika, Vol. 47, No. 4, pp. 76–88, July 2011.

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Bespalova, E.I. Determining the natural frequencies of an elastic parallelepiped by the advanced Kantorovich–Vlasov method. Int Appl Mech 47, 410–421 (2011). https://doi.org/10.1007/s10778-011-0467-9

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  • DOI: https://doi.org/10.1007/s10778-011-0467-9

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