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Analytical Solutions to the Differential Equation of Transverse Vibrations of a Piecewise Homogeneous Beam in the Frequency Domain for the Boundary Conditions of Various Types

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Abstract

We obtain an analytical solution for the differential equation of transverse vibrations of a piecewise homogeneous beam in the frequency domain for various types of boundary conditions. All calculations use only addition, multiplication, and inversion of square matrices of second order. The formulas are such that, when using them for layer-by-layer recalculation, the rounding error does not accumulate since the exponential functions in some expressions have exponents with nonpositive real parts.

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Funding

The author was supported by the State Task to the Sobolev Institute of Mathematics (project no. 0314–2019–0011).

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  1. Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia

    A. L. Karchevsky

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  1. A. L. Karchevsky
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Correspondence to A. L. Karchevsky.

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Translated by B.L. Vertgeim

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Karchevsky, A.L. Analytical Solutions to the Differential Equation of Transverse Vibrations of a Piecewise Homogeneous Beam in the Frequency Domain for the Boundary Conditions of Various Types. J. Appl. Ind. Math. 14, 648–665 (2020). https://doi.org/10.1134/S1990478920040043

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