Geodesic
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
Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 4, pp. 48-68

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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 involved are 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.
Keywords: equation of transverse vibrations of a beam, layer-by-layer recalculation. . 
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     author = {A. L. Karchevsky},
     title = {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},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {48--68},
     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2020_23_4_a3/}
}
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A. L. Karchevsky. 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. Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 4, pp. 48-68. http://geodesic.mathdoc.fr/item/SJIM_2020_23_4_a3/