Geodesic
Dynamic problem for a thin-walled bar with a monosymmetric profile
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 26 (2020) no. 2, pp. 63-69

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The paper presents an analytical solution to the dynamic problem for a thin-walled elastic rod, the cross-section of which has one axis of symmetry. The solution is constructed for an arbitrary dynamic load and two types of boundary conditions: hinged support in constrained torsion and free warping of the end sections of the rod; rigid fastening with constrained torsion and absence of warping. The peculiarity of the mathematical model lies in the fact that the differential equations of motion contain a complete system of inertial terms. Spectral expansions obtained as a result of using the method of integral transformations are represented as an effective method for solving linear non-stationary problems in mechanics. The structural algorithm of the method of finite multicomponent integral transformations proposed by Yu.E. Senitsky is used.
Keywords: thin-walled bar, symmetric profile, boundary value problem, dynamic load, natural vibrations, natural vibration frequency, forced vibrations, integral transformations. 
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     author = {T. B. Elekina and E. S. Vronskaya},
     title = {Dynamic problem for a thin-walled bar with a monosymmetric profile},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {63--69},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2020_26_2_a4/}
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T. B. Elekina; E. S. Vronskaya. Dynamic problem for a thin-walled bar with a monosymmetric profile. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 26 (2020) no. 2, pp. 63-69. http://geodesic.mathdoc.fr/item/VSGU_2020_26_2_a4/