On solutions of the equation of small transverse vibrations of a moving canvas
DOI:
https://doi.org/10.21638/spbu01.2022.214Abstract
The paper considers a model problem of one-dimensional small transverse vibrations of a canvas moving at a constant speed, which is fixed in a hinged manner. The oscillatory process is described by a linear differential equation of the 4th order with constant coefficients. In the model under consideration, the Coriolis force is taken into account, which leads to the appearance of a term with a mixed derivative in the differential equation. This effect makes it impossible to use the classical method of separating variables. However, families of exact solutions of the oscillation equation in the form of a traveling wave have been constructed. For the initial-boundary value problem, it was established that the solution can be constructed in the form of a Fourier series according to the system of eigenfunctions of the auxiliary problem on beam vibrations. For the considered oscillatory process, the law of conservation of energy is established and the uniqueness of the solution to the initialboundary value problem is proved.Keywords:
the equation of vibrations of a moving canvas, the law of conservation of energy, exact solutions
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Литература
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Published
2022-07-06
How to Cite
Romanenkov А. M. (2022). On solutions of the equation of small transverse vibrations of a moving canvas. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 9(2), 346–356. https://doi.org/10.21638/spbu01.2022.214
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Mechanics
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
