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JOURNALS // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika // Archive

Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2020 Number 2, Pages 3–8 (Mi vmumm4309)

This article is cited in 2 papers

Mathematics

Oscillation equation of a beam with fixed and pivotally supporter ends

I. A. Rudakov

Bauman Moscow State Technical University

Abstract: The problem of existence of periodic solutions of a quasilinear equation of forced oscillations of an I-beam whose one end is fixed and the second one is pivotally supported is studied. Properties of the differential operator are given and the theorem on the existence of a countable number of solutions is proved in the case the nonlinear term has a power growth.

Key words: equation of beam vibrations, periodic solutions, eigenvalues, Fourier series, variational method.

UDC: 517.956.35

Received: 07.02.2018


 English version:
Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2020, 75:2, 53–57

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