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

Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2019 Number 5, Pages 61–65 (Mi vmumm3631)

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Action of moving loads on the Bernoulli–Euler and Timoshenko beams

T. I. Zhdan

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A dynamic behavior of Bernoulli–Euler and Timoshenko beams subjected to a moving concentrated load is considered. A solution of this problem is found and analyzed in the form of a convergent series in the case of a stretched beam and a beam lying on an elastic foundation. The parameter ranges where the results of these two models are coincident are found. It is shown that, under certain conditions, a resonance is possible in such a system.

Key words: elastic foundation, resonance, Bernoulli–Euler model, Timoshenko model, bending moment, moving load.

UDC: 531

Received: 11.03.2018


 English version:
Moscow University Mathematics Bulletin, Moscow University Måchanics Bulletin, 2019, 74:5, 123–127

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