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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2015, Number 5, Pages 23–33
(Mi vmumm263)
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This article is cited in 1 scientific paper (total in 1 paper)
Mechanics
Limit equations of motion for mechanical systems with vibrating elements
A. A. Markeevaa, M. A. Levinb a "Dantai"
b Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
This paper studies mechanical systems with rapidly oscillating elements. We suggested a method to obtain limiting equations of such systems when the oscillation frequency tends to infinity. We considered a mechanical system with an arbitrary number of degrees of freedom subject to rapid periodic vibrations with zero mean. Its motion can be described by second-order equations. Also we obtained an explicit form of the limiting equations of motion written in the form of a system of first-order differential equations.
Key words:
mechanical systems with vibrating elements, limiting equations, convergence of solutions, pendulum with a vibrating suspension point.
Received: 21.03.2014
Citation:
A. A. Markeeva, M. A. Levin, “Limit equations of motion for mechanical systems with vibrating elements”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2015, no. 5, 23–33; Moscow University Mechanics Bulletin, 70:5 (2015), 112–121
Linking options:
https://www.mathnet.ru/eng/vmumm263 https://www.mathnet.ru/eng/vmumm/y2015/i5/p23
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