Comptes Rendus
no. 9
On the vibrations of a string with a concentrated mass and rapidly oscillating density
Timur R. Gadyl'shin1
1 Ufa State Aviation Technical University, Karl Marx st., 12, Ufa 450000, Russia
Comptes Rendus. Mécanique, Volume 343 (2015) no. 9, pp. 476-481.

The paper is devoted to the vibrations of a string I with a concentrated mass ε−1ϰQ(ε−1x) and rapidly oscillating density q(x,μ−1x), where q(x,ζ) is a 1-periodic in ζ function, Q(ξ) is a function with compact support, the integral of which is equal to one, 0∈I, μ,ε are small positive parameters, ϰ∈R. By combining homogenization and the method of matched asymptotic expansions, we construct solutions to the problems up to O(ε+μ).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2015.08.001
Mots clés : Vibration of a string, Rapidly oscillating density, Concentrated mass, Homogenization, Method of matched asymptotic expansions
Timur R. Gadyl'shin 1

1 Ufa State Aviation Technical University, Karl Marx st., 12, Ufa 450000, Russia 
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Timur R. Gadyl'shin. On the vibrations of a string with a concentrated mass and rapidly oscillating density. Comptes Rendus. Mécanique, Volume 343 (2015) no. 9, pp. 476-481. doi : 10.1016/j.crme.2015.08.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2015.08.001/

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