Article ID Journal Published Year Pages File Type
823531 Comptes Rendus Mécanique 2015 6 Pages PDF
Abstract

The paper is devoted to the vibrations of a string I   with a concentrated mass ε−1ϰQ(ε−1x)ε−1ϰQ(ε−1x) and rapidly oscillating density q(x,μ−1x)q(x,μ−1x), where q(x,ζ)q(x,ζ) is a 1-periodic in ζ   function, Q(ξ)Q(ξ) is a function with compact support, the integral of which is equal to one, 0∈I0∈I, μ,εμ,ε are small positive parameters, ϰ∈Rϰ∈R. By combining homogenization and the method of matched asymptotic expansions, we construct solutions to the problems up to O(ε+μ)O(ε+μ).

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Physical Sciences and Engineering Engineering Engineering (General)
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