Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
823531 | Comptes Rendus Mécanique | 2015 | 6 Pages |
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).
Keywords
Related Topics
Physical Sciences and Engineering
Engineering
Engineering (General)
Authors
Timur R. Gadyl'shin,