On the vibrations of a string with a concentrated mass and rapidly oscillating density
Timur Rustemovich Gadylshin · Comptes Rendus Mécanique · 2015
The paper is devoted to the vibrations of a string I with a concentrated mass ε − 1 ϰ Q ( ε − 1 x ) and rapidly oscillating density q ( x , μ − 1 x ) , 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 ) .