RUS  ENG
Full version
JOURNALS // Journal of Siberian Federal University. Mathematics & Physics // Archive

J. Sib. Fed. Univ. Math. Phys., 2013 Volume 6, Issue 3, Pages 349–356 (Mi jsfu321)

This article is cited in 2 papers

Spectrum of One-dimensional Vibrations of a Layered Medium Consisting of a Kelvin–Voigt Material and a Viscous Incompressible Fluid

Vladlena V. Shumilova

Institute for Problems in Mechanics of RAS, Moscow, Russia

Abstract: The paper considers a mathematical model for natural vibrations of a periodic layered medium. The medium consists of a viscoelastic Kelvin–Voigt material and a viscous incompressible fluid. For the given model, two homogenized models are derived. They correspond to the cases of transverse and longitudinal vibrations of the layered medium. It is shown that the spectrum of each homogenized model is the union of roots of the corresponding quadratic equations.

Keywords: spectrum, layered medium, homogenized model, viscoelasticity, viscous fluid.

UDC: 517.958 + 534-18

Received: 24.12.2012
Received in revised form: 11.02.2013
Accepted: 11.03.2013

Language: English



© Steklov Math. Inst. of RAS, 2025