Asymptotic behavior of the spectrum of one-dimensional vibrations in a layered medium consisting of elastic and Kelvin-Voigt viscoelastic materials

DOI10.1134/S0081543816080137zbMath1383.74037OpenAlexW2580727055MaRDI QIDQ521553

V. V. Shumilova, Alexei S. Shamaev

Publication date: 11 April 2017

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543816080137

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Vibrations in dynamical problems in solid mechanics (74H45) Linear constitutive equations for materials with memory (74D05) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (5)

Asymptotics of the spectrum of one-dimensional natural vibrations in a layered medium consisting of viscoelastic material and viscous fluid ⋮ Unnamed Item ⋮ Spectrum of one-dimensional eigenoscillations of a medium consisting of viscoelastic material with memory and incompressible viscous fluid ⋮ Spectrum of one-dimensional natural vibrations of layered medium consisting of elastic material and viscous incompressible fluid ⋮ Spectrum of natural vibrations of a layered medium consisting of a Kelvin-Voigt material and a viscous incompressible fluid

Cites Work

• Spectral analysis of integro-differential equations in viscoelasticity theory
• The spectrum band structure of the three-dimensional Schrödinger operator with periodic potential
• Asymptotic formulas for the eigenvalues of a periodic Schrödinger operator and the Bethe-Sommerfeld conjecture
• О спектре одномерных колебаний в среде из слоев упругого материала и вязкоупругого материала Кельвина–Фойгта
• THE MULTIDIMENSIONAL SCHRÖDINGER OPERATOR WITH A PERIODIC POTENTIAL
• On an extension of the method of two-scale convergence and its applications
• Perturbation theory for the Schrödinger operator with a periodic potential
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