Small transverse vibrations of visco-elastic rods

DOI10.1134/S0001434611050208zbMath1291.74122MaRDI QIDQ650500

I. V. Gorokhova

Publication date: 25 November 2011

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

Sobolev spaceanalytic functionself-adjoint operatorspectral problemoperator penciltransverse vibrationvisco-elastic rod

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) General topics in linear spectral theory for PDEs (35P05) Vibrations in dynamical problems in solid mechanics (74H45) Asymptotic distributions of eigenvalues in context of PDEs (35P20) PDEs in connection with mechanics of deformable solids (35Q74)

Cites Work

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• Spectral properties of a fourth order differential equation
• On the accumulation of eigenvalues of operator pencils connected with the problem of vibrations in a viscoelastic rod
• On positive spectra of one class of polynomial operator pencils
• On an operator pencil arising in the problem of beam oscillation with internal damping
• On a fourth-order problem with spectral and physical parameters in the boundary condition

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