This article is cited in 3 papers

Small Transverse Vibrations of Visco-Elastic Rods

I. V. Gorokhova

South Ukrainian State K. D. Ushynsky Pedagogical University, Odessa

Abstract: We study the spectral problem related to the description of small transverse vibrations of homogeneous visco-elastic rods. The left end of the rod is hinged at the joint. The right end is attached to a concentrated mass. The spectrum of this problem is described and asymptotic formulas for eigenvalues are obtained.

Keywords: visco-elastic rod, transverse vibration, Sobolev space, spectral problem, operator pencil, self-adjoint operator, analytic function.

UDC: 517

Received: 28.10.2009
Revised: 25.06.2010

DOI: 10.4213/mzm8763

 English version: Mathematical Notes, 2011, 89:6, 792–798

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