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Spectrum of an operator arising elastic system with local K‐V damping
Author(s) -
Xu G.Q.,
Mastorakis N.E.
Publication year - 2008
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200700109
Subject(s) - spectrum (functional analysis) , operator (biology) , continuous spectrum , mathematical analysis , beam (structure) , bernoulli's principle , mathematics , physics , vibration , point (geometry) , countable set , frequency spectrum , pure mathematics , geometry , quantum mechanics , optics , spectral density , biochemistry , chemistry , statistics , repressor , transcription factor , gene , thermodynamics
In this paper, we analyze the spectrum of an operator arising in elastic system with local K‐V damping, whose vibration is modelled as the Euler–Bernoulli beam. Suppose that the beam is clamped at both ends, at its internal bonded a patch made of smart material that produces the Kelvin–Voigt damping. Our aim is to study the spectrum of the operator determined by such a system. By a detail analysis, we show that the spectrum consists of the point spectrum and continuous spectrum, in which the point spectrum is a denumerable set, and the continuous spectrum is a segment on the real axis. Under certain conditions, the continuous spectrum is possibly the whole half line, and also degenerates possibly one point. For a special case, we give the asymptotic expression of the point spectrum.