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On damping in two‐layer elastic‐viscoelastic media
Author(s) -
Renardy M.
Publication year - 2004
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.200310091
Subject(s) - viscoelasticity , exponential function , elastic modulus , relaxation (psychology) , infinity , materials science , mathematical analysis , moduli , zero (linguistics) , physics , derivative (finance) , mechanics , composite material , mathematics , quantum mechanics , psychology , social psychology , linguistics , philosophy , financial economics , economics
We consider one‐dimensional wave propagation through two layers consisting, respectively, of an elastic and a viscoelastic medium. We show that, if the instantaneous elastic modulus of the viscoelastic medium is infinite, then there exists a family of modes with frequencies going to infinity, but damping rates going to zero. Hence the overall rate of damping is not exponential. On the other hand, there is a possibility of faster than exponential damping (i.e., the damping rate goes to infinity with frequency) if the elastic moduli of the two media are matched and the derivative G ′ (0) of the relaxation modulus of the viscoelastic medium is ‐∞.
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