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Guided waves in a stratified elastic and locally perturbed domain: theoretical and numerical aspects
Author(s) -
Cristofol Michel
Publication year - 2000
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/1099-1476(20000925)23:14<1257::aid-mma164>3.0.co;2-d
Subject(s) - monotonic function , mathematics , infimum and supremum , essential spectrum , mathematical analysis , operator (biology) , dispersion (optics) , electromagnetism , elasticity (physics) , domain (mathematical analysis) , spectrum (functional analysis) , physics , optics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene , thermodynamics
This article presents new results concerning guided waves in a three‐dimensional unbounded stratified and locally perturbed elastic medium. On the one hand, we numerically show non‐monotonic dispersion curves, a phenomenon not yet encountered in fields other than elasticity. On the other hand, we prove that the infimum of the essential spectrum of the studied operator depends on the possible non‐monotonicity of such curves. This link is a new result with respect to equivalent situations coming from acoustics or electromagnetism. The numerical study underlines, besides the non‐monotonic dispersion curves, the appearance of generalized Stoneley waves. Copyright © 2000 John Wiley & Sons, Ltd.