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Trapped modes along a periodic array of freely floating obstacles
Author(s) -
Dias Gonçalo A. S.,
Videman Juha H.
Publication year - 2014
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/mma.3342
Subject(s) - mathematics , operator (biology) , hilbert space , mathematical analysis , spectrum (functional analysis) , reduction (mathematics) , harmonic , boundary value problem , space (punctuation) , periodic boundary conditions , boundary (topology) , linear map , motion (physics) , classical mechanics , geometry , pure mathematics , acoustics , physics , computer science , chemistry , repressor , quantum mechanics , biochemistry , transcription factor , gene , operating system
We consider the coupled problem describing the motion of a linear array of three‐dimensional obstacles floating freely in a homogeneous fluid layer of finite depth. The interaction of time‐harmonic waves with the floating objects is analyzed under the usual assumptions of linear water‐wave theory. Quasi‐periodic boundary conditions and a simplified reduction scheme turn the system into a linear spectral problem for a self‐adjoint operator in Hilbert space. Based upon the operator formulation, we derive a sufficient condition for the nonemptiness of its discrete spectrum. Various examples of obstacles that generate trapped modes are given. Copyright © 2014 John Wiley & Sons, Ltd.