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Trapped‐mode and gap‐band effects in elastic waveguides with obstacles
Author(s) -
Glushkova Natalia,
Glushkov Evgeny,
Golub Mikhail,
Boström Anders
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810683
Subject(s) - harmonic , energy (signal processing) , plane (geometry) , fourier transform , boundary value problem , physics , plane wave , mode (computer interface) , mathematical analysis , transmission (telecommunications) , computational physics , optics , mathematics , geometry , acoustics , quantum mechanics , telecommunications , computer science , operating system
Traveling wave propagation in elastic waveguides with obstacles in the form of cracks, voids, inclusions or surface irregularities is considered. The investigation is focused on the trapped–mode phenomena featured by the time–averaged harmonic wave energy localization near the obstacles in the form of energy vortices. The latter results, in particular, in narrow gap bands in the frequency plots of transmission coefficients. The study is carried out using analytically based computer models relying on wave expressions in terms of path Fourier integrals, Green's matrices for the laminate structures, and asymptotics for body and traveling waves derived from those integrals. The connection between the resonance effects and natural frequencies (spectral points of the related boundary value problems) in the complex frequency plane is analyzed as well. Examples of spectral points touching the real axis in the course of varying crack size are presented. The eigenforms associated with such discrete spectral points lying in a continuous spectrum depict strong wave energy localization. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)