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Wave propagation in an elastically supported string with point‐wise defects: gap‐band and pass‐band effects
Author(s) -
Glushkov E.,
Glushkova N.,
Wauer J.
Publication year - 2011
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.201000039
Subject(s) - pointwise , string (physics) , physics , waveguide , mathematical analysis , eigenvalues and eigenvectors , resonance (particle physics) , diffraction , point (geometry) , optics , mathematics , computational physics , quantum mechanics , geometry
Wave excitation, propagation and diffraction phenomena as well as related resonance trap‐mode, gap‐band and pass‐band effects occurring in one‐dimensional waveguides with obstacles are considered. The waveguide is a spring‐supported string with pointwise changed cross‐section and/or spring force. The analysis is based on semi‐analytical solution in terms of the waveguide's Green functions with unknown coefficients. The latter are obtained from a linear algebraic system whose eigenvalues are spectral points of the problem considered. One of the purposes is to examine the relation between the spectral point allocation in the complex frequency plane and the resonance wave phenomena observed. It is shown that pass‐band phenomena are controlled by natural frequencies approaching to the real axis.