Band gap Green's functions and localized oscillations

DOI10.1098/rspa.2007.0007zbMath1131.74026OpenAlexW1965790903MaRDI QIDQ5438442

Slepyan, Leonid I., Alexander B. Movchan

Publication date: 23 January 2008

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rspa.2007.0007

zbMATH Keywords

asymptotic solutionlattice structureslocalized defect modes

Mathematics Subject Classification ID

Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics (74H10) Waves in solid mechanics (74J99) Systems arising from the discretization of structural vibration problems (70J50)

Related Items (17)

Application of matrix-valued integral continued fractions to spectral problems on periodic graphs with defects ⋮ Explicit formula for amplitudes of waves in lattices with defects and sources and its application for defects detection ⋮ Asymptotics of eigenfrequencies in the dynamic response of elongated multi-structures ⋮ Asymptotics of dynamic lattice Green's functions ⋮ Study of anomalous wave propagation and reflection in semi-infinite elastic metamaterials ⋮ Asymptotic and numerical models of waves in tunable multi-scale structures ⋮ Lamb waves in discrete homogeneous and heterogeneous systems: dispersion properties, asymptotics and non-symmetric wave propagation ⋮ Dynamics of structural interfaces: filtering and focussing effects for elastic waves ⋮ Waves in lattices with imperfect junctions and localized defect modes ⋮ Wave propagation through periodic lattice with defects ⋮ Scattering on a square lattice from a crack with a damage zone ⋮ Dynamic anisotropy and localization in elastic lattice systems ⋮ Matrix representations of multidimensional integral and ergodic operators ⋮ High-frequency spectral analysis of thin periodic acoustic strips: Theory and numerics ⋮ Resonant waves and localization phenomena in lattices ⋮ Waves in elastic bodies with discrete and continuous dynamic microstructure ⋮ Algebra of multidimensional periodic operators with defects

Cites Work

• Unnamed Item
• Discrete scattering theory: Green's function for a square lattice
• Vibrations of Lattice Structures and Phononic Band Gaps

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