Spatial localization of linear elastic waves in composite materials with defects

• Published in: Zeitschrift für angewandte Mathematik und Mechanik 2014-12, Vol.94 (12), p.1001-1010
• Main Authors: Andrianov, I.V., Danishevs'kyy, V.V., Kushnierov, I.A.
• Format: Article
• Language: English
• Subjects: Attenuation; Composite material; Composite materials; Defects; Density; dispersion; elastic wave; Localization; Perturbation methods; Plugs; Position (location); wave localization
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.201200273

We study the phenomenon of a spatial localization of elastic waves in periodic composite materials with local defects. The wave spectrum in heterogeneous composite solids includes pass and stop frequency bands. If the frequency of the signal falls within a stop band, the group velocity vanishes and the wave attenuates exponentially. In such a case, a local perturbation of the microstructure may lead to the localization of the wave energy in the vicinity of the defect. Longitudinal tension‐compression waves in a layered composite and transverse antiplane shear waves in a unidirectional fibrous composite are considered. Local perturbations of the density and of the volume fractions of the components are taken into account. The analysis is based on the transfer‐matrix method and on the plane‐wave expansions method. As the result, the frequencies of the wave localization and the corresponding attenuation factors are determined. The authors study the phenomenon of a spatial localization of elastic waves in periodic composite materials with local defects. The wave spectrum in heterogeneous composite solids includes pass and stop frequency bands. If the frequency of the signal falls within a stop band, the group velocity vanishes and the wave attenuates exponentially. In such a case, a local perturbation of the microstructure may lead to the localization of the wave energy in the vicinity of the defect. Longitudinal tension‐compression waves in a layered composite and transverse antiplane shear waves in a unidirectional fibrous composite are considered. Local perturbations of the density and of the volume fractions of the components are taken into account. The analysis is based on the transfer‐matrix method and on the plane‐wave expansions method. As the result, the frequencies of the wave localization and the corresponding attenuation factors are determined.