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A dispersive nonlocal model for shear wave propagation in laminated composites with periodic structures. (English) Zbl 1406.74555

Summary: In this paper, the problem of shear-wave propagation with oblique incidence in a triclinic laminated composite with perfect contact between the layers and periodic distribution between them is studied. An asymptotic dispersive method for the description of the dynamic processes is proposed. By assuming a single-frequency dependency of the solution for the two-dimensional wave equation in a periodic composite material, the higher-order terms for the displacement in asymptotic expansions are studied. Analytic solution for the average model is presented with the graphical illustration for a boundary problem. Numerical examples show that the dispersion curve is in good agreement with the results in previous literatures. The effects of the unit cell size, wave number and incident angle on the wave propagation and dispersion relation are also examined.

MSC:

74Q05 Homogenization in equilibrium problems of solid mechanics
74E30 Composite and mixture properties
74A50 Structured surfaces and interfaces, coexistent phases
74J05 Linear waves in solid mechanics
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