A dispersive nonlocal model for shear wave propagation in laminated composites with periodic structures

• A methodology for Shear-wave propagation in a periodic composite is proposed.
• Difference between the classical and dynamic homogenizations is exhibited.
• Dispersion effects for the slowness curve are shown.
• The transverse phase velocity increases as the incident angle increases.

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.