Dynamic effective properties of semi-infinite random unidirectional fiber-reinforced composites subjected to anti-plane shear waves

Based on the theory of elastodynamics, and employing the effective medium method and the image method, the propagation of shear waves in semi-infinite random unidirectional fiber-reinforced composites is investigated. The dispersion relation for the effective wave number in the random composites is derived. The numerical solutions of the dynamic effective properties are obtained by using an iterative scheme. The image method is applied to satisfy the traction free boundary condition of the semi-infinite composite. The effective wave fields are expressed by using the wave function expansion method, and the expanded modal coefficients are determined by satisfying the continuous boundary conditions around the fibers. Analyses show that the variation of the dynamic effective properties in the semi-infinite composite is significantly different from that in the infinite composite. The maximum dynamic effective properties near the surface increase with the increase of the incident wave number, the volume fraction of fibers, and the properties ratio of the two phases.