A theoretical study is presented on the propagation of a plane sinusoidal wave through a material that is reinforced with parallel fibers in one direction. The wave propagates in a direction normal to the fibers, and both fiber and matrix are made of linear elastic materials. An integral formulation for the scattered wave solution of an isolated fiber is used to study the multiple scattering in an infinite slab of the composite material. The transmitted and reflected waves from the composite and from a homogeneous slab are shown to be similar. By matching the two sets of results, formulas expressed in terms of the isolated fiber solution are derived for the wave speed, the effective density, and the modulus of the composite. In general, the effective density and modulus so defined are complex numbers and depend on the wave frequency. This fact indicates the possible existence of dissipation and dispersion in the composite under dynamic loadings. A series solution is presented for a composite containing circular fibers, and approximate closed form results are obtained for the limiting case of very long wavelength. As expected, the material does not exhibit dispersion and dissipation at this limit. © 1969, Acoustical Society of America. All rights reserved.
