J. Mech. Phys. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA So lid s, 1974, Vol. 22, pp. 217 to 229. Porpmon Press. Printed in Great Britain. ELASTIC WAVES IN A FIBER-REINFORCED COMPOSITE By S. K. BOSE and A. K. MAL Mechanics and Structure Department, Universityof California, Los Angeles (Received 26th Murch 1973) THE PROPAGATION of time-harmonic elastic waves in a fiber-reinforced composite is studied. zyxwvutsrqponm The circular fibers are assumed to be parallel to each other and randomly distributed with a statistically uniform distribution. The direction of propagation and the associated particle motion are considered to be normal to the fibers. It is shown that the average waves in the composite separate into com- pressional and shear types. General formulae for the complex wave number giving the phase velocity and the damping are obtained. It is shown that these formulae lead to the Hashin-Rosen expressions for the transverse bulk modulus and the lower bound for the transverse rigidity, if the correlation in the positions of the fibers can be ignored. The correlation terms, for exponential correlation, are shown to have a significant effect on the damping property of the composite, especially at high frequencies and concentrations. 1. INTR~DU~I~N zyxwvutsrqponmlkjihgfedcbaZYXWVUT WE CONSIDER a fiber-reinforced composite which consists of a homogeneous, isotropic, elastic medium, containing long, parallel, randomly distributed, circular fibers of identical properties. For wave propagation in such a medium, ACHENBACH and HERRMANN (1968) included the matrix-fiber interaction by using an effective stiffness method in which the displacement of the central line of the fiber is equated to the displacement of the matrix. Their predicted results gave no dispersion and attenuation of waves propagating normal to the fibers. BOSE and MAL (1973) (hereafter referred to as (I)) discussed the propagation of longitudinal shear waves, with special emphasis on the randomness of the fiber positions in a transverse plane. The distribution was assumed to be uniform. In (I), the method of solution consisted of first solving the scattering problem by a large number N of arbitrarily distributed fibers; the resulting equations were then averaged by considering the fiber positions to be random; and these averaged equations were solved by using LAX’S (1952) ‘quasi- crystalline’ approximation, which is known to be good even for a dense system of scatterers. In this paper, we consider the corresponding problem in which both the direction of propagation and the particle motion of the wave are at right angles to the fibers. The method of solution is a generalization of the previous one in (I). 2. ARBITRARY CONFIGURATION OF N FIBERS We suppose the fibers to be located within a large region S in a matrix extending to infinity. Let 5 p, p be the Lam6 constants and the density of the matrix, and 1’, p’, p’ be the corresponding quantities for the fibers. Labelling the fibers by suffixes 1, 2, . . ., N, let (rt eJ be the polar coordinates of the center 0, of the ith 16 217