This paper provides an theoretical analysis of the properties of fibre reinforced composite materials under antiplane waves. A self-consistent scheme is adopted in calculating the effective material constants. A new averaging technique is developed to account for the effects of the waveform. The model is then used to evaluate the effective dynamic properties of composites with randomly distributed fibers. Typical examples are presented to show the effects of different pertinent parameters upon the effective wave speed and the attenuation.

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