Propagation of axial shear waves in elastic composites reinforced with random or regular sets of unidirected fibers

Abstract

This work is devoted to the problem of axial shear elastic wave propagation in composites reinforced with a set of unidirected cylindrical fibers. The effective field method and quasicrystalline approximation are used for the development of the dispersion equation for the wavenumber of the mean (coherent) wave field propagating in the composite. This dispersion equation serves for all frequencies of the incident field, properties and volume concentrations of the fibers. In the method, peculiarities in spatial distributions of inclusions are taken into account via a specific correlation function of the fiber set. Such a function may be constructed for random as well as for regular sets of fibers. Thus, wave propagation in random composites as well as in composites with regular fiber arrangements may be considered. In the case of a random set of fibers, different branches of the wave propagation in the composites with an epoxy matrix and glass fibers are obtained and analyzed. Such branches are constructed also for composites with regular lattices of fibers, and the position of the pass bands, where waves can propagate, and stop bands, where waves exponentially attenuate, in the frequency region are indicated. The comparison of the obtained approximate solutions with some exact solutions of the wave propagation problem for regular composites is presented.