Elastic waves in random composites via a differential scheme
The overall dynamic response of random elastic media may be described by the wave number, k, of the coherent wave, which is given by \(k(\omega)=\omega /c(\omega)+i\alpha (\omega)\), here c(\(\omega)\) and \(\alpha\) (\(\omega)\) are the phase velocity and attenuation, respectively, and \(\omega\) is radian frequency. Recently a method has been formulated for predicting k in terms of the microstructure [e.g. the authors J. Mech. Phys. Solids 33, 471-487 (1985; Zbl 0576.73021); the first author, Z. Angew. Math. Phys. 36, 921-926 (1985; Zbl 0588.73003)]. While the method incorporates the causality of the coherent wave via applications of the Kramers-Kronig (K-K) relations, it is confined to the case of small scattering density. In this paper we present an extension of this method, for elastic waves, which takes into account multiple scattering effects by invoking the concept of differential effective media. This concept,which is well-known in the statics of composites, is extended to the dynamic case by taking into account the causality of the coherent wave. Waves propagation in a random fibrous composite is investigated and results are compared with those following from alternative approaches.
scientific article; zbMATH DE number 3988779