Some approaches to harmonic wave propagation in elastic solids with random microstructure

We address two approaches to the problem of the one-dimensional wave propagation in elastic solids with random microstructure characterized by random elastic and mass properties. They are the method of integral spectral decomposition and the Fokker-Planck-Kolmogorov equation for describing the apparatus of continuous Markov processes. Merits and deficiencies of each approach are discussed. The studied approaches are shown to cover a number of problems of the harmonic wave propagation in heterogeneous or stochastic media. Therefore by means of a preliminary analysis of a particular problem and accounting for the strong and weak side of each approach one can find an appropriate solution strategy.