Wavelet analysis of the evolution of a solitary wave in a composite material

The evolution of a solitary wave propagating through a microstructural material (composite) is studied on the basis of wavelet analysis. A specific feature of the solution technique proposed is the use of Mexican hat (MH) wavelets, which are elastic wavelets, i.e., they are solutions of the basic system of wave equations for an elastic material with a microstructure. The initial wave profile is also chosen in the form of the MH-wavelet. Primary attention is given to the relationship among the profile behavior, wave bottom length, and characteristic microstructure length. A computer analysis conducted demonstrates that the approach proposed allows us to detect the basic wave effects: splitting of the wave into two modes with different phase velocities, simultaneous propagation of both modes in the components of the composite, and strong dependence of the evolution rate on the characteristic lengths of the wave and microstructure.