Wavelet-Based Time–Frequency Analysis of Nonlinear Acoustic Wave Propagation in Heterogeneous Media

Propagation of acoustic waves in a heterogeneous media, layered geology or composite structure, is a big challenge because it becomes difficult to analyse it exactly. The conventional Fourier techniques do not sufficiently represent transient and localised processes of nonlinearities. In this work an analysis framework of wavelets-based time-frequency analysis is revealed with the object of the inquiry of nonlinear waves of acoustics in non-homogeneous media. The method uses adaptive wavelet transforms that are used together with numerical solutions of the nonlinear acoustic wave equation that allows a high degree of spatial localization of harmonic generation, shock formation and scattering capacities. Spatial discretization is done using finite-differences schemes whereas multiresolution decomposition in time signals is done using wavelet packets. The outcome of the simulation of composite layered structures has shown that there are frequency shifts and nonlinear effects that are localised and are not considered by the traditional analysis. An original aspect of the proposed research is in its synergic approach combined with computational acoustics where wavelet analytic provides a less holistic view of the nonlinear wave phenomena. Its practical uses are in nondestructive testing of composite materials, analysis of seismic waves in geophysics, and prediction of performance of acoustic device under nonlinear operation. This framework allows the computational acoustics to increase diagnostic power through the reconciliation of high level mathematical tools with wave propagation physics.