Wavelets: Theoretical concepts and vibrations related applications

In this paper we provide a review of wavelet analysis in the context of applications to vibrations problems. First, we give an introduction to the important concepts and mathematical properties of wavelets within the framework of time–frequency analysis of signals. Next, wavelet analysis is discussed as applied to relevant themes in vibrations, such as time-varying spectra estimation, random field synthesis, system identification, damage detection, and material characterization. In view of the large number of related books and journal articles published in recent decades, the list of selected references in the paper is not meant to be exhaustive. Nevertheless, the cited references aim to point out the salient features of wavelet analysis, and to identify significant contributions in each theme, with the goal of expediting additional research and development efforts