شاخص های آنی رفتار سازه بر اساس تجزیه و تحلیل موجک الگویی مداوم

In this contribution, four instantaneous indicators are proposed to characterize the non-linear behaviour of mechanical structures from their transient responses. These indicators are developed from the Cauchy wavelet analysis of the accelerometric responses of the structure. They are based on the notion of ridges and skeletons introduced for the wavelet processing of signals that are assumed to be defined as a sum of asymptotic amplitude and phase-modulated terms. The proposed indicators are then applied to the data collected at the University of Liège. Some preliminary results are given for the characterization of the non-linear behaviour of the beam.

Since its first definition in the early1980s by French researchers, especiallyGrossman n and Morlet [1], the growth of wavelet research in mathematics has been exponential with significant contributions from numerous authors and its application in signal and image processing has been successful. Although some authors (see reference [2]) highlighted the potential benefits of using wavelets for the analysis of engineering data, wavelet analysis is still far from being systematically used in mechanical engineering, certainly due to the ignorance of the properties of the wavelet transform. Our aim is to promote the use of wavelet analysis for processing the time variation of the spectral content of transient responses of mechanical structures. The use of a time–frequencyrepres entation of measured signals is more adapted in the sense that it highlights the maximum amount of information within the data and it makes the parameter identification procedure much easier. The continuous Cauchywave let transform (CCWT) is defined and instantaneous indicators, based on the properties of the CCWT applied to asymptotic signals, are proposed to characterize the ‘modal’ behaviour of the structure under testing. Accelerometric responses of buildings under non-destructive shocks have been processed with the CCWT in reference [3] for the assessment of the modal characteristics of buildings. Here, the procedure is applied to the accelerometric responses of a non-linear beam to an impact force obtained in the LTAS-VIS of the Universityof Li"ege.

Four instantaneous indicators based on the CCWT are proposed and their study (especiallythe discrepancyfrom the linear case) facilitates the characterisation and allows the localisation of the non-linear behaviour of structures. The procedure is applied to transient responses of structures and has the advantage of not requiring knowledge of the excitation forces. Further investigations are under study.