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TU Berlin

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Dr.-Ing. Richard Büssow

Former Academic Staff

Wavelet transformation of structure bourne sound signals for dispersion characterisation and source localisation

The work addresses the definition of a wavelet that is adapted to analyse a flexural impulse response. The wavelet gives the opportunity to directly analyse the dispersion characteristics of a pulse. The aim is to localize a source or to measure material parameters.
The work also consists of a brief discussion of the energy density over time or frequency that is obtained with the wavelet transform. An efficient algorithm is suggested to calculate the continuous transform with the Morlet wavelet. The energy values of the Wavelet transform are compared with the power spectrum of the Fourier transform. Useful definitions for power spectra obtained with the Wavelet transform are given. The focus of this part is on simple measures to evaluate the transform with the Morlet wavelet in an efficient way. The use of the transform and the defined values is shown in examples.
Part of the work is the response functions for infinite beams and plates with a force excitation at the origin of the coordinate system and its application to time reversal and time frequency analysis. The response function for Euler-Bernoulli beams and plates is derived. Interpretation concerning energy conservation and mobility are given.
Based on the results is the definition of a new wavelet, the bending wavelet, which is meant to analyse the flexural impulse response. An overview of the mathematical properties of the bending wavelet is presented. An algorithm to extract the dispersion characteristics with the use of genetic algorithms is outlined. The application of the wavelet is shown in an example.
The impulse response of a finite beam is measured in an experiment and compared with that predicted theoretically. The experimental data before the first reflection of the pulse showed good agreement with the theory. The transform with the bending wavelet is performed with the measured impulse response. It is shown that one is able to localize a source with the use of the bending wavelet.

Dissertation :
Supervisor : Prof.Dr. B.A.T. Petersson


B.A.T. Petersson and R. Büssow (2006). Path sensitivity and uncertainty propagation in SEA. Journal of Sound and Vibration, 300, 479-489


Dr.-Ing. Richard Büssow
Abteilung TK 4
Experte für Schall und Schwingungen
MAN Turbo AG
Steinbrinkstr. 1
D-46145 Oberhausen
Tel.:+49 208 692-2535
Fax: +49 208 692-9058

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