WAVELET TRANSFORM ANALYSIS OF TRANSIENT WAVE-PROPAGATION IN A DISPERSIVE MEDIUM

The wavelet transform is applied to the analysis of transient waves pr opagating in a dispersive medium. Experimental techniques are employed to measure the transient flexural vibrations of an impact excited uni form beam. The similarity in the fundamental characteristics of the an alysis tool and the physical phenomena are exploited during the decomp osition of the measured signals. The wavelet transform of the accelera tion response resulted in a time-scale representation which provided a clear exposition of the time evolution of the spectral components dur ing the dispersion process. The relation between the wavelet transform and the group properties of the dispersed waveform are emphasized. In the applications to finite systems, the efficacy of the wavelet trans form is demonstrated by analyzing complex transient wave-interference patterns which evolve over wide spectral ranges. An interesting period ic pulse reformation phenomena is uncovered on a uniform beam with fre e boundaries. Following the dispersion and the multiple reflections of the bending waves, the original impulsive waveform is found to be rec onstituted periodically in time. Based on the physical examples, the a dvantages and shortcomings of the wavelet transform are discussed.