Wavelet transform analysis of transient wave propagation in a dispersive medium

The wavelet transform is applied to the analysis of transient waves propagating in a dispersive medium. Experimental techniques are employed to measure the transient flexural vibrations of an impact excited uniform beam. The similarity in the fundamental characteristics of the analysis tool and the physical phenomena are exploited during the decomposition of the measured signals. The wavelet transform of the acceleration response resulted in a time-scale representation which provided a clear exposition of the time evolution of the spectral components during 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 transform is demonstrated by analyzing complex transient wave-interference patterns which evolve over wide spectral ranges. An interesting periodic pulse reformation phenomena is uncovered on a uniform beam with free boundaries. Following the dispersion and the multiple reflections of the bending waves, the original impulsive waveform is found to be reconstituted periodically in time. Based on the physical examples, the advantages and shortcomings of the wavelet transform are discussed.