1. To facilitate an understanding of the harmonic analysis involved in the new method, it is compared in Figs. 8-12with that of the standard one. The new method was based on the calculation of single-cycle FFTs of the resultant signal. These FFTs were referenced to the indices that located the positions of the shock-wave fronts. This is illustrated in the bottom trace of Fig. 8. The standard method, on the other hand, was based on the calculation of multiple-cycle and overlapping FFTs of the original signal. Each consecutive FFT was advanced by a certain percentage of the FFT length. This is illustrated in the top trace of Fig. 8, where the percentage of overlap was 50% and the FFT length was 1024points.
2. Thepower ofthenewmethod is illustrated through thediscussion ofFigs. 10-12. In Fig.10, FFTs for the twomethods are compared. The figure demonstrates thatthenewmethodisgreatlysuperiortothestandardoneinidentifying transverse oscillations.InFigs. 11and 12,contourplotsoftheFFT analysesareshownforthe standardandthenewmethodsalong withtheapproximatevariationoftangentialand radial-acoustic modes. The results obtained with the new method, Fig. 12, represent a significant improvement over those obtained with the standard one, Fig. 11. Individual frequencies in Fig.12, which follow the global trends of the transverse modes, arereadily discernible.
3. Inthissubsection,motor 03031-C(C)isdiscussedasanexampleofthedifferent pressurewavesthatarepresentinapulse-triggeredunstableenvironment.Assuch, the new data analysis method was applied to the resultant signal from one of the Kistler 603B2 transducers in the motor headend. The resulting contour plot is repeated in Figs. 13-15, where it is compared with analytical approximations of thevariationwith timeof thefrequency of different modesof acousticoscillation. The contourplotwasalsocompared with afrequency analysisofthevibrationsof thecasing, duringpulse-triggeredunstableoperation,of amotor similartothat of 03031-C(C), Fig. 16.
4. As was specified above, the contour plots in Figs. 13-15 were based on 1024-point FFTs that contained 300 points of signal, the rest of the FFT being filled with zeros (seeFig. 9). Therefore the effective frequency resolution of the FFTsbased on a250-ksample/s sampling rate was 0.83 kHz.