Papers by Author: M. Majewski

Abstract: In this paper, we compare the values of the resonant frequency computed according to the OMI algorithm, DFT, and interpolated DFT methods for a set of 100 free decaying oscillations. It is unequivocally demonstrated that the performance of the different methods can be listed in the following order: (1) OMI, (2) YM, (3) YM_C, (4) Agrež, and finally (5) the well known Yoshida method, Y. For very short signals the order of the best methods is different: (1) OMI, (2) YM_C. It is pointed out that the DFT methods, including the Yoshida method, are discouraged for analysis of signals that are too short. This effect is explained in terms of spectral leakage. By contrast, short free decaying signals can be successfully analyzed with the OMI and the YM_C method. We conclude that the use of the OMI and the YM, i.e. the interpolated DFT method, can substantially increase the resolution of low-frequency resonant mechanical spectrometers (the decrease in dispersion of experimental points and the minimization of relative errors can be readily obtained.) For this reason a much more precise estimation of the logarithmic decrement is also simultaneously feasible.

Abstract: In this work, we present the comparison between different methods used to compute the logarithmic decrement, δ . The parametric OMI method and interpolated DFT (IpDFT) methods are used to compute the δ from free decaying oscillations embedded in an experimental noise typical for low-frequency mechanical spectrometers. The results are reported for δ = 5×10^-4, = 1.12345 Hz and different sampling frequencies, = 1 kHz and 4 kHz. A new YM algorithm yields the smallest dispersion in experimental points of the logarithmic decrement and the smallest relative errors among all investigated IpDFT methods. In general, however, the IpDFT methods suffer from spectral leakage and frequency resolution. Therefore it is demonstrated that the performance of different methods to compute the δ can be listed in the following order: (1) OMI, (2) YM, (3) YM_C, and (4) the Yoshida method, Y. For short free decays the order of the best performers is different: (1) OMI and (2) YM_C. It is important to emphasize that IpDFT methods (including the Yoshida method, Y) are discouraged for signals that are too short. In conclusion, the best methods to compute the logarithmic decrement are the OMI and the YM. These methods will pave the way toward high-resolution mechanical spectroscopy HRMS.

Abstract: The advantages of the OMI algorithm to compute the logarithmic decrement and the resonant frequency from free decaying oscillations is reported. The OMI algorithm is proved to be the best solution in the computation of the logarithmic decrement and the resonant frequency for high damping levels.