Toward High-Resolution Mechanical Spectroscopy HRMS - Logarithmic Decrement

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 theδfrom free decaying oscillations embedded in an experimental noise typical for low-frequency mechanical spectrometers. The results are reported forδ= 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 theδcan be listed in the following order: (1) OMI, (2) YM, (3) YMC, and (4) the Yoshida method, Y. For short free decays the order of the best performers is different: (1) OMI and (2) YMC. 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.