Toward High-Resolution Mechanical Spectroscopy HRMS - Resonant Frequency –Young’s Modulus

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) YMC, (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) YMC. 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 YMCmethod. 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.