Advances in Computational High-Resolution Mechanical Spectroscopy HRMSPart I: Logarithmic Decrement

• Published in: IOP conference series. Materials Science and Engineering Vol. 31; no. 1
• Main Authors: Majewski, M, Pilat, A, Magalas, L B
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 20.02.2012
• Subjects: Fourier transforms; High resolution; Methods; Optimization; Sampling; Spectrometers; Spectrum analysis
• ISSN: 1757-8981; 1757-899X
• DOI: 10.1088/1757-899X/31/1/012018

The comparison between different methods used to compute the logarithmic decrement in high-resolution mechanical spectroscopy (HRMS) is analyzed. The performance of parametric OMI method (Optimization in Multiple Intervals) and interpolated discrete Fourier transform (IpDFT) methods are investigated as a function of the sampling frequency used to digitize free decaying oscillations in low-frequency resonant mechanical spectrometers. It is clearly demonstrated that a new Yoshida-Magalas (YM) method is the most powerful IpDFT-based method which outperforms the standard Yoshida (Y) method and other DFT-based methods. Four IpDFT methods and the OMI method are carefully analyzed as a function of the sampling frequency. The results presented in this work clearly show that the relative error in the estimation of the logarithmic decrement depends both on the length of free decaying signal and on the sampling frequency. The effect of the sampling frequency was not yet reported in the literature. The performance of different methods used in the computations of the logarithmic decrement can be listed in the following order: (1) the OMI, (2) the Yoshida-Magalas YM, (3) the Yoshida-Magalas YMC, and finally (4) the Yoshida Y.