Advances in Computational High-Resolution Mechanical Spectroscopy HRMS Part II: Resonant Frequency – Young's Modulus

In this paper, we compare the values of the resonant frequency f0 of free decaying oscillations computed according to the parametric OMI method (Optimization in Multiple Intervals) and nonparametric DFT-based (discrete Fourier transform) methods as a function of the sampling frequency. The analysis is carried out for free decaying signals embedded in an experimental noise recorded for metallic samples in a low-frequency resonant mechanical spectrometer. The Yoshida method (Y), the Agrez' method (A), and new interpolated discrete Fourier transform (IpDFT) methods, that is, the Yoshida-Magalas (YM) and (YMC) methods developed by the authors are carefully compared for the resonant frequency f0 = 1.12345 Hz and the logarithmic decrement, δ = 0.0005. Precise estimation of the resonant frequency (Youngs' modulus ∼ f02) for real experimental conditions, i.e., for exponentially damped harmonic signals embedded in an experimental noise, is a complex task. In this work, various computing methods are analyzed as a function of the sampling frequency used to digitize free decaying oscillations. The importance of computing techniques to obtain reliable and precise values of the resonant frequency (i.e. Young's modulus) in materials science is emphasized.