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) 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.

• Periodical: Solid State Phenomena (Volume 184)
• Pages: 473-478
• DOI: https://doi.org/10.4028/www.scientific.net/SSP.184.473
• Online since: January 2012
• Authors: Leszek B. Magalas, M. Majewski
• Keywords: Discrete Fourier Transform (DFT), Frequency Estimation, Interpolated DFT, Mechanical Spectroscopy, Resonant Frequency, Young's Modulus

References

[1] L.B. Magalas, Determination of the logarithmic decrement in mechanical spectroscopy, Sol. St. Phen. 115 (2006) 7-14.

[2] L.B. Magalas, M. Majewski, Recent advances in determination of the logarithmic decrement and the resonant frequency in low-frequency mechanical spectroscopy, Sol. St. Phen. 137 (2008) 15-20.

DOI: 10.4028/www.scientific.net/ssp.137.15

[3] L.B. Magalas, T. Malinowski, Measurement techniques of the logarithmic decrement, Sol. St. Phen. 89 (2003) 247-260.

DOI: 10.4028/www.scientific.net/ssp.89.247

[4] L.B.  Magalas, M. Majewski, Ghost internal friction peaks, ghost asymmetrical peak broadening and narrowing. Misunderstandings, consequences and solution, Mater. Sci. Eng. A 521-522 (2009) 384-388.

DOI: 10.1016/j.msea.2008.10.073

[5] L.B. Magalas, A. Stanisławczyk, Advanced techniques for determining high and extreme high damping: OMI – A new algorithm to compute the logarithmic decrement, Key Eng. Materials 319 (2006) 231-240.

DOI: 10.4028/www.scientific.net/kem.319.231

[6] L.B. Magalas, Snoek-Köster relaxation. New insights – New paradigms, J. de Phys. IV, 6 (C8) (1996) 163-172.

DOI: 10.1051/jp4:1996834

[7] L.B. Magalas, Mechanical spectroscopy – fundamentals, Sol. St. Phen. 89 (2003) 1-22.

[8] I. Yoshida, T. Sugai, S. Tani, M. Motegi, K. Minamida, H. Hayakawa, Automation of internal friction measurement apparatus of inverted torsion pendulum type, J. Phys. E: Sci. Instrum. 14 (1981) 1201-1206.

DOI: 10.1088/0022-3735/14/10/024

[9] D. Agrež, A frequency domain procedure for estimation of the exponentially damped sinusoids, 12 MTC: 2009 IEEE Instrumentation and Measurement Technology Conference, 1-3 (2009) 1295-1300.

DOI: 10.1109/imtc.2009.5168660

[10] K. Duda, L.B. Magalas, M. Majewski, T.P. Zieliński, DFT-based estimation of damped oscillation parameters in low-frequency mechanical spectroscopy, IEEE Transactions on Instrumentation and Measurement, 60 (2011) 3608 - 3618.

DOI: 10.1109/tim.2011.2113124

[11] J. Rubianes, L.B. Magalas, G. Fantozzi, J. San Juan, The Dislocation-Enhanced Snoek Effect (DESE) in high-purity iron doped with different amounts of carbon, J. de Phys. 48 (C-8) (1987) 185-190.

DOI: 10.1051/jphyscol:1987825

[12] L.B. Magalas, A. Piłat, Zero-Point Drift in resonant mechanical spectroscopy, Sol. St. Phen. 115 (2006) 285-292.

DOI: 10.4028/www.scientific.net/ssp.115.285

[13] L.B. Magalas, J.F. Dufresne, P. Moser, The Snoek-Köster relaxation in iron, J. de Phys. 42 (C-5) (1981) 127-132.

DOI: 10.1051/jphyscol:1981519

[14] S. Etienne, S. Elkoun, L. David, L.B. Magalas, Mechanical spectroscopy and other relaxation spectroscopies, Sol. St. Phen. 89 (2003) 31-66.

DOI: 10.4028/www.scientific.net/ssp.89.31

[15] L.B. Magalas, S. Gorczyca, The Dislocation-Enhanced Snoek Effect – DESE in iron, J. de Phys. 46 (C-10) (1985) 253-256.

DOI: 10.1051/jphyscol:19851057

[16] L.B. Magalas, P. Moser, I.G. Ritchie, The Dislocation-Enhanced Snoek Peak in Fe-C alloys, J. de Phys. 44 (C-9) 645-649. a b c d Fig. 1.  The values computed for 100 free decaying oscillations (d = 5×10-4, = 1. 12345 Hz, = 1 kHz, S/N= 32 dB) according to different methods: OMI, YM, YMC, A, and Y. Dispersion in decreases with increasing the length of free decaying oscillations in a different way for different methods. (Note the strong dispersion for the Yoshida method, Y. ) a b c d Fig. 2.   Variation of the minimal and the maximal relative errors of Young's modulus (E~) as a function of the length of analyzed signals for the OMI, YMC, and Y methods (a, b) and the OMI, YM, and A methods (c, d). a b c Fig. 3.   Variation of computed values of the resonant frequency (a) and the relative error of Young's modulus (E~) (b) for the OMI method and DFT methods: DFTL and DFTLC. (Note that points obtained from the DFTL method are outside the scale of Figs. 3a and 3b). Fig. 3c. The minimal and maximal relative errors of the Young modulus for the OMI method and the values obtained from the DFTLC method for 100 free decaying oscillations. (Note that points obtained from the DFTL method are outside the scale of Fig. 3c).