Recent Advances in Determination of the Logarithmic Decrement and the Resonant Frequency in Low-Frequency Mechanical Spectroscopy

2008 ◽  
pp. 15-20
Author(s):  
Leszek B. Magalas ◽  
M. Majewski
Keyword(s):  
Resonant Frequency ◽  
Low Frequency ◽  
Logarithmic Decrement ◽  
Mechanical Spectroscopy ◽  
Recent Advances

Recent Advances in Determination of the Logarithmic Decrement and the Resonant Frequency in Low-Frequency Mechanical Spectroscopy

2008 ◽  
Vol 137 ◽  
pp. 15-20 ◽  
Author(s):  
Leszek B. Magalas ◽  
M. Majewski
Keyword(s):  
Resonant Frequency ◽  
Low Frequency ◽  
Logarithmic Decrement ◽  
Mechanical Spectroscopy ◽  
Recent Advances

The advantages of the OMI algorithm to compute the logarithmic decrement and the resonant frequency from free decaying oscillations is reported. The OMI algorithm is proved to be the best solution in the computation of the logarithmic decrement and the resonant frequency for high damping levels.

Determination of the Logarithmic Decrement in Mechanical Spectroscopy

2006 ◽  
Vol 115 ◽  
pp. 7-14 ◽  
Author(s):  
Leszek B. Magalas
Keyword(s):  
Resonant Frequency ◽  
High Precision ◽  
Logarithmic Decrement ◽  
Mechanical Spectroscopy ◽  
Harmonic Oscillations

The comparison between the classical methods and a new algorithm OMI used to compute the logarithmic decrement is reported. The OMI algorithm is tested in the computation of the logarithmic decrement from exponentially damped harmonic oscillations. The OMI algorithm yields high precision in the computation of the logarithmic decrement and the resonant frequency, and the smallest dispersion of experimental points.

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

2012 ◽  
Vol 184 ◽  
pp. 473-478 ◽  
Author(s):  
Leszek B. Magalas ◽  
M. Majewski
Keyword(s):  
High Resolution ◽  
Resonant Frequency ◽  
Low Frequency ◽  
Dft Method ◽  
Logarithmic Decrement ◽  
Mechanical Spectroscopy ◽  
Dft Methods ◽  
Spectral Leakage ◽  
Precise Estimation ◽  
Relative Errors

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.

Toward High-Resolution Mechanical Spectroscopy HRMS - Logarithmic Decrement

2012 ◽  
Vol 184 ◽  
pp. 467-472 ◽  
Author(s):  
Leszek B. Magalas ◽  
M. Majewski
Keyword(s):  
High Resolution ◽  
Low Frequency ◽  
Logarithmic Decrement ◽  
Frequency Resolution ◽  
Mechanical Spectroscopy ◽  
Spectral Leakage ◽  
Experimental Noise ◽  
Relative Errors ◽  
The Way

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.

Zero-Point Drift in Low-Frequency Mechanical Spectroscopy

2006 ◽  
Vol 115 ◽  
pp. 285-292 ◽  
Author(s):  
Leszek B. Magalas ◽  
A. Piłat
Keyword(s):  
Low Frequency ◽  
Zero Point ◽  
Logarithmic Decrement ◽  
Torsion Pendulum ◽  
Mechanical Spectroscopy ◽  
Mechanical Loss ◽  
Harmonic Oscillations

The concept of the ‘zero-point drift’, ZPD, is introduced and analyzed on the basis of mechanical loss measurements carried out in a low-frequency mechanical spectrometer – inverted torsion pendulum. It is demonstrated that the ZPD, which modifies damped harmonic oscillations leads to false values of the logarithmic decrement computed from several widely accepted algorithms.

scholarly journals Enhancement of a New Methodology Based on the Impulse Excitation Technique for the Nondestructive Determination of Local Material Properties in Composite Laminates

2020 ◽  
Vol 11 (1) ◽  
pp. 101
Author(s):  
Carlo Boursier Niutta
Keyword(s):  
Resonant Frequency ◽  
Elastic Properties ◽  
Composite Laminates ◽  
Concentrated Mass ◽  
Modal Shape ◽  
Nondestructive Determination ◽  
Material Orientation ◽  
Impulse Excitation ◽  
Clamping System

A new approach for the nondestructive determination of the elastic properties of composite laminates is presented. The approach represents an improvement of a recently published experimental methodology based on the Impulse Excitation Technique, which allows nondestructively assessing local elastic properties of composite laminates by isolating a region of interest through a proper clamping system. Different measures of the first resonant frequency are obtained by rotating the clamping system with respect to the material orientation. Here, in order to increase the robustness of the inverse problem, which determines the elastic properties from the measured resonant frequencies, information related to the modal shape is retained by considering the effect of an additional concentrated mass on the first resonant frequency. According to the modal shape and the position of the mass, different values of the first resonant frequency are obtained. Here, two positions of the additional mass, i.e., two values of the resonant frequency in addition to the unloaded frequency value, are considered for each material orientation. A Rayleigh–Ritz formulation based on higher order theory is adopted to compute the first resonant frequency of the clamped plate with concentrated mass. The elastic properties are finally determined through an optimization problem that minimizes the discrepancy on the frequency reference values. The proposed approach is validated on several materials taken from the literature. Finally, advantages and possible limitations are discussed.

Magnetic Permeability and Relaxation Frequency in High Frequency Magnetic Materials.

2001 ◽  
Vol 674 ◽  
Author(s):  
M.I. Rosales ◽  
H. Montiel ◽  
R. Valenzuela
Keyword(s):  
High Frequency ◽  
Domain Walls ◽  
Magnetocrystalline Anisotropy ◽  
Low Frequency ◽  
Frequency Dispersion ◽  
Anisotropy Constant ◽  
Relaxation Frequency ◽  
Resonance Relaxation ◽  
Frequency Behavior

ABSTRACTAn investigation of the frequency behavior of polycrystalline ferrites is presented. It is shown that the low frequency dispersion (f < 10 MHz) of permeability is associated with the bulging of pinned domain walls, and has a mixed resonance-relaxation character, closer to the latter. It is also shown that there is a linear relationship between the magnetocrystalline anisotropy constant, K1, and the relaxation frequency. The slope of this correlation depends on the grain size. Such a relationship could allow the determination of this basic parameter from polycrystalline samples.

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