scholarly journals Critical Assessment Of The Issues In The Application Of Hilbert Transform To Compute The Logarithmic Decrement

2015 ◽  
Vol 60 (2) ◽  
pp. 1105-1108
Author(s):  
M. Majewski ◽  
L.B. Magalas
Keyword(s):  
Internal Friction ◽  
Hilbert Transform ◽  
Computing Methods ◽  
Critical Assessment ◽  
Logarithmic Decrement ◽  
High Dispersion ◽  
Mechanical Spectroscopy ◽  
Transform Method ◽  
Twin Method ◽  
Selection Of

Abstract The parametric OMI (Optimization in Multiple Intervals), the Yoshida-Magalas (YM) and a novel Hilbert-twin (H-twin) methods are advocated for computing the logarithmic decrement in the field of internal friction and mechanical spectroscopy of solids. It is shown that dispersion in experimental points results mainly from the selection of the computing methods, the number of oscillations, and noise. It is demonstrated that conventional Hilbert transform method suffers from high dispersion in internal friction values. It is unequivocally demonstrated that the Hilbert-twin method, which yields a ‘true envelope’ for exponentially damped harmonic oscillations is superior to conventional Hilbert transform method. The ‘true envelope’ of free decaying strain signals calculated from the Hilbert-twin method yields excellent estimation of the logarithmic decrement in metals, alloys, and solids.

scholarly journals Hilbert-Twin – A Novel Hilbert Transform-Based Method To Compute Envelope Of Free Decaying Oscillations Embedded In Noise, And The Logarithmic Decrement In High-Resolution Mechanical Spectroscopy HRMS

2015 ◽  
Vol 60 (2) ◽  
pp. 1091-1098 ◽  
Author(s):  
L.B. Magalas ◽  
M. Majewski
Keyword(s):  
Hilbert Transform ◽  
Computing Methods ◽  
Logarithmic Decrement ◽  
The Novel ◽  
Mechanical Spectroscopy ◽  
Discrete Hilbert Transform ◽  
Twin Method ◽  
The Hilbert Transform ◽  
Time Invariant ◽  
Efficient Elimination

Abstract In this work, we present a novel Hilbert-twin method to compute an envelope and the logarithmic decrement, δ, from exponentially damped time-invariant harmonic strain signals embedded in noise. The results obtained from five computing methods: (1) the parametric OMI (Optimization in Multiple Intervals) method, two interpolated discrete Fourier transform-based (IpDFT) methods: (2) the Yoshida-Magalas (YM) method and (3) the classic Yoshida (Y) method, (4) the novel Hilbert-twin (H-twin) method based on the Hilbert transform, and (5) the conventional Hilbert transform (HT) method are analyzed and compared. The fundamental feature of the Hilbert-twin method is the efficient elimination of intrinsic asymmetrical oscillations of the envelope, aHT (t), obtained from the discrete Hilbert transform of analyzed signals. Excellent performance in estimation of the logarithmic decrement from the Hilbert-twin method is comparable to that of the OMI and YM for the low- and high-damping levels. The Hilbert-twin method proved to be robust and effective in computing the logarithmic decrement and the resonant frequency of exponentially damped free decaying signals embedded in experimental noise. The Hilbert-twin method is also appropriate to detect nonlinearities in mechanical loss measurements of metals and alloys.

scholarly journals Hilbert-Twin – A Novel Hilbert Transform-Based Method To Compute The Elastic Modulus In High-Resolution Mechanical Spectroscopy HRMS

2015 ◽  
Vol 60 (2) ◽  
pp. 1099-1103
Author(s):  
M. Majewski ◽  
L.B. Magalas
Keyword(s):  
Fourier Transform ◽  
Elastic Modulus ◽  
High Resolution ◽  
Resonant Frequency ◽  
Discrete Fourier Transform ◽  
Hilbert Transform ◽  
Dynamic Elastic Modulus ◽  
Mechanical Spectroscopy ◽  
Dft Methods ◽  
Twin Method

Abstract A novel Hilbert-twin (H-twin) method is introduced as an alternative method for the computation of the resonant frequency for exponentially damped free decays embedded in noise. We also present the comparison among the following methods used to compute the dynamic elastic modulus in solids: the parametric OMI (Optimization in Multiple Intervals), the Yoshida-Magalas (YM) interpolated discrete Fourier transform, the Hilbert-twin (H-twin), and discrete Fourier transform (DFT) methods. It is concluded that the OMI and YM methods are the best methods to compute the elastic modulus from discrete exponentially damped free-elastic decays embedded in unavoidable noise.

Mechanical Spectroscopy Study on the Light Soaking Effect on Hydrogenated Amorphous Silicon

2012 ◽  
Vol 184 ◽  
pp. 416-421 ◽  
Author(s):  
H. Mizubayashi ◽  
I. Sakata ◽  
H. Tanimoto
Keyword(s):  
Internal Friction ◽  
Temperature Dependence ◽  
Amorphous Silicon ◽  
Hydrogenated Amorphous Silicon ◽  
Wide Distribution ◽  
Activation Energies ◽  
Mechanical Spectroscopy ◽  
Induced Changes ◽  
Mild Temperature ◽  
Hydrogenated Amorphous

For hydrogenated amorphous silicon (a-Si:H) films deposited at temperatures between 423 K and 623 K (a-Si:H423Kand so on), the light-induced changes in the internal friction between 80 K and 400 K were studied. The internal friction is associated with H2motion in microvoid networks, and shows the mild temperature dependence between about 80 K and 300 K (Q-180-300K) and the almost linear increase above 300 K (Q-1>300K). BothQ-180-300KandQ-1>300Kdecrease with increasing the deposition temperature, and show the mild temperature dependence ina-Si:H623K. The white light soaking with 100 mW/cm2(WLS100and so on) below 300 K caused a change inQ-180-300Kand no changes inQ-1>300K, respectively, and the light-induced changes inQ-180-300Krecovered after annealing at 423 K. The wide distribution of activation energies for H2motions between microvoids indicate that most of neighboring microvoids are connected through windows, i.e., the microvoid networks are existing ina-Si:H, and the spatially loose or solid structures are responsible for the low or high activation energies for the H2motion between microvoids, respectively. Furthermore, the light-induced hydrogen evolution (LIHE) was observed for WLS200to WLS400in a vacuum between 400 and 500 K, resulting in the disappearance of the internal friction due to the H2motion in the microvoid network.

High-Temperature Mechanical Relaxation due to Dislocation Motion inside Dislocation Networks

2008 ◽  
Vol 137 ◽  
pp. 21-28 ◽  
Author(s):  
Andre Rivière ◽  
Michel Gerland ◽  
Veronique Pelosin
Keyword(s):  
Internal Friction ◽  
Relaxation Effect ◽  
Dislocation Motion ◽  
Relaxation Peak ◽  
Mechanical Relaxation ◽  
In Situ Tem ◽  
Mechanical Spectroscopy ◽  
Internal Friction Peak ◽  
First Case ◽  
Dislocation Walls

Internal friction peaks observed in single or polycrystals are clearly due to a dislocation relaxation mechanism. Because a sample observed by transmission electron microscopy (TEM) often exhibits in the same time various dislocation microstructures (isolated dislocations, dislocation walls, etc.) it is very difficult to connect the observed relaxation peak with a particular dislocation microstructure. Using isothermal mechanical spectroscopy (IMS), it is easier to compare, for instance, the evolution of a relaxation peak with measurement temperature to the microstructural evolution observed by in-situ TEM at the same temperatures. IMS was used to study a relaxation peak in a 5N aluminium single crystal firstly 1% cold worked and then annealed at various temperatures. TEM experiments performed in the same material at various temperatures equal to the temperatures used for the damping experiments made possible to link this internal friction peak with a relaxation effect occurring inside dislocation walls. In two other experiments in a 4N aluminium polycrystal and in a metal matrix composite with SiC whiskers, it is shown that the observed relaxation peaks are connected to the motion of dislocations inside polygonization boundaries in the first case and in dislocation pile-ups around each whisker in the second one. Theoretical models proposed to explain such relaxation peaks due to a dislocation motion inside a dislocation wall or network are discussed.

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.

Sign in / Sign up

Export Citation Format

Share Document