Frequency-domain analysis thick

Ultrasonic correlation analysis in frequency (Fourier transformation of frequency) domain analysis was utilized to measure a thickness of the sample and to image the structure of the material. This technique comprises four processes (1) calculation of the spectrum, (2) division by the power spectrum of a pulse or other component, (3) Fourier transformation into the frequency domain, and (4) analysis and imaging in the frequency domain. Here we obtain much higher resolution in the imaging and thickness measurements by applying the echo analysis developed in earthquake theory [12] and the thickness measurements methods for a thin layer [13,14]. 

However these techniques fall short in detecting soft layers below stiff layers (Kramer and Stewart, 2004). A relatively new technique that can be used to determine subsurface thickness and wave propagation velocities without necessity of borings is the Multi Channel Analysis of Surface Waves (MASW) test (Nazarian and Stokoe, 1983 Suto, 2007). In this test series of vertical receivers are place on the ground in line with an impact source. The output of the receivers are recorded and transformed into the frequency domain. The phase angles between the recoded responses are used to compute an apparent travel time of the surface waves. The surface wave phase velocity is... 

In this work, we perform a sensitivity analysis of selected parameters of a commercial 26650 LiFePO/graphite cell and investigate their effect on the simulated impedance spectrum. Basic values such as layer thickness and particle radii are taken from literature and preceding measurements. The model implemented within the commercial Finite Element Method (FEM) software COMSOL Multiphysics is then solved in the frequency domain. To demonstrate the capabilities of this method, variations in state of charge, particle radius, solid state diffusion coefficient and reaction rate are analysed. These parameters evoke characteristic and also unusual properties of the observed impedance spectrum. 

Figure 7 shows the time domain data for PE of 5 mm thickness, which is typical of the waveforms obtained from the polymers examined. The data were sampled at the rate of 2ns/word, which is fast enough to memorize the waveform in the MHz range. Similar waveform data were obtained for the PE sample with a thickness of 2 mm. Then the power spectra for these time domain data were calculated using FFT analysis, and those for PE of 2 mm and 5 mm thicknesses re shown in Fig. 8, revealing broad frequency components up to 12MHz and the maximum amplitude at different positions. 

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