scholarly journals Analytic resolution of time-domain half-space Green's functions for internal loads by a displacement potential-Laplace-Hankel-Cagniard transform method

2020 ◽  
Vol 476 (2235) ◽  
pp. 20190610
Author(s):  
Ronald Y. S. Pak ◽  
Xiaoyong Bai
Keyword(s):  
Half Space ◽  
Time Domain ◽  
Surface Force ◽  
Point Load ◽  
Wave Group ◽  
Branch Points ◽  
Transform Method ◽  
Displacement Potential ◽  
Starting Point ◽  
The Time Domain

A refined yet compact analytical formulation is presented for the time-domain elastodynamic response of a three-dimensional half-space subject to an arbitrary internal or surface force distribution. By integrating Laplace and Hankel transforms into a method of displacement potentials and Cagniard's inversion concept, it is shown that the solution can be derived in a straightforward manner for the generalized classical wave propagation problem. For the canonical case of a buried point load with a step time function, the response is proved to be naturally reducible with the aid of a parametrized Bessel function integral representation to six wave-group integrals on finite contours in the complex plane that stay away from all branch points and the Rayleigh pole except possibly at the starting point of the contours. On the latter occasions, the possible singularities of the integrals can be rigorously extracted by an extended method of asymptotic decomposition, rendering the residual numerical computation a simple exercise. With the new solution format, the arrival time of each wave group is derivable by simple criteria on the contour. Typical results for the time-domain response for an internal point force as well as the degenerate case of a surface point source are included for comparison and illustrations.

scholarly journals Study of Blockage Diagnosis for Hydrocyclone Using Vibration-Based Technique Based on Wavelet Denoising and Discrete-Time Fourier Transform Method

Processes ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 440 ◽  
Author(s):  
Guanghui Wang ◽  
Qun Liu ◽  
Chuanzhen Wang ◽  
Lulu Dong ◽  
Dan Dai ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Standard Deviation ◽  
Frequency Domain ◽  
Discrete Time ◽  
Time Domain ◽  
Wavelet Denoising ◽  
Transform Method ◽  
Fourier Transform Method ◽  
The Time Domain ◽  
Separation Devices

Hydrocyclones are extensively known as important separation devices which are used in many industrial fields. However, the general method to estimate device performance is time-consuming and has a high cost. The aim of this paper was to investigate the blockage diagnosis for a lab-scale hydrocyclone using a vibration-based technique based on wavelet denoising and the discrete-time Fourier transform method. The results indicate that the farther away the installation location from feed inlet the more regular the frequency is, which reveals that the installation plane near to the spigot generated the regular frequency distribution. Furthermore, the acceleration amplitude under blockage degrees 0%, 50% and 100% fluctuates as a sine shape with increasing time, meanwhile the vibration frequency of the hydrocyclone rises with increasing throughput. Moreover, the distribution of four dimensional and five non-dimensional parameters for the time domain shows that the standard deviation, compared to the others, reduced gradually with increases in blockage degree. Thus, the standard deviation was used to evaluate the online diagnosis of the blockage. The frequency domain distribution under different throughput reveals that the characteristic peaks consisting of the faulty frequency and multiple frequency were produced by the faulty blockage and the feed pump, respectively. Hence, the faulty peak of 16–17 Hz was adopted to judge the real-time blockage of the hydrocyclone, i.e., the presence of the characteristic peak marks the blockage, and its value is proportional to the blockage degree. The application of the online monitoring system demonstrates that the combination of the time domain and the frequency domain could admirably detect the running state and rapidly recognize blockage faults.

The Pulse Signal Preprocessing and Feature Points Recognition Based on MATLAB

2014 ◽  
Vol 716-717 ◽  
pp. 1334-1337
Author(s):  
Liang Yu He ◽  
Min Sheng Liu ◽  
Qi Yue Chen
Keyword(s):  
Pulse Wave ◽  
Pulse Signal ◽  
Noise Signal ◽  
Local Information ◽  
Feature Points ◽  
Threshold Method ◽  
Transform Method ◽  
Starting Point ◽  
The Time Domain ◽  
Matlab Programming

For the pulse wave signal acquired by the pulse analyzer, it’s necessary to remove the large number of noise signal by noise reduction processing. For signal noising processing using wavelet transform method in the time domain and frequency domain and the signals can characterize the ability of local information, and it is self-adaptive. Determine the main wave peak and trough points based on extreme value method and pulse wave periodicity, using the threshold method to determine the dicrotic wave starting point and dicrotic wave peaks, we also use the MATLAB programming to implement the algorithm.

Time‐domain solution for horizontal coaxial dipoles on a half‐space

Geophysics ◽  
1986 ◽  
Vol 51 (9) ◽  
pp. 1850-1852 ◽  
Author(s):  
David C. Bartel
Keyword(s):  
Frequency Domain ◽  
Half Space ◽  
Time Domain ◽  
Inverse Laplace Transform ◽  
Direct Solution ◽  
Current Waveform ◽  
Laplace Domain ◽  
Homogeneous Half Space ◽  
The Time Domain ◽  
The Magnetic Field

The practice of transforming frequency‐domain results into the time domain is fairly common in electromagnetics. For certain classes of problems, it is possible to obtain a direct solution in the time domain. A summary of these solutions is given in Hohmann and Ward (1986). Presented here is another problem which can be solved directly in the time domain—the magnetic field of horizontal coaxial dipoles on the surface of a homogeneous half‐space. Solutions are presented for both an impulse transmitter current and a step turnon in the transmitter current. The solution in the time domain is obtained by taking the inverse Laplace transform of the product of the frequency‐domain solution and the Laplace‐domain representation of the current waveform.

Benchmarked computation of time-domain viscoelastic Love numbers for adiabatic mantles

2019 ◽  
Vol 218 (3) ◽  
pp. 2136-2149 ◽  
Author(s):  
S B Kachuck ◽  
L M Cathles
Keyword(s):  
Density Profile ◽  
Time Domain ◽  
Correspondence Principle ◽  
Equations Of Motion ◽  
Vertical Surface ◽  
Harmonic Load ◽  
Transform Method ◽  
Isostatic Adjustment ◽  
Love Numbers ◽  
The Time Domain

SUMMARYThe viscoelastic load Love numbers encapsulate the Earth’s rheology in a remarkably efficient fashion. When multiplied by a sudden increment of spherical harmonic load change, they give the horizontal and vertical surface displacements and gravity change at all later times. Incremental glacial load changes thus need only be harmonically decomposed, multiplied by the Love numbers and summed to predict the Earth’s response to glacial load redistributions. The computation of viscoelastic Love numbers from the elastic, viscous and adiabatic profiles of the Earth is thus the foundation upon which many glacial isostatic adjustment models are based. Usually, viscoelastic Love numbers are computed using the Laplace transform method, employing the correspondence principle to convert the viscoelastic equations of motion into the elastic equations with complex material parameters. This method works well for a fully non-adiabatic Earth, but can accommodate realistic partially adiabatic and fully adiabatic conditions only by changing the Earth’s density profile. An alternative method of Love number computation developed by Cathles (1975) avoids this dilemma by separating the elastic and viscous equations of motion. The separation neglects a small solid-elastic/fluid-elastic transition for compressible deformation, but allows freely defining adiabatic, partially adiabatic or fully non-adiabatic profiles in the mantle without changing the Earth’s density profile. Here, we update and fully describe this method and show that it produces Love numbers closely similar to those computed for fully non-adiabatic earth models computed by the correspondence principle, finite element and other methods. The time-domain method produces Love numbers as good as those produced by other methods and can also realistically accommodate any degree of mantle adiabaticity. All method implementations are available open source.

scholarly journals A New Method to Calculate Induced Current of Thin Wire over Anisotropic Ground under HPM

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Le Cao
Keyword(s):  
Half Space ◽  
Time Domain ◽  
Response Analysis ◽  
Induced Current ◽  
Thin Wire ◽  
High Power Microwave ◽  
Time Response Analysis ◽  
Time Domain Integral Equation ◽  
The Time Domain ◽  
Power Microwave

The time response analysis of wire structures is often carried out in free space or isotropic half-space, but the real ground is usually layered and has anisotropic properties. In this paper, the induced current of a thin wire over layered anisotropic half-space under a high-power microwave (HPM) is calculated by using the time-domain integral equation (TDIE) method. The reflection coefficient of a layered anisotropic medium is obtained by the general transmitting matrix (GTM) method combined with Fourier transform. The variation of the induced current on the thin wire under different incident conditions is analyzed.

scholarly journals Transition radiation in a nonlinear and infinite one-dimensional structure: a comparison of solution methods

2021 ◽  
Author(s):  
Andrei B. Fărăgău ◽  
Chris Keijdener ◽  
João M. de Oliveira Barbosa ◽  
Andrei V. Metrikine ◽  
Karel N. van Dalen
Keyword(s):  
Time Domain ◽  
Integral Transform ◽  
Hybrid Methods ◽  
Time Domain Method ◽  
Transform Method ◽  
Transition Zones ◽  
Domain Method ◽  
Solution Methods ◽  
The Time Domain ◽  
D Model

AbstractTransition zones in railway tracks are locations with a significant variation of track properties (i.e. foundation stiffness) encountered near structures such as bridges and tunnels. Due to strong amplification of the track’s response, transition zones are prone to rapid degradation. To investigate the degradation mechanisms in transition zones, researchers have developed a multitude of models, some of them being very complex. This study compares three solution methods, namely an integral-transform method, a time-domain method, and a hybrid method, with the goal of solving these systems efficiently. The methods are compared in terms of accuracy, computational efficiency, and feasibility of application to more complex systems. The model employed in this paper consists of an infinite, inhomogeneous, and piecewise-linear 1-D structure subjected to a moving constant load. Although the 1-D model is not particularly demanding computationally, it is used to make qualitative observations as to which method is most suitable for the 2-D and 3-D models, which could lead to significant gains. Results show that all three methods can reach similar accuracy levels, and in doing so, the time-domain method is most computationally efficient. The integral-transform method appears to be efficient in dealing with frequency-dependent parameters, while the time-domain and hybrid methods are efficient in dealing with a smooth nonlinearity. For multi-dimensional models, if nonlinearities and inhomogeneities are considered throughout the depth, the time-domain method is likely to be most efficient; however, if nonlinearities and inhomogeneities are limited to the surface layers, the integral-transform and hybrid methods have the potential to be more efficient than the time-domain one. Finally, although the 1-D model presented in this study is mainly used to assess the three methods, it can also be used for preliminary designs of transition zones in railway tracks.

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