Discussion on Commonly Methods for Analysis of Drill String Acoustic Spectral Characteristics

2012 ◽  
Vol 226-228 ◽  
pp. 466-469 ◽  
Author(s):  
Yong Wang Liu ◽  
Zhi Chuan Guan ◽  
Guan Shan Zhao ◽  
Zhi Qiang Long
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Transfer Matrix ◽  
Numerical Algorithm ◽  
Difference Method ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Spectral Characteristics ◽  
Drill String ◽  
Impulse Function

Finite difference method and transfer matrix method were used to get spectrum response curve of unit impulse function signal to research the spectrum characteristics of acoustic traveling though the drill string. Similarities and differences of the two methods were discussed through analysis of spectrum curve get from the two approaches. The results show that: The distribution of band-pass and band-stop get by the two calculating methods is basically the same, some transmission coefficient of finite difference method is less than 1, is not completely transmission phenomenon. Analysis of the reason for this is that the transfer matrix method is an analytic method, finite difference method is a numerical algorithm. From the calculation precision of speaking, analytic algorithm is higher than that of numerical algorithm. But to verify the reliability of two methods needs based on laboratory experiment or field test.

Interpolating matrix method: A finite difference method for arbitrary arrangement of mesh points

1988 ◽  
Vol 75 (2) ◽  
pp. 444-468 ◽  
Author(s):  
Seiichi Koshizuka ◽  
Yoshiaki Oka ◽  
Yasumasa Togo ◽  
Shunsuke Kondo
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Matrix Method

Fractional Chebyshev Finite Difference Method for Solving the Fractional-Order Delay BVPs

2015 ◽  
Vol 12 (06) ◽  
pp. 1550033 ◽  
Author(s):  
M. M. Khader
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Fractional Order ◽  
Difference Method ◽  
Matrix Method ◽  
Fractional Derivatives ◽  
Numerical Technique ◽  
Operational Matrix ◽  
Operational Matrix Method ◽  
Chebyshev Finite Difference Method

In this paper, we implement an efficient numerical technique which we call fractional Chebyshev finite difference method (FChFDM). The fractional derivatives are presented in terms of Caputo sense. The algorithm is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the fractional derivatives. This operational matrix method can be regarded as a nonuniform finite difference scheme. The error bound for the fractional derivatives is introduced. We used the introduced technique to solve numerically the fractional-order delay BVPs. The application of the proposed method to introduced problem leads to algebraic systems which can be solved by an appropriate numerical method. Several numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method.

scholarly journals MATHEMATICAL JUSTIFICATION OF FIBER SENSORS BASED ON FIBER BRAGG GRATINGS

2021 ◽  
Vol 117 (2) ◽  
pp. 129-135
Author(s):  
Waldemar Wójcik
Keyword(s):  
Monitoring System ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Fiber Optic ◽  
Spectral Characteristics ◽  
Fiber Optic Sensors ◽  
Fiber Gratings ◽  
Fiber Sensors ◽  
Bragg Fiber

Nowadays, the most promising approach is the use of fiber-optic sensors as a key element of the monitoring system. Fiber-optic sensors (FOS) have a number of advantages, the most important of which include immunity to electromagnetic interference, low weight and the possibility of their inclusion in the measured structure. The use of such sensors in the monitoring system will make it possible to simplify the measurement and obtain reliable data, as well as to obtain all new possibilities for measuring various quantities simultaneously.The most perspective are the sensors based on the Bragg fiber gratings. Bragg fiber gratings have several advantages, for instance, they allow creating the distributed measuring massifs, which contain several sensors. As well, they are insensitive to the optic power source vibrations. Variety of using the fiber sensors based on the Bragg fiber gratings has led to producing the Bragg fiber gratings with different spectral characteristics.The article herein considers the issues of the Bragg fiber gratings mathematical modeling using the transfer matrix method. Transfer matrix method allows defining the optical components spectral characteristics based on the bound modes theory and description of electromagnetic wave, passing through an optic fiber. In the article there have been analyzed the Bragg fiber gratings in compliance with spectral features, such as transmission and reflectance spectra.

scholarly journals RESEARCH OF PARAMETERS OF FIBER-OPTICAL MEASURING SYSTEMS

2019 ◽  
Vol 9 (2) ◽  
pp. 28-31
Author(s):  
Waldemar Wójcik ◽  
Aliya Kalizhanova ◽  
Gulzhan Kashaganova ◽  
Ainur Kozbakova ◽  
Zhalau Aitkulov ◽  
...  
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Fiber Optic ◽  
Spectral Characteristics ◽  
Fiber Optic Sensors ◽  
Spectral Features ◽  
Fiber Gratings ◽  
Bragg Fiber ◽  
Electromagnetic Disturbances

At present there exist a lot of technical devices, the failure of which can be connected not only with huge financial losses, but with the treat to the environment as well. Therefore, an important problem is the effective devices conditions diagnostics, including electronic components and check of their operation. Timely faults detecting allows introducing the prevention measures and avoiding serious consequences. Fiber-optic sensors have several advantages, more important of which include the immunity to electromagnetic disturbances, little weight and possibility to be included into the structure being measured. The most perspective are the sensors based on the Bragg fiber gratings. Bragg fiber gratings have several advantages, for instance, they allow creating the distributed measuring massifs, which contain several sensors. As well, they are insensitive to the optic power source vibrations. Variety of using the fiber sensors based on the Bragg fiber gratings has led to producing the Bragg fiber gratings with different spectral characteristics. Homogeneous Bragg fiber gratings have the spectra with solid side lobes, which can influence at the temperature sensor processing characteristics. To level the side lobes there is applied the apodization method, which is one of the means to affect the spectral form. The article herein considers the issues of the Bragg fiber gratings mathematical and computer modeling using the transfer matrix method. Transfer matrix method allows defining the optical components spectral characteristics based on the bound modes theory and description of electromagnetic wave, passing through an optic fiber. In the article there have been analyzed the Bragg fiber gratings in compliance with spectral features, such as transmission and reflectance spectra. As well, there has been carried out the experiment with influence of various parameters at the Bragg fiber gratings spectral characteristics. There have been studied the Bragg fiber gratings spectral features and selected the grating optimal parameters for designing the fiber-optic sensors based on the Bragg fiber gratings.

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