General Equations for Transmission Lines

Metzger, G.

doi:10.1016/b978-0-12-493050-6.50008-4

Cited by 3 publications

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“…Let u = u(x, t)-voltage distribution in such telegraph line. It was established that this function is the solution of the homogeneous problem (1)-( 2)-(3) (see, for example [13][14][15]).…”

Section: Resultsmentioning

confidence: 99%

Model Problems on Oscillations of Mechanical and Biological Membranes

Kostikov,

Romanenkov

2023

Inventions

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Various models of membrane oscillations emerging in the theory of elasticity of mechanical systems, biomechanics of the internal ear of vertebrata, and in the theory of electrical circuits are discussed in the article. The considered oscillations have different natures, but their mathematical models are described using similar initial boundary value problems for the second-order hyperbolic equation with the nontrivial boundary condition. The differential equations in these problems are the same. Thus, for example, the model of voltage distribution in the telegraph line emerges for the one-dimensional equation of oscillations. The model of oscillations of a circular homogeneous solid membrane, a membrane with a hole, and the model of gas oscillations in a sphere and spherical region emerge for the two-dimensional and three-dimensional operators, but take into account the radial symmetry of oscillations. The model problem on membrane oscillation can be considered as the problem on ear drum membrane oscillations. The unified approach to reducing the corresponding problems to the initial boundary value problem with zero boundary conditions is suggested. The technique of formulating the solution in the form of a Fourier series using eigenfunctions of the corresponding Sturm–Liouville problem is described.

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“…Let u = u(x, t)-voltage distribution in such telegraph line. It was established that this function is the solution of the homogeneous problem (1)-( 2)-(3) (see, for example [13][14][15]).…”

Section: Resultsmentioning

confidence: 99%

Model Problems on Oscillations of Mechanical and Biological Membranes

Kostikov,

Romanenkov

2023

Inventions

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“…where D is the inner diameter of the outer conductor, d is the diameter of the inner conductor and ε r is the relative dielectric constant of the dielectric material (Metzger and Vabre 1969).…”

Section: Working Principle Of Etdr Distributed Strain Sensingmentioning

confidence: 99%

Development of an electrical time domain reflectometry (ETDR) distributed strain sensor

Lin

Thaduri

Abatan

2005

Meas. Sci. Technol.

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In this paper, a detailed description for the ETDR distributed strain sensing mechanism of a coaxial cable was presented, and a signal calibration algorithm for interpreting ETDR signal waveforms was developed. In addition, a prototype coaxial ETDR distributed strain sensor with improved signal sensitivity was presented. The ETDR signal responses of the prototype sensor subjected to a concentrated lateral compression load and distributed axial tension load were experimentally tested. The test results showed that the prototype sensor has a substantially improved signal sensitivity over a commercial RG-174 cable of comparable size. It was also shown that the relation between the impedance change of the sensor and the applied axial tensile strain depends primarily on the mechanical stress–strain response of the sensor. From the test results, it was demonstrated that this relation could be empirically established with the aid of the calibration algorithm.

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A Major Step Forward: The Computer Arts Society and Event One

Mason

2024

Springer Series on Cultural Computing

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General Equations for Transmission Lines

Cited by 3 publications

References 0 publications

Model Problems on Oscillations of Mechanical and Biological Membranes

Model Problems on Oscillations of Mechanical and Biological Membranes

Development of an electrical time domain reflectometry (ETDR) distributed strain sensor

A Major Step Forward: The Computer Arts Society and Event One

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