Closed-form expressions for the steady-state response of damped transmission line conductors considering their bending stiffness

2020 ◽  
Vol 26 (15-16) ◽  
pp. 1319-1329
Author(s):  
Marcelo A Ceballos ◽  
José E Stuardi
Keyword(s):  
Steady State ◽  
Transmission Line ◽  
Numerical Models ◽  
Mechanical Impedance ◽  
Steady State Solution ◽  
Bending Stiffness ◽  
Analytical Models ◽  
Dispersive Media ◽  
Overhead Transmission Line ◽  
Damper Design

This paper begins with a brief compilation of analytical models typically used to calculate the dynamic response of a conductor span belonging to an overhead transmission line, with a Stockbridge-type damper located near one of its ends. In most of analyses found in the literature, the calculation of the response is done through the superposition of waves that propagate in both longitudinal directions impinging and reflecting at the span ends and at the damper attachment points. The approach proposed in this paper allows obtaining the response as the steady-state solution of the governing differential equations providing suitable analytical expressions for conductors with bending stiffness, which are dispersive media for propagating waves. Using these analytical solutions, the influence of bending stiffness on the efficiency and on the optimal mechanical impedance of the damper, which are of great importance in damper design, can be described explicitly. At the same time, the proposed methodology avoids the need of numerical models or approximate formulas to calculate the bending strains in critical points of the conductor with a single damper.

scholarly journals Magnetic field-aligned plasma currents in gravitational fields

2015 ◽  
Vol 33 (3) ◽  
pp. 257-266 ◽  
Author(s):  
O. E. Garcia ◽  
E. Leer ◽  
H. L. Pécseli ◽  
J. K. Trulsen
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Low Frequency ◽  
Slow Motion ◽  
Steady State Solution ◽  
Plasma Pressure ◽  
Analytical Models ◽  
Polar Regions ◽  
Gravitational Fields ◽  
Field Lines

Abstract. Analytical models are presented for currents along vertical magnetic field lines due to slow bulk electron motion in plasmas subject to a gravitational force. It is demonstrated that a general feature of this problem is a singularity in the plasma pressure force that develops at some finite altitude when a plasma that is initially in static equilibrium is set into slow motion. Classical fluid models thus do not allow general steady-state solutions for field-aligned currents. General solutions have to be non-stationary, varying on time scales of many periods of a plasma equivalent to the Brunt–Väisälä frequency. Except for very special choices of parameters, a steady-state solution exists only in an average sense. The conditions at large altitudes turn out to be extremely sensitive to even small changes in parameters at low altitudes. Low frequency fluctuations detected at large altitudes in the polar regions need not be caused by local low frequency instabilities, but merely reflect small fluctuations in conditions at low altitudes.

Experimental and numerical study of the wave run-up along a vertical plate

2010 ◽  
Vol 654 ◽  
pp. 363-386 ◽  
Author(s):  
B. MOLIN ◽  
O. KIMMOUN ◽  
Y. LIU ◽  
F. REMY ◽  
H. B. BINGHAM
Keyword(s):  
Free Surface ◽  
Steady State ◽  
Vertical Plate ◽  
Numerical Study ◽  
Numerical Models ◽  
Plane Waves ◽  
Surface Profile ◽  
Experimental Tests ◽  
Steady State Solution ◽  
Reflected Wave

Results from experiments on wave interaction with a rigid vertical plate are reported. The 5m long plate is set against the wall of a 30m wide basin, at 100m from the wavemaker. This set-up is equivalent to a 10m plate in the middle of a 60m wide basin. Regular waves are produced, with wavelengths of 1.6m, 1.8m and 2m, and steepnesses H/L (H being the double amplitude and L being the wavelength) ranging from 2% to 5%. Free-surface elevations along the plate are measured with a row of 20 gauges. The focus is on the time evolution of the free-surface profile along the plate. At all steepnesses, strong deviations from the predictions of linear theory gradually take place as the reflected wave field develops in the basin. This phenomenon is attributed to third-order interactions between the incoming and reflected wave systems, on the weather side of the plate. The measured profiles along the plate are compared with the predictions of two numerical models: an approximate model based on the tertiary interaction theory of Longuet-Higgins & Phillips (J. Fluid Mech., vol. 12, 1962, p. 333) for plane waves, which provides a steady-state solution, and a fully nonlinear numerical wavetank based on extended Boussinesq equations. In most of the experimental tests, despite the large distance from the wavemaker to the plate and the small amplitude of the incident wave, no steady state is attained by the end of the exploitable part of the records.

scholarly journals 3D Stress Analysis of Multilayered Functionally Graded Plates and Shells under Moisture Conditions

2022 ◽  
Vol 12 (1) ◽  
pp. 512
Author(s):  
Salvatore Brischetto ◽  
Roberto Torre
Keyword(s):  
Steady State ◽  
Diffusion Equation ◽  
Stress Analysis ◽  
Numerical Models ◽  
Functionally Graded ◽  
Analytical Models ◽  
Direct Result ◽  
Equilibrium Equations ◽  
Plates And Shells ◽  
Moisture Conditions

This paper presents the steady-state stress analysis of single-layered and multilayered plates and shells embedding Functionally Graded Material (FGM) layers under moisture conditions. This solution relies on an exact layer-wise approach; the formulation is unique despite the geometry. It studies spherical and cylindrical shells, cylinders, and plates in an orthogonal mixed curvilinear coordinate system (α, β, z). The moisture conditions are defined at the external surfaces and evaluated in the thickness direction under steady-state conditions following three procedures. This solution handles the 3D Fick diffusion equation, the 1D Fick diffusion equation, and the a priori assumed linear profile. The paper discusses their assumptions and the different results they deliver. Once defined, the moisture content acts as an external load; this leads to a system of three non-homogeneous second-order differential equilibrium equations. The 3D problem is reduced to a system of partial differential equations in the thickness coordinate, solved via the exponential matrix method. It returns the displacements and their z-derivatives as a direct result. The paper validates the model by comparing the results with 3D analytical models proposed in the literature and numerical models. Then, new results are presented for one-layered and multilayered FGM plates, cylinders, and cylindrical and spherical shells, considering different moisture contents, thickness ratios, and material laws.

scholarly journals Gaining a better understanding of the extrusion process in fused filament fabrication 3D printing: a review

2021 ◽  
Author(s):  
Bahaa Shaqour ◽  
Mohammad Abuabiah ◽  
Salameh Abdel-Fattah ◽  
Adel Juaidi ◽  
Ramez Abdallah ◽  
...  
Keyword(s):  
3D Printing ◽  
Numerical Models ◽  
Extrusion Process ◽  
Analytical Models ◽  
Limiting Factor ◽  
Fused Filament Fabrication ◽  
Promising Tool ◽  
Relevant Work ◽  
3D Printing Technique ◽  
Required Quality

AbstractAdditive manufacturing is a promising tool that has proved its value in various applications. Among its technologies, the fused filament fabrication 3D printing technique stands out with its potential to serve a wide variety of applications, ranging from simple educational purposes to industrial and medical applications. However, as many materials and composites can be utilized for this technique, the processability of these materials can be a limiting factor for producing products with the required quality and properties. Over the past few years, many researchers have attempted to better understand the melt extrusion process during 3D printing. Moreover, other research groups have focused on optimizing the process by adjusting the process parameters. These attempts were conducted using different methods, including proposing analytical models, establishing numerical models, or experimental techniques. This review highlights the most relevant work from recent years on fused filament fabrication 3D printing and discusses the future perspectives of this 3D printing technology.

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