VIBRATIONS ON POWER LINES IN A STEADY WIND: V. RESONANCE OF STRINGS WITH STRENGTHENED ENDS

1938 ◽  
Vol 16a (12) ◽  
pp. 215-225
Author(s):  
R. Ruedy
Keyword(s):  
Total Mass ◽  
Linear Density ◽  
Unit Length ◽  
Standing Waves ◽  
Power Lines ◽  
Resonance Frequencies ◽  
The Law

The resonance frequencies, and in particular all the overtones of a string along which the linear density varies according to the law ρ(1 + λx/L)m, are slightly higher than the frequencies of a uniform string of the same total mass when the ratio between the mass of an element at the end and a corresponding element at the centre is varied between 1 and 25. In order to bring a string with strengthened ends into resonance it is necessary not only that the force acting on unit length of the string be of the same frequency as one of the resonance frequencies, and that its strength varies along the string in proportion to the amplitudes of the corresponding standing waves, but it must also be proportional to the mass of each element. It is therefore more difficult to produce true resonance in a string with strengthened ends than in a uniform string.

VIBRATION OF POWER LINES IN A STEADY WIND: IV. NATURAL FREQUENCIES OF VIBRATION OF STRINGS WITH STRENGTHENED ENDS

1938 ◽  
Vol 16a (7) ◽  
pp. 138-148
Author(s):  
R. Ruedy
Keyword(s):  
Natural Frequencies ◽  
Unit Length ◽  
The Other ◽  
Power Lines ◽  
Odd Order ◽  
Small Influence ◽  
Even Order ◽  
The Law ◽  
The Masses

When the mass of unit length of a string of length 2L, instead of being uniform, increases from the centre toward the ends according to the law (1 + x/L)m, the natural frequencies of vibration are lower than those of the uniform string, but the ratios between the frequencies of successive overtones remain virtually unchanged, and with the exception of the first one or two overtones agree with those of a uniform string having a mass per unit length (2(1 + λ)(m+2)/2 − 1)/λ(m + 2) times that at the centre of the strengthened string. The reduction in the natural frequencies of vibration is, of course, larger the greater the ratio between the masses at the two ends, whereas the value of m has a relatively small influence. The overtones form two distinct series: one, corresponding to the harmonics of even order, is always present; the other, corresponding to the harmonics of odd order, is suppressed when the density of the string increases from one end to the other (unsymmetrical span).

Formation of Standing Waves in Radial Tires

1984 ◽  
Vol 12 (1) ◽  
pp. 44-63 ◽  
Author(s):  
Y. D. Kwon ◽  
D. C. Prevorsek
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Unit Length ◽  
Standing Waves ◽  
Rolling Resistance ◽  
Damping Coefficient ◽  
Circular Membrane ◽  
Critical Speeds ◽  
Steel Cord ◽  
The Individual

Abstract Radial tires for automobiles were subjected to high speed rolling under load on a testing wheel to determine the critical speeds at which standing waves started to form. Tires of different makes had significantly different critical speeds. The damping coefficient and mass per unit length of the tire wall were measured and a correlation between these properties and the observed critical speed of standing wave formation was sought through use of a circular membrane model. As expected from the model, desirably high critical speed calls for a high damping coefficient and a low mass per unit length of the tire wall. The damping coefficient is particularly important. Surprisingly, those tire walls that were reinforced with steel cord had higher damping coefficients than did those reinforced with polymeric cord. Although the individual steel filaments are elastic, the interfilament friction is higher in the steel cords than in the polymeric cords. A steel-reinforced tire wall also has a higher density per unit length. The damping coefficient is directly related to the mechanical loss in cyclic deformation and, hence, to the rolling resistance of a tire. The study shows that, in principle, it is more difficult to design a tire that is both fuel-efficient and free from standing waves when steel cord is used than when polymeric cords are used.

scholarly journals Modeling the seam strength of denim garments by using fuzzy expert system

2021 ◽  
Vol 16 ◽  
pp. 155892502198897
Author(s):  
Joy Sarkar ◽  
Md Abdullah Al Faruque ◽  
Moni Sankar Mondal
Keyword(s):  
Fuzzy Logic ◽  
Expert System ◽  
Linear Density ◽  
Unit Length ◽  
Coefficient Of Determination ◽  
Sewing Thread ◽  
External Forces ◽  
Fuzzy Logic Expert System ◽  
The Relationship ◽  
Sufficient Strength

The main purpose of this study is to predict and develop a model for forecasting the Seam Strength (SS) of denim garments with respect to the thread linear density (tex) and Stitches Per Inch (SPI) by using a Fuzzy Logic Expert System (FLES). The seam strength is an important factor for the serviceability of any garments. As seams bound the fabric pieces together in a garment, the seams must have sufficient strength to execute this property even in the unexpected severe conditions where the garments are subjected to loads or any additional internal or external forces. Sewing thread linear density and number of stitches in a unit length of the seam are the two of the most important factors that affect the seam strength of any garments. But the relationship among these two specific variables and the seam strength is complex and non-linear. As a result, a fuzzy logic based model has been developed to demonstrate the relationship among these parameters and the developed model has been validated by the experimental trial. The coefficient of determination ( R2) was found to be 0.98. The mean relative error also lies withing acceptable limit. The results have suggested a very good performance of the model in the case of the prediction of the seam strength of the denim garments.

Stand und Entwicklung des Fachplanungsrechts im Spiegel der jüngeren höchstrichterlichen Rechtsprechung

2020 ◽  
Vol 53 (4) ◽  
pp. 535-574
Author(s):  
Boas Kümper
Keyword(s):  
Environmental Law ◽  
Legal Protection ◽  
European Court Of Justice ◽  
Power Lines ◽  
The Public ◽  
General Law ◽  
Court Of Justice ◽  
European Court ◽  
The Law ◽  
Environmental Relevance

The report surveys in two parts the development of the law on project-related planning and thus relates in particular to the planning and approval of space-consuming infrastructure projects such as traffic routes and power lines. For this purpose, German administrative law has long provided for the specific instrument of plan approval (Planfeststellung). In this context, the Federal Administrative Court has extensive first-instance jurisdiction and uses this to shape large parts of German approval law, including beyond the actual area of plan approval law, be it in terms of legal protection and procedure, be it with regard to the requirements of substantive environmental law. On the other hand, the revision of the law on environmental protection induced by the decisions of the Aarhus Compliance Committee and the European Court of Justice has been used by the German legislator to extend procedural specifics of the plan approval to other approval decisions of environmental relevance. This firstly indicates the contours of a general law on project approval and, secondly, the nature of the plan approval as an instrument for the implementation of projects in the public interest is more strongly emphasized.

scholarly journals Topological Network Properties of Fractal-Like Metallic Nanoparticle Patterns and Their Effects on Optical Resonances

2018 ◽  
Vol 8 (8) ◽  
pp. 1310
Author(s):  
Naoya Kihara ◽  
Osamu Sakai
Keyword(s):  
Unit Length ◽  
Theoretical Models ◽  
Topological Properties ◽  
Metallic Nanoparticle ◽  
Diffusion Limited Aggregation ◽  
Complex Network Theory ◽  
Geometrical Properties ◽  
Optical Resonances ◽  
Resonance Frequencies ◽  
Network Topologies

Fractal-like nanoparticle two-dimensional patterns forming in diffusion-limited aggregation show variant spatial patterns. However, they have invariant statistical properties in their network topologies, even though their formation is completely in self-assembled processes. One of the outputs from these topological properties is optical resonances at invariant frequencies, which is a required feature of a metamaterial alternative. Fractal-like metallic patterns studied here in both experiments and theoretical models exhibit similar resonance frequencies in the infrared-ray range, and they depend on the unit length of nanoparticles composing arbitrary fractal-like structures. The scheme of analysis applied here using complex network theory does not only reveal the topological properties of the nanoparticle network, but points out their optical and possibly other physical potentials arising from their geometrical properties.

scholarly journals Reduction in the Electromagnetic Interference Generated by AC Overhead Power Lines on Buried Metallic Pipelines with Screening Conductors

Electricity ◽  
2021 ◽  
Vol 2 (3) ◽  
pp. 316-329
Author(s):  
Arturo Popoli ◽  
Leonardo Sandrolini ◽  
Andrea Cristofolini
Keyword(s):  
Electromagnetic Interference ◽  
Numerical Study ◽  
Unit Length ◽  
Soil Surface ◽  
Power Lines ◽  
Induced Voltage ◽  
Element Analysis ◽  
Cylindrical Steel ◽  
Overhead Power Lines ◽  
Overhead Power Line

This paper presents a numerical study on the reduction in the voltage and current induced on a 13.5 km buried metallic pipeline by an overhead power line. The mitigation effectiveness of different configurations and cross-section shapes of screening conductors is computed by means of a methodology that combines a 2D Finite Element Analysis with circuital analysis. A 35.72% reduction of the maximum induced voltage is obtained when 4 cylindrical steel screening conductors with 8 mm radius are buried 0.25m below the soil surface, along the pipeline path. The maximum induced pipeline current is reduced by 26.98%. A parametric study is also performed, to assess the influence of the per-unit-length admittance to earth of the screening conductors on the mitigation efficacy. The results show that screening conductors may help in reducing the inductive coupling between overhead power lines and buried metallic pipelines, and that the assumption of perfectly insulated screening conductors leads to an underestimation of the produced mitigation effect.

Modulated Beams in a Plasma with a Magnetic Field

1961 ◽  
Vol 16 (12) ◽  
pp. 1313-1319
Author(s):  
E. Canobbio ◽  
R. Croci
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Energy Loss ◽  
Single Particle ◽  
Linear Density ◽  
Energy Output ◽  
Straight Beam ◽  
Resonance Frequencies ◽  
Steady Magnetic Field ◽  
Cerenkov Effect

The radiation emitted by a linear density-modulated beam of ions parallel to a steady magnetic field and by a straight beam perpendicular to the field into a non dissipative plasma is investigated. In both cases the energy output becomes infinite at the “ion” and “electron resonance frequencies”.From the expression for the radiation of the beam which is parallel to the external magnetic field the energy loss of a single particle by ČERENKOV effect is also derived.

VIBRATIONS ON POWER LINES IN A STEADY WIND: VI. FORCED VIBRATIONS OF UNIFORM STRINGS AND OF STRINGS WITH STRENGTHENED ENDS UNDER THE ACTION OF UNIFORM PERIODIC FORCES

1939 ◽  
Vol 17a (1) ◽  
pp. 1-13
Author(s):  
R. Ruedy
Keyword(s):  
Plane Wave ◽  
Standing Waves ◽  
Wave Pattern ◽  
Power Lines ◽  
Practical Calculation ◽  
Square Root ◽  
Damping Force ◽  
Force And Motion ◽  
At Resonance ◽  
Point To Point

A study of the complete equation expressing the action of a driving force, periodic in time but constant throughout the length of the string and opposed by a damping force proportional to the velocity, leads to formulae suitable for the practical calculation of the shape of standing waves that are produced by a plane wave of sound or by a steady wind. At resonance the amplitude at the midpoint of a uniform string set into a plane wave of sound is proportional to the diameter, to the square root of the intensity of the wave (G erg per sq. cm. per sec.), and inversely proportional to the order of the overtone and to the square root of the frequency. Damping causes the lag between force and motion to differ from point to point, particularly near the nodes, so that even at resonance the wave pattern is not rigorously stationary. On the average, the lag increases from the value zero, obtained when the ratio v/v0 between applied frequency and fundamental frequency is zero, to ±π/2 when v/v0 = 1, increases again from −π/2 through 0 at v/v0 = 2, to π/2 at v/v0 = 3, and so on.

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