scholarly journals Electrical Conductivity of Thin Wires

1986 ◽  
Vol 12 (2) ◽  
pp. 103-109 ◽  
Author(s):  
R. Dimmich ◽  
F. Warkusz
Keyword(s):  
Electrical Conductivity ◽  
Boundary Conditions ◽  
Cross Section ◽  
Electron Scattering ◽  
Circular Cross Section ◽  
Boltzmann Transport ◽  
Wire Surface ◽  
Thin Wires ◽  
The Wire ◽  
Metal Wires

An expression for the electrical conductivity of thin metal wires of a circular cross-section has been derived taking account of conduction-electron scattering at grain boundaries and the wire surface. An angular-dependent specularity parameter has been introduced and possible fluctuations of the wire diameter along its length have been taken into account. Boltzmann transport equations have been solved for the boundary conditions proposed by Dingle.

Elastic–plastic deformation and residual stresses in helical springs

2019 ◽  
Vol 16 (3) ◽  
pp. 448-475
Author(s):  
Vladimir Kobelev
Keyword(s):  
Residual Stresses ◽  
Closed Form ◽  
Cross Section ◽  
Circular Cross Section ◽  
Content Type ◽  
Closed Form Solutions ◽  
Helical Springs ◽  
First Case ◽  
Setting Process ◽  
The Wire

Purpose The purpose of this paper is to develop the method for the calculation of residual stress and enduring deformation of helical springs. Design/methodology/approach For helical compression or tension springs, a spring wire is twisted. In the first case, the torsion of the straight bar with the circular cross-section is investigated, and, for derivations, the StVenant’s hypothesis is presumed. Analogously, for the torsion helical springs, the wire is in the state of flexure. In the second case, the bending of the straight bar with the rectangular cross-section is studied and the method is based on Bernoulli’s hypothesis. Findings For both cases (compression/tension of torsion helical spring), the closed-form solutions are based on the hyperbolic and on the Ramberg–Osgood material laws. Research limitations/implications The method is based on the deformational formulation of plasticity theory and common kinematic hypotheses. Practical implications The advantage of the discovered closed-form solutions is their applicability for the calculation of spring length or spring twist angle loss and residual stresses on the wire after the pre-setting process without the necessity of complicated finite-element solutions. Social implications The formulas are intended for practical evaluation of necessary parameters for optimal pre-setting processes of compression and torsion helical springs. Originality/value Because of the discovery of closed-form solutions and analytical formulas for the pre-setting process, the numerical analysis is not necessary. The analytical solution facilitates the proper evaluation of the plastic flow in torsion, compression and bending springs and improves the manufacturing of industrial components.

Natural Frequencies of In-Plane Vibration of Arcs

1983 ◽  
Vol 50 (2) ◽  
pp. 449-452 ◽  
Author(s):  
T. Irie ◽  
G. Yamada ◽  
K. Tanaka
Keyword(s):  
Boundary Conditions ◽  
Cross Section ◽  
Natural Frequencies ◽  
Circular Cross Section ◽  
Plane Vibration

The natural frequencies of in-plane vibration are presented for uniform arcs with circular cross section under all combinations of boundary conditions.

scholarly journals Geometrical Modeling of Steel Ropes

2013 ◽  
Vol 8 (2) ◽  
pp. 85-92 ◽  
Author(s):  
Eva Stanová
Keyword(s):  
Cross Section ◽  
Geometric Modeling ◽  
Circular Cross Section ◽  
Geometrical Model ◽  
Wire Axis ◽  
Geometrical Modeling ◽  
Steel Rope ◽  
Different Shapes ◽  
The Wire

Abstract The paper deals with the mathematical geometric modeling of the ropes of circular cross- section. Such rope can be formed from strands of different shapes. There is considered steel rope made up of six strands, whose crosssection has oval, triangular or circular profil in this paper. The wires of these types of the strands are presented by parametric equations of the wire axis. The equations are implemented in the Pro/Engineer Wildfire V5 software for creating the geometrical model of the strand.

Finite amplitude convection cells

1967 ◽  
Vol 30 (3) ◽  
pp. 577-600 ◽  
Author(s):  
J. L. Robinson
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Boundary Conditions ◽  
Boundary Layers ◽  
Cross Section ◽  
Circular Cross Section ◽  
Maximum Heat ◽  
Mean Field Equations

In this paper we consider two-dimensional steady cellular motion in a fluid heated from below at large Rayleigh number and Prandtl number of order unity. This is a boundary-layer problem and has been considered by Weinbaum (1964) for the case of rigid boundaries and circular cross-section. Here we consider cells of rectangular cross-section with three sets of velocity boundary conditions: all boundaries free, rigid horizontal boundaries and free vertical boundaries (referred to here as periodic rigid boundary conditions), and all boundaries rigid; the vertical boundaries of the cells are insulated. It is shown that the geometry of the cell cross-section is important, such steady motion being not possible in the case of free boundaries and circular cross-section; also that the dependence of the variables of the problem on the Rayleigh number is determined by the balances in the vertical boundary layers.We assume only those boundary layers necessary to satisfy the boundary conditions and obtain a Nusselt number dependence $N \sim R^{\frac{1}{3}}$ for free vertical boundaries. For the periodic rigid case, Pillow (1952) has assumed that the buoyancy torque is balanced by the shear stress on the horizontal boundaries; this is equivalent to assuming velocity boundary layers beside the vertical boundaries (rather than the vorticity boundary layers demanded by the boundary conditions) and leads to a Nusselt number dependence N ∼ R¼. If it is assumed that the flow will adjust itself to give the maximum heat flux possible the two models are found to be appropriate for different ranges of the Rayleigh number and there is good agreement with experiment.An error in the application of Rayleigh's method in this paper is noted and the correct method for carrying the boundary-layer solutions round the corners is given. Estimates of the Nusselt numbers for the various boundary conditions are obtained, and these are compared with the computed results of Fromm (1965). The relevance of the present work to the theory of turbulent convection is discussed and it is suggested that neglect of the momentum convection term, as in the mean field equations, leads to a decrease in the heat flux at very high Rayleigh numbers. A physical argument is given to derive Gill's model for convection in a vertical slot from the Batchelor model, which is appropriate in the present work.

scholarly journals Improved Formulae for the Inductance of Straight Wires

2014 ◽  
Vol 3 (1) ◽  
pp. 31 ◽  
Author(s):  
H. A. Aebischer ◽  
B. Aebischer
Keyword(s):  
Cross Section ◽  
Geometric Mean ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Mutual Inductance ◽  
Arithmetic Mean ◽  
Analytical Approximations ◽  
Analytical Formulae ◽  
The Wire ◽  
Dimensional Integral

The best analytical formulae for the self-inductance of rectangular coils of circular cross section available in the literature were derived from formulae for the partial inductance of straight wires, which, in turn, are based on the well-known formula for the mutual inductance of parallel current filaments, and on the exact value of the geometric mean distance (GMD) for integrating the mutual inductance formula over the cross section of the wire. But in this way, only one term of the mutual inductance formula is integrated, whereas it contains also other terms. In the formulae found in the literature, these other terms are either completely neglected, or their integral is only coarsely approximated. We prove that these other terms can be accurately integrated by using the arithmetic mean distance (AMD) and the arithmetic mean square distance (AMSD) of the wire cross section. We present general formulae for the partial and mutual inductance of straight wires of any cross section and for any frequency based on the use of the GMD, AMD, and AMSD. Since partial inductance of single wires cannot be measured, the errors of the analytical approximations are computed with the help of exact computations of the six-dimensional integral defining induction. These are obtained by means of a coordinate transformation that reduces the six-dimensional integral to a three-dimensional one, which is then solved numerically. We give examples of an application of our analytical formulae to the calculation of the inductance of short-circuited two-wire lines. The new formulae show a substantial improvement in accuracy for short wires.

Size effect variation of the electrical conductivity of metals

1950 ◽  
Vol 203 (1073) ◽  
pp. 223-240 ◽  
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Magnetic Fields ◽  
Cross Section ◽  
Theoretical Work ◽  
Transverse Magnetic ◽  
Experimental Results ◽  
Metallic Films ◽  
Thin Wires ◽  
General Statistical

This paper records experiments and theoretical work concerned with the variation of conductivity with size in metals. Experimental results for the conductivity in thin wires of pure sodium of varying diameter in the absence of a magnetic field and also in the presence of longitudinal and transverse magnetic fields are given. Using the general statistical theory of metals the variation of resistance with size in the case of conductivity wires of square cross-section is calculated for comparison with the first set of experiments. A theoretical investigation follows of the alteration in conductivity produced in metallic films by the application of transverse magnetic fields, and this is compared with the corresponding experimental results obtained on the sodium cylinders.

On the Proper Boundary Conditions for a Beam

1992 ◽  
Vol 59 (4) ◽  
pp. 915-922 ◽  
Author(s):  
H. Fan ◽  
G. E. O. Widera
Keyword(s):  
Asymptotic Expansion ◽  
Boundary Conditions ◽  
Cross Section ◽  
Boundary Data ◽  
Circular Cross Section ◽  
Numerical Calculations ◽  
Analysis Technique ◽  
Outer Expansion ◽  
Beam Theories

Employing the asymptotic expansion approach, the boundary conditions of a beam are reconsidered in the present paper. Gregory and Wan’s (1984) decay analysis technique is extended here to formulate the boundary conditions for the outer expansion. Among the various prescribed boundary data, most of the attention is focused on the displacement case because engineering beam theories employ incorrect conditions for these data. Numerical calculations are carried out for the displacement prescribed beam having a circular cross-section.

Natural Frequencies of Out-of-Plane Vibration of Arcs

1982 ◽  
Vol 49 (4) ◽  
pp. 910-913 ◽  
Author(s):  
T. Irie ◽  
G. Yamada ◽  
K. Tanaka
Keyword(s):  
Boundary Conditions ◽  
Cross Section ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Circular Cross Section ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Plane Vibration ◽  
Out Of Plane

The natural frequencies of out-of-plane vibration based on the Timoshenko beam theory are calculated numerically for uniform arcs of circular cross section under all combination of boundary conditions, and the results are presented in some figures.

scholarly journals Transverse Vibration of Rotating Tapered Cantilever Beam with Hollow Circular Cross-Section

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Zhongmin Wang ◽  
Rongrong Li
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Cantilever Beam ◽  
Cross Section ◽  
Transverse Vibration ◽  
Slenderness Ratio ◽  
Circular Cross Section ◽  
Dimensionless Parameters ◽  
Inner Radius ◽  
Tapered Cantilever Beam

Problems related to the transverse vibration of a rotating tapered cantilever beam with hollow circular cross-section are addressed, in which the inner radius of cross-section is constant and the outer radius changes linearly along the beam axis. First, considering the geometry parameters of the varying cross-sectional beam, rotary inertia, and the secondary coupling deformation term, the differential equation of motion for the transverse vibration of rotating tapered beam with solid and hollow circular cross-section is derived by Hamilton variational principle, which includes some complex variable coefficient terms. Next, dimensionless parameters and variables are introduced for the differential equation and boundary conditions, and the differential quadrature method (DQM) is employed to solve this differential equation with variable coefficients. Combining with discretization equations for the differential equation and boundary conditions, an eigen-equation of the system including some dimensionless parameters is formulated in implicit algebraic form, so it is easy to simulate the dynamical behaviors of rotating tapered beams. Finally, for rotating solid tapered beams, comparisons with previously reported results demonstrate that the results obtained by the present method are in close agreement; for rotating tapered hollow beams, the effects of the hub dimensionless angular speed, ratios of hub radius to beam length, the slenderness ratio, the ratio of inner radius to the root radius, and taper ratio of cross-section on the first three-order dimensionless natural frequencies are more further depicted.

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