On a Magnetic Damper Consisting of a Circular Magnetic Flux and a Conductor of Arbitrary Shape. Part I: Derivation of the Damping Coefficients

1984 ◽  
Vol 106 (1) ◽  
pp. 46-51 ◽  
Author(s):  
Kosuke Nagaya ◽  
Hiroyuki Kojima
Keyword(s):  
Boundary Condition ◽  
Exact Solution ◽  
Magnetic Flux ◽  
Electromagnetic Fields ◽  
Arbitrary Shape ◽  
Fourier Expansion ◽  
Polar Coordinates ◽  
Damping Coefficients ◽  
Theoretical Results ◽  
Good Agreement

Theoretical results for finding the damping coefficients of a magnetic damper consisting of a circular magnetic flux and an arbitrarily shaped conductor have been obtained. In the analysis the exact solution in polar coordinates for the governing equation of the electromagnetic fields is utilized. The boundary condition for arbitrarily shaped boundaries of the conductor is satisfied directly by means of the Fourier expansion collocation method. To discuss the accuracy of the present approximate results, the analysis also has been performed on damper consisting of a circular flux and a circular conductor. The comparison between the present results and the exact ones for the typical damper shows very good agreement.

A Rotary Magnetic Damper Consisting of Several Sector Magnets and an Arbitrarily Shaped Conductor With a Circular Cavity

1986 ◽  
Vol 108 (4) ◽  
pp. 314-321
Author(s):  
Yasuo Karube ◽  
Kosuke Nagaya
Keyword(s):  
Boundary Condition ◽  
Electromagnetic Field ◽  
Magnetic Flux ◽  
Differential Equations ◽  
Fourier Expansion ◽  
Step Function ◽  
Circular Cavity ◽  
Damping Force ◽  
Damping Coefficients ◽  
Unit Step

In this paper, the damping force and the damping coefficient of a rotary magnetic damper consisting of several sector magnets and an arbitrarily shaped plate conductor with a circular cavity have been obtained theoretically. The unit step function is applied to solve the differential equations of the electromagnetic field, and the boundary condition of the outer arbitrarily shaped boundary of the plate conductor is satisfied directly by making use of the Fourier expansion collocation method. Numerical calculations have been carried out for the dimensionless damping coefficients with the variations of various factors such as the magnetic flux range, the outer shape and the radius of the inner circular cavity of the conductor, the position and the number of the magnets.

On a Magnetic Damper Consisting of a Circular Magnetic Flux and a Conductor of Arbitrary Shape. Part II: Applications and Numerical Results

1984 ◽  
Vol 106 (1) ◽  
pp. 52-55 ◽  
Author(s):  
Kosuke Nagaya
Keyword(s):  
Numerical Calculation ◽  
Magnetic Fields ◽  
Magnetic Flux ◽  
Arbitrary Shape ◽  
Companion Paper ◽  
Numerical Results ◽  
Typical Case ◽  
Potential Fields ◽  
Damping Coefficients ◽  
Theoretical Results

A method of numerical calculation for obtaining the damping coefficients and potential fields has been presented for magnetic dampers by utilizing the theoretical results given by the authors in a companion paper (Part I). The study developed in this paper is concerned with dampers consisting of the following conductors and magnetic fluxes: (a) a rectangular conductor and an eccentric circular flux, (b) a circular conductor and an eccentric circular flux, and (c) polygonal conductors of various shapes and a concentric circular flux. Numerical results for the damping coefficients, and potential lines of the magnetic fields have been obtained for these dampers. The results obtained are compared with those of the typical case of the conductor with a concentric circular flux.

scholarly journals The elastic stability of a thin twisted strip—II

1937 ◽  
Vol 161 (905) ◽  
pp. 197-220 ◽  
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Main Part ◽  
Fourier Expansion ◽  
Elastic Stability ◽  
Numerical Work ◽  
The Stability ◽  
Good Agreement

I—In a previous paper the present writer discussed both theoretically and experimentally the equilibrium and elastic stability of a thin twisted strip, and the results obtained by the theory were found to be in good agreement with observation. It has, however, been pointed out by Professor Southwell, F. R. S., that the solution of the stability equations which was given in that paper may only be regarded as an approximate solution for, although it satisfies exactly the differential equations and two boundary conditions along the edge of the strip, it only satisfies the two remaining boundary conditions approximately. The author has also noticed that the coefficients n a m in the Fourier expansion of θ 2 cos mθ which were used in A are incorrect when m = 0, and this has led to errors in the numerical work so that the values of ᴛb 2 / π 2 h which are given in Table I of A are wrong. In the present paper a solution of the stability equations is obtained which satisfies all the boundary conditions. This solution is very much more complicated than the approximate solution and much greater labour is required for the numerical work. The numerical work for the approximate solution of A has also been revised and the corrected results are given in 9, 10. It is found that the results for the approximate solution are in good agreement with those obtained from the exact solution and that both agree moderately well with the experimental results which are given in A. The main part of this paper is an extension of the previous work and is concerned with the stability of a thin twisted strip when it is subjected to a tension along its length. The theory has been compared with experiment and satisfactorily good agreement between them was found.

Dynamic Characteristics of Hydrostatic Thrust Air Bearing With Actively Controlled Restrictor

1988 ◽  
Vol 110 (1) ◽  
pp. 156-161 ◽  
Author(s):  
Yuichi Sato ◽  
K. Maruta ◽  
M. Harada
Keyword(s):  
Dynamic Characteristics ◽  
Dynamic Stiffness ◽  
Phase Lag ◽  
Air Bearing ◽  
Plate Vibrations ◽  
Damping Coefficients ◽  
Stiffness And Damping ◽  
Air Film ◽  
Theoretical Results ◽  
Good Agreement

The dynamic characteristics of a hydrostatic thrust air bearing with an actively controlled orifice restrictor are investigated theoretically and experimentally. Theoretical results show that the dynamic stiffness and damping coefficients can be increased simultaneously when the restrictor area is controlled with appropriate phase-lag to the change of air film thickness, that is, plate vibrations. Consequently stability of the bearing can be improved. Experimental results show fairly good agreement with theoretical ones.

Vibrations of a Thick-Walled Pipe or a Ring of Arbitrary Shape in Its Plane

1983 ◽  
Vol 50 (4a) ◽  
pp. 757-764 ◽  
Author(s):  
K. Nagaya
Keyword(s):  
Wave Propagation ◽  
Arbitrary Shape ◽  
Fourier Expansion ◽  
Equation Of Motion ◽  
Circular Ring ◽  
Theory Of Elasticity ◽  
Polar Coordinates ◽  
Elliptical Ring ◽  
Vibration Problems ◽  
Plane Strain Assumption

This paper is concerned with a method for solving in-plane vibration problems of thick-walled pipes and rings of arbitrary shape. The solution to the equation of motion based on the theory of elasticity under the plane-strain assumption is obtained exactly by using polar coordinates. The boundary conditions along both the outer and the inner surfaces of the ring of arbitrary shape are satisfied directly by means of the Fourier expansion collocation method which has been developed in the author’s previous reports concerning vibration, dynamic response, and wave propagation problems of plates and rods with various shapes. Numerical calculations have been carried out for a thick elliptical ring, a rectangular ring with rounded corners, and a rectangular ring with a circular inner boundary. To discuss the accuracy of the present analysis, the results of a thick circular ring have also been calculated, and the present results are compared with the previously published ones.

A Rotary Magnetic Damper or Brake Consisting of a Number of Sector Magnets and a Circular Conductor

1989 ◽  
Vol 111 (1) ◽  
pp. 97-104 ◽  
Author(s):  
Kosuke Nagaya ◽  
Yasuo Karube
Keyword(s):  
Analytical Solution ◽  
Magnetic Flux ◽  
Eddy Current ◽  
Experimental Tests ◽  
Numerical Calculations ◽  
Damping Coefficient ◽  
Braking Force ◽  
Theoretical Results ◽  
Good Agreement

This paper is concerned with a method for analyzing a rotary magnetic damper (eddy current brake) consisting of a number of sector magnets and a circular conductor. The analytical solution to obtain an eddy current, a braking force, and a damping coefficient is obtained by dividing the magnetic flux into the narrow sectors. Numerical calculations have been carried out for the variation of the flux range, the position, and the number of the magnets. Experimental tests are also carried out to verify the present theoretical results. The theoretical results are in good agreement wtih the experimental ones.

Investigating the Nonlinear Optical Response of Pepper Oil under Low Power Irradiation with Continuous Wave Visible Laser Beam

2020 ◽  
pp. 131-138
Keyword(s):  
Refractive Index ◽  
Nonlinear Refractive Index ◽  
Nonlinear Optical ◽  
Continuous Wave ◽  
Diffraction Integral ◽  
Visible Laser ◽  
Limiting Property ◽  
Kirchhoff Diffraction Integral ◽  
Theoretical Results ◽  
Good Agreement

The nonlinear optical properties of pepper oil are studied by diffraction ring patterns and Z-scan techniques with continuous wave beam from solid state laser at 473 nm wavelength. The nonlinear refractive index of the sample is calculated by both techniques. The sample show high nonlinear refractive index. Based on Fresnel-Kirchhoff diffraction integral, the far-field intensity distributions of ring patterns have been calculated. It is found that the experimental results are in good agreement with the theoretical results. Also the optical limiting property of pepper oil is reported. The results obtained in this study prove that the pepper oil has applications in nonlinear optical devices.

scholarly journals Hydrodynamic Forces Exerting on an Oscillating Cylinder under Translational Motion in Water Covered by Compressed Ice

Water ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 822
Author(s):  
Yury Stepanyants ◽  
Izolda Sturova
Keyword(s):  
Lift Force ◽  
Wave Motion ◽  
Translational Motion ◽  
Added Mass ◽  
Hydrodynamic Forces ◽  
Wave Resistance ◽  
Translational Velocity ◽  
Damping Coefficients ◽  
Incompressible Ideal Fluid ◽  
Theoretical Results

This paper presents the calculation of the hydrodynamic forces exerted on an oscillating circular cylinder when it moves perpendicular to its axis in infinitely deep water covered by compressed ice. The cylinder can oscillate both horizontally and vertically in the course of its translational motion. In the linear approximation, a solution is found for the steady wave motion generated by the cylinder within the hydrodynamic set of equations for the incompressible ideal fluid. It is shown that, depending on the rate of ice compression, both normal and anomalous dispersion can occur in the system. In the latter case, the group velocity can be opposite to the phase velocity in a certain range of wavenumbers. The dependences of the hydrodynamic loads exerted on the cylinder (the added mass, damping coefficients, wave resistance and lift force) on the translational velocity and frequency of oscillation were studied. It was shown that there is a possibility of the appearance of negative values for the damping coefficients at the relatively big cylinder velocity; then, the wave resistance decreases with the increase in cylinder velocity. The theoretical results were underpinned by the numerical calculations for the real parameters of ice and cylinder motion.

Studies of local structures for Cu2+ centers in M2Zn(SO4)2·6H2O (M = NH4 and Rb) crystals

2021 ◽  
Vol 76 (4) ◽  
pp. 299-304
Author(s):  
Fu Chen ◽  
Jian-Rong Yang ◽  
Zi-Fa Zhou
Keyword(s):  
Crystal Field ◽  
Elongation Ratio ◽  
Paramagnetic Resonance ◽  
Local Structures ◽  
Epr Parameters ◽  
Structure Constants ◽  
Crystal Field Parameters ◽  
Electron Paramagnetic ◽  
Theoretical Results ◽  
Good Agreement

Abstract The electron paramagnetic resonance (EPR) parameters (g factor g i , and hyperfine structure constants A i , with i = x, y, z) and local structures for Cu2+ centers in M2Zn(SO4)2·6H2O (M = NH4 and Rb) are theoretically investigated using the high order perturbation formulas of these EPR parameters for a 3d 9 ion under orthorhombically elongated octahedra. In the calculations, contribution to these EPR parameters due to the admixture of d-orbitals in the ground state wave function of the Cu2+ ion are taken into account based on the cluster approach, and the required crystal-field parameters are estimated from the superposition model which enables correlation of the crystal-field parameters and hence the studied EPR parameters with the local structures of the Cu2+ centers. Based on the calculations, the Cu–H2O bonds are found to suffer the axial elongation ratio δ of about 3 and 2.9% along the z-axis, meanwhile, the planar bond lengths may experience variation ratio τ (≈3.8 and 1%) along x- and y-axis for Cu2+ center in (NH4)2Zn(SO4)2·6H2O and Rb2Zn(SO4)2·6H2O, respectively. The theoretical results show good agreement with the observed values.

DIELECTRIC CONSTANT AND SEEBECK COEFFICIENT FOR SEMICONDUCTORS: THERMODYNAMIC AND DFT STUDIES

2013 ◽  
Vol 12 (06) ◽  
pp. 1350057 ◽  
Author(s):  
HSIU-YA TASI ◽  
CHAOYUAN ZHU
Keyword(s):  
Boundary Condition ◽  
Dielectric Constant ◽  
Seebeck Coefficient ◽  
Gas Phase ◽  
Present Method ◽  
Dielectric Constants ◽  
Semiconductor Materials ◽  
Electronic Polarizability ◽  
Seebeck Coefficients ◽  
Good Agreement

Dielectric constants and Seebeck coefficients for semiconductor materials are studied by thermodynamic method plus ab initio quantum density functional theory (DFT). A single molecule which is formed in semiconductor material is treated in gas phase with molecular boundary condition and then electronic polarizability is directly calculated through Mulliken and atomic polar tensor (APT) density charges in the presence of the external electric field. This electronic polarizability can be converted to dielectric constant for solid material through the Clausius–Mossotti formula. Seebeck coefficient is first simulated in gas phase by thermodynamic method and then its value divided by its dielectric constant is regarded as Seebeck coefficient for solid materials. Furthermore, unit cell of semiconductor material is calculated with periodic boundary condition and its solid structure properties such as lattice constant and band gap are obtained. In this way, proper DFT function and basis set are selected to simulate electronic polarizability directly and Seebeck coefficient through chemical potential. Three semiconductor materials Mg 2 Si , β- FeSi 2 and SiGe are extensively tested by DFT method with B3LYP, BLYP and M05 functionals, and dielectric constants simulated by the present method are in good agreement with experimental values. Seebeck coefficients simulated by the present method are in reasonable good agreement with experiments and temperature dependence of Seebeck coefficients basically follows experimental results as well. The present method works much better than the conventional energy band structure theory for Seebeck coefficients of three semiconductors mentioned above. Simulation with periodic boundary condition can be generalized directly to treat with doped semiconductor in near future.

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