scholarly journals Magnetoelastic Principal Parametric Resonance of a Rotating Electroconductive Circular Plate

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
Zhe Li ◽  
Yu-da Hu ◽  
Jing Li
Keyword(s):  
Magnetic Field ◽  
Circular Plate ◽  
Parametric Resonance ◽  
Magnetic Induction ◽  
Multiple Scales ◽  
Resonance Amplitude ◽  
Thin Circular Plate ◽  
Detuning Parameter ◽  
Principal Parametric Resonance ◽  
Magnetic Induction Intensity

Nonlinear principal parametric resonance and stability are investigated for rotating circular plate subjected to parametric excitation resulting from the time-varying speed in the magnetic field. According to the conductive rotating thin circular plate in magnetic field, the magnetoelastic parametric vibration equations of a conductive rotating thin circular plate are deduced by the use of Hamilton principle with the expressions of kinetic energy and strain energy. The axisymmetric parameter vibration differential equation of the variable-velocity rotating circular plate is obtained through the application of Galerkin integral method. Then, the method of multiple scales is applied to derive the nonlinear principal parametric resonance amplitude-frequency equation. The stability and the critical condition of stability of the plate are discussed. The influences of detuning parameter, rotation rate, and magnetic induction intensity are investigated on the principal parametric resonance behavior. The result shows that stable and unstable solutions exist when detuning parameter is negative, and the resonance amplitude can be weakened by changing the magnetic induction intensity.

Principal parametric resonance of axially accelerating viscoelastic strings with an integral constitutive law

2005 ◽  
Vol 461 (2061) ◽  
pp. 2701-2720 ◽  
Author(s):  
Li-Qun Chen
Keyword(s):  
Steady State ◽  
Parametric Resonance ◽  
Multiple Scales ◽  
Constitutive Law ◽  
Transverse Motion ◽  
Viscoelastic Parameters ◽  
Principal Parametric Resonance ◽  
Linearized Stability ◽  
Speed Fluctuation ◽  
Axial Speed

The steady-state transverse responses and the stability of an axially accelerating viscoelastic string are investigated. The governing equation is derived from the Eulerian equation of motion of a continuum, which leads to the Mote model for transverse motion. The Kirchhoff model is derived from the Mote model by replacing the tension with the averaged tension over the string. The method of multiple scales is applied to the two models in the case of principal parametric resonance. Closed-form expressions of the amplitudes and the existence conditions of steady-state periodical responses are presented. The Lyapunov linearized stability theory is employed to demonstrate that the first (second) non-trivial steady-state response is always stable (unstable). Numerical calculations show that the two models are qualitatively the same, but quantitatively different. Numerical results are also presented to highlight the effects of the mean axial speed, the axial-speed fluctuation amplitude, and the viscoelastic parameters.

Microstructure and Properties of Cu-17Fe Alloy Aged Treatment in High Magnetic Field

2011 ◽  
Vol 194-196 ◽  
pp. 1270-1274
Author(s):  
Ke Ming Liu ◽  
De Ping Lu ◽  
Hai Tao Zhou ◽  
Sheng Fa Wen ◽  
Shi Yong Wei ◽  
...  
Keyword(s):  
Magnetic Field ◽  
High Magnetic Field ◽  
Magnetic Induction ◽  
Solid Solubility ◽  
Aging Treatment ◽  
Heat Treating ◽  
Hardness Tester ◽  
Energy Spectrometer ◽  
Magnetic Induction Intensity ◽  
Scanning Electron

Aging treatment of Cu-17Fe alloy was investigated by a vacuum heat treating furnace in high magnetic furnace. The microstructures were documented using scanning electron microscopy (SEM). The solid solubility of Fe in Cu matrix was analysed by energy spectrometer (EDS). The mechanical properties were measured with a Vickers hardness tester. The electrical conductivity was measured with a micro-ohmmeter. The results showed that high magnetic field can promote spheroidization of the Fe dendrites, the spheroidization intensifies and the solid solubility decreases with the increasing magnetic induction intensity of the high magnetic field exerted to the alloy, the solid solubility of Fe is minimum when the magnetic induction intensity is 10T at 500°C during precipitation. And Cu-17Fe alloy has a good strength/conductivity combination of 110Hv/63%IACS after aging treatment of 10T at 500°C for 1h.

Simulation Research on the Magnetic Field of the Positioning Permanent Magnet for MEMS inside Human Body Based on Ansoft

2014 ◽  
Vol 596 ◽  
pp. 67-71
Author(s):  
Xiu Quan Liu ◽  
Yan Hong Li
Keyword(s):  
Magnetic Field ◽  
Permanent Magnet ◽  
Magnetic Dipole ◽  
Human Body ◽  
Magnetic Induction ◽  
Dipole Model ◽  
Magnetization Direction ◽  
Simulation Research ◽  
Magnetic Induction Intensity ◽  
The Magnetic Field

the magnetic dipole model of the cylindrical permanent magnet was introduced. Then, based on Ansoft software, the simulation model of the cylindrical permanent magnet was established, and the influence of some parameters, such as the height, radius and magnetization direction on the magnetic induction intensity ,were studied; at the same time, under these two models the calculation was compared, the result shows the the magnetic dipole model is applied on condition that distance is nine times greater than the cylindrical permanent magnet size.

Electromagnetic Nondestructive Testing Model and Surface Magnetic Field Analysis for Circumferential Cracks on Metal Rod

2019 ◽  
Vol 2 (4) ◽  
Author(s):  
Feng Jiang ◽  
Shulin Liu ◽  
Shaojie Xin ◽  
Hongli Zhang
Keyword(s):  
Magnetic Field ◽  
Analytical Model ◽  
Magnetic Induction ◽  
Crack Depth ◽  
Field Analysis ◽  
Surface Magnetic Field ◽  
Circumferential Crack ◽  
Inner Surface ◽  
Magnetic Induction Intensity ◽  
The Magnetic Field

Abstract In this paper, an analytical model for a metal rod with a coating layer is proposed to evaluate circumferential crack from the signals of the surface magnetic field. In the proposed model, magnetic vector equations for four regions of space were built, and series expressions of the magnetic field were proposed by the truncated region eigenfunction method. The calculation results can show the three-dimensional distribution of axial and radial magnetic induction intensities on the surface of a metal rod clearly. In addition, the analytical model is verified by using comsol finite element simulation, which also demonstrates that induced eddy currents on the inner surface of the metal rod with cracks appear to be propelled toward the inner layer of the metal rod and the presence of a circumferential crack directly causes a decrease in the induced eddy current on the inner surface of the rod. The results calculated from the analytical model indicated that the model is capable of providing an accurate variation in the magnetic field due to circumferential cracks at different depths. The analytical results showed that the radial magnetic induction intensity increases by 0.16 × 10−3 T, while the axial magnetic induction intensity decreases by 0.3 × 10−3 T as the crack depth increases from 0 to 3 mm.

The Effects of Static Magnetic Field in Leaching Cadmium and Arsenic by Acidthiobacillus ferrooxidans

2014 ◽  
Vol 675-677 ◽  
pp. 90-93
Author(s):  
Li Li Lu ◽  
Dong Wei Li ◽  
Xiang Dong Wei ◽  
Chan Juan Liao ◽  
Jiao Lian Jiang ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Static Magnetic Field ◽  
Magnetic Induction ◽  
Mining Area ◽  
Low Energy ◽  
Leaching Rate ◽  
Environmental Friendly ◽  
Metal Recycling ◽  
Low Energy Consumption ◽  
Magnetic Induction Intensity

In view of the pollution of heavy metals in tailings of mining area, considering some metal recycling, in this paper, the method which was environmental friendly, mild reaction, short process, low energy consumption was applied to leaching As and Cd in tailings. Before leaching, Static Magnetic Field was used to deal with leach liquor, to research the effect of leaching rate for As and Cd. The results showed that under the conditions of pulp density 5%, inoculum 10%, leaching temperature 30°C, pH 2.0, magnetic induction intensity separately were 2mT , 5mT , 8mT and 11mT, the leaching rates of As and Cd were increased respectively about 8% and 2%. Besides, magnetic induction intensity also effected. The best magnetic induction intensity in bioleaching of As and Cd were respectively 2mT and 8mT.

Principal Parametric Resonance of Axially Accelerating Viscoelastic Strings

2005 ◽  
Author(s):  
Li-Qun Chen
Keyword(s):  
Steady State ◽  
Parametric Resonance ◽  
Multiple Scales ◽  
Transverse Motion ◽  
Viscoelastic Parameters ◽  
Principal Parametric Resonance ◽  
Linearized Stability ◽  
Speed Fluctuation ◽  
The Stability ◽  
Axial Speed

The steady-state transverse responses and the stability of an axially accelerating viscoelastic string are investigated. The governing equation is derived from the Eulerian equation of motion of a continuum, which leads to the Mote model for transverse motion. The Kirchhoff model is derived from the Mote model by replacing the tension with the averaged tension over the string. The method of multiple scales is applied to the two models in the case of principal parametric resonance. Closed-form expressions of the amplitudes and the existence conditions of steady-state periodical responses are presented. The Lyapunov linearized stability theory is employed to demonstrate that the first (second) nontrivial steady-state response is always stable (unstable). Numerical calculations show that the two models are qualitatively the same, but quantitatively different. Numerical results are also presented to highlight the effects of the mean axial speed, the axial speed fluctuation amplitude, and the viscoelastic parameters.

scholarly journals Influence of magnetic field and working voltage on the tripping performance in spherical cylindrical ECP

2021 ◽  
Vol 261 ◽  
pp. 02033
Author(s):  
Jianping Zhang ◽  
Baodong Ren
Keyword(s):  
Magnetic Field ◽  
Magnetic Induction ◽  
Optimization Design ◽  
Fine Particles ◽  
Magnetic Confinement ◽  
Operating Conditions ◽  
Dust Removal ◽  
Trapping Effect ◽  
Trapping Performance ◽  
Magnetic Induction Intensity

In order to further improve the trapping effect of fine particles, a new electrostatic cyclone precipitator (ECP) with magnetic confinement was proposed, the overall efficiencies of fine particles under different operating conditions were numerically simulated, and the influence of working voltage on the dust-removal effect of fine particles with and without magnetic field were discussed. The results show that increasing working voltage or magnetic induction intensity improves the trapping performance of spherical cylindrical magnetically confinement ECP, and the lifting effect gradually weakens while increasing the same amplitude. The results can offer technical reference for the optimization design of greatly improving the ECP dust-removal performance.

A time-varying stiffness rotor-active magnetic bearings system under parametric excitation

2008 ◽  
Vol 222 (3) ◽  
pp. 447-458 ◽  
Author(s):  
U H Hegazy ◽  
Y A Amer
Keyword(s):  
Parametric Resonance ◽  
Parametric Excitation ◽  
Multiple Scales ◽  
Magnetic Bearings ◽  
Time Varying ◽  
Active Magnetic Bearings ◽  
Principal Parametric Resonance ◽  
Non Linear ◽  
Response Function Method ◽  
Non Linear System

The method of multiple scales is applied to investigate the non-linear oscillations and dynamic behaviour of a rotor-active magnetic bearings (AMBs) system, with time-varying stiffness. The rotor-AMB model is a two-degree-of-freedom non-linear system with quadratic and cubic non-linearities and parametric excitation in the horizontal and vertical directions. The case of principal parametric resonance is considered and examined. The steady-state response and the stability of the system at the principal parametric resonance case for various parameters are studied numerically, applying the frequency response function method. It is shown that the system exhibits many typical non-linear behaviours including multiple-valued solutions, jump phenomenon, hardening and softening non-linearity. Different effects of the system parameters on the non-linear response of the rotor are also reported. Results are compared with available published work.

scholarly journals A Theoretical Model of Residual Magnetic Field around a Pre-Magnetized Casing String

Energies ◽  
2020 ◽  
Vol 13 (16) ◽  
pp. 4226
Author(s):  
Yucai Shi ◽  
Dongyue Jia ◽  
Zhichuan Guan ◽  
Yuqiang Xu ◽  
Weixing Yang ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetic Induction ◽  
Current Model ◽  
Superposition Principle ◽  
Potential Method ◽  
Detection Distance ◽  
Magnetic Field Model ◽  
The Individual ◽  
Magnetic Poles ◽  
Magnetic Induction Intensity

In the field of petroleum drilling engineering, passive magnetic ranging technology is generally used for specialized drilling operations such as connecting relief wells, preventing wellbore collisions, guiding parallel horizontal wells, etc. Although pre-magnetized casing strings have been used to improve the detection distance and accuracy, the theoretical mechanism is not well understood. Based on the equivalent current model of a permanent magnet, a theoretical magnetic field model around the pre-magnetized casing string was established by using the vector potential method and vector superposition principle and validated by the COMSOL Multiphysics software. Our results show that connecting pre-magnetized individual casings with homogeneous magnetic poles can enlarge the magnetic induction intensity around the total casing string. Furthermore, the magnitude close to the casing coupling is significantly larger than that close to the middle of the individual casing. Connecting pre-magnetized individual casings with heterogeneous magnetic poles results in a low magnetic induction intensity around the total casing string. In order to improve the detection distance and accuracy of the magnetic ranging, the pre-magnetized individual casings should be connected with homogeneous magnetic poles. The results of this study can provide guidelines for the development of passive magnetic ranging technology.

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