scholarly journals Nonlinear Restoring Force Characteristic and Vibration of a Rotating Shaft Supported by a Repulsive Magnetic Bearing (Influences of Both the Axial Displacement and the Magnetic Length Ratio)

2011 ◽  
Vol 77 (778) ◽  
pp. 2169-2180 ◽  
Author(s):  
Tomohiro SUGAI ◽  
Tsuyoshi INOUE ◽  
Yukio ISHIDA
Keyword(s):  
Magnetic Bearing ◽  
Axial Displacement ◽  
Length Ratio ◽  
Force Characteristic ◽  
Rotating Shaft ◽  
Restoring Force ◽  
Nonlinear Restoring Force ◽  
Magnetic Length

Vibration of the Vertical Rigid Rotor Supported by a Repulsive-Type Magnetic Bearing: Effects of Both the Axial Displacement and the Magnetical Anisotropicities of Magnets

2007 ◽  
Author(s):  
Tsuyoshi Inoue ◽  
Yukio Ishida ◽  
Tomohiro Sugai
Keyword(s):  
Permanent Magnet ◽  
Magnetic Bearing ◽  
Axial Displacement ◽  
Rigid Rotor ◽  
Rotating Shaft ◽  
Restoring Force ◽  
Uniform Magnetization ◽  
Nonlinear Force ◽  
Linear And Nonlinear ◽  
Force Characteristics

Magnetic bearing is considered for the usage in various industries. This paper investigates vibration of the rotating shaft supported passively by a repulsive-type magnetic bearing. The permanent magnet on the market not only has strong nonlinear force characteristics, but also may have a few percents of non-uniform magnetization characteristics. Also nonlinear force characteristics change as axial displacement of the shaft. Restoring force of a repulsive-type magnetic bearing is evaluated numerically considering the effects of both the axial displacement of the shaft and the magnetical anisotropicities of the inner and outer magnets. The occurrences of not only the linear and nonlinear parametric characteristics, but also the excitational forces for each pattern of magnetical anisotropicities are observed and they are evaluated in terms of the axial displacement. Furthermore, the influence of each magnetical anisotropicity pattern on the occurrences of various resonance phenomena is clarified.

scholarly journals Identification of the Nonlinear Restoring Force Characteristic of a Rubber Mounting

PAMM ◽  
2003 ◽  
Vol 2 (1) ◽  
pp. 270-271 ◽  
Author(s):  
J.-U. Bruns ◽  
M. Lindner ◽  
K. Popp
Keyword(s):  
Force Characteristic ◽  
Restoring Force ◽  
Nonlinear Restoring Force

Dynamics of a Simple Model for a Wind-Loaded Nonlinear Structure: Bifurcations of Codimension One and Two

1998 ◽  
Vol 65 (2) ◽  
pp. 505-512 ◽  
Author(s):  
K. Yagasaki
Keyword(s):  
Vortex Shedding ◽  
Degree Of Freedom ◽  
Force Characteristic ◽  
Restoring Force ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Nonlinear Restoring Force ◽  
Codimension One ◽  
Theoretical Predictions ◽  
The Cross

The motion induced by vortex shedding of a structure with nonlinear restoring force is investigated. In particular, a conclusion about nonexistence of bounded motions obtained for a similar problem in the previous study is improved by taking into account the nonlinear restoring force characteristic. The vortex shedding frequency is assumed to be close to the natural frequency of the cross-wind oscillation and the along-wind oscillation is not excited, so that a single-degree-of-freedom model representing the cross-wind motions is obtained. The averaging method is applied to the single-degree-of-freedom system, and the normal form and center manifold theories are used to discuss bifurcations of codimension one, saddle-node and Hopf bifurcations. Moreover, it is shown that a multiple bifurcation of codimension two, called the Bogdanov-Takens bifurcation, occurs in the averaged system. The implications of the averaging results on the dynamics of the original single-degree-of-freedom system are described. Numerical examples are also given with numerical simulation results for both the averaged and original systems to demonstrate our theoretical predictions.

Contact Whirling Vibration of a Rotating Shaft Supported by a Repulsive Magnetic Bearing and the Influence of the Axial Displacement on Its Suppression

2011 ◽  
Author(s):  
Tomohiro Sugai ◽  
Tsuyoshi Inoue ◽  
Yukio Ishida
Keyword(s):  
Rotational Speed ◽  
Critical Speed ◽  
Nonlinear Coefficient ◽  
Magnetic Bearing ◽  
Axial Displacement ◽  
Damping Coefficient ◽  
Rotating Shaft ◽  
Escape Speed

A rotating shaft supported by a repulsive magnetic bearing may contact with a backup bearing during the passage of the critical speed as the damping coefficient of the repulsive magnetic bearing is small. This paper investigates the contact vibration during passage of the critical speed. Particularly, the influence of the axial displacement of the repulsive magnetic bearing on the escape speed from the contact vibration is focused. As a result, it is clarified that the rotational speed of the escapement from the contact vibration decreases as the axial displacement increases. It is explained by the change of both the linear stiffness and nonlinear coefficient in the increase of the axial displacement.

Nonparametric nonlinear restoring force and excitation identification with Legendre polynomial model and data fusion

2021 ◽  
pp. 147592172199474
Author(s):  
Bin Xu ◽  
Ye Zhao ◽  
Baichuan Deng ◽  
Yibang Du ◽  
Chen Wang ◽  
...  
Keyword(s):  
Data Fusion ◽  
Legendre Polynomial ◽  
Structural Parameters ◽  
Polynomial Model ◽  
Magnetorheological Damper ◽  
Dynamic Responses ◽  
Identification Accuracy ◽  
Restoring Force ◽  
Nonlinear Restoring Force ◽  
Dynamic Loadings

Identification of nonlinear restoring force and dynamic loadings provides critical information for post-event damage diagnosis of structures. Due to high complexity and individuality of structural nonlinearities, it is difficult to provide an exact parametric mathematical model in advance to describe the nonlinear behavior of a structural member or a substructure under strong dynamic loadings in practice. Moreover, external dynamic loading applied to an engineering structure is usually unknown and only acceleration responses at limited degrees of freedom of the structure are available for identification. In this study, a nonparametric nonlinear restoring force and excitation identification approach combining the Legendre polynomial model and extended Kalman filter with unknown input is proposed using limited acceleration measurements fused with limited displacement measurements. Then, the performance of the proposed approach is first illustrated via numerical simulation with multi-degree-of-freedom frame structures equipped with magnetorheological dampers mimicking nonlinearity under direct dynamic excitation or base excitation using noise-polluted measurements. Finally, a dynamic experimental study on a four-story steel frame model equipped with a magnetorheological damper is carried out and dynamic response measurement is employed to validate the effectiveness of the proposed method by comparing the identified dynamic responses, nonlinear restoring force, and excitation force with the test measurements. The convergence and the effect of initial estimation errors of structural parameters on the final identification results are investigated. The effect of data fusion on improving the identification accuracy is also investigated.

Soft X-ray emission from an anharmonic collisional nanoplasma by a laser–nanocluster interaction

2021 ◽  
Vol 87 (3) ◽  
Author(s):  
R. Nemati Siahmazgi ◽  
S. Jafari
Keyword(s):  
Electric Field ◽  
Laser Beam ◽  
Resonant Frequency ◽  
Restoring Force ◽  
Cluster Radius ◽  
X Ray ◽  
Nonlinear Restoring Force ◽  
Cluster Temperature ◽  
Argon Clusters ◽  
Helium Neon

The purpose of the present paper is to investigate the generation of soft X-ray emission from an anharmonic collisional nanoplasma by a laser–nanocluster interaction. The electric field of the laser beam interacts with the nanocluster and leads to ionization of the cluster atoms, which then produces a nanoplasma. Because of the nonlinear restoring force in an anharmonic nanoplasma, the fluctuations and heating rate of, as well as the power radiated by, the electrons in the nanocluster plasma will be notably different from those arising from a linear restoring force. By comparing the nonlinear restoring force state (which arises from an anharmonic cluster) with that of the linear restoring force (in harmonic clusters), the cluster temperature specifically changes at the resonant frequency relative to the linear restoring force, while the variation of the anharmonic cluster radius is almost identical to that of the harmonic cluster radius. In addition, it is revealed that a sharp peak of X-ray emission arises after some picoseconds in deuterium, helium, neon and argon clusters.

Harmonic Oscillations of Nonlinear Two-Degree-of-Freedom Systems

1955 ◽  
Vol 22 (1) ◽  
pp. 107-110
Author(s):  
T. C. Huang
Keyword(s):  
Nonlinear System ◽  
Degrees Of Freedom ◽  
Forced Oscillations ◽  
Viscous Damping ◽  
Free Oscillations ◽  
Response Curves ◽  
Harmonic Oscillations ◽  
Restoring Force ◽  
Nonlinear Restoring Force ◽  
Two Degree Of Freedom

Abstract In this paper an investigation is made of equations governing the oscillations of a nonlinear system in two degrees of freedom. Analyses of harmonic oscillations are illustrated for the cases of (1) the forced oscillations with nonlinear restoring force, damping neglected; (2) the free oscillations with nonlinear restoring force, damping neglected; and (3) the forced oscillations with nonlinear restoring force, small viscous damping considered. Amplitudes of oscillations and frequency equations are derived based on the mathematically justified perturbation method. Response curves are then plotted.

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