Rigid Rotor Model for Field-Reversed Configurations, Revisited

1991 ◽  
Vol 60 (9) ◽  
pp. 2960-2965 ◽  
Author(s):  
Roberto A. Clemente
Keyword(s):  
Rigid Rotor ◽  
Field Reversed Configurations ◽  
Rotor Model

scholarly journals Bichromatic Photoassociation Spectroscopy for the Determination of Rotational Constants of Cs2 0 u + Long-Range State below the 6S1/2 + 6P1/2 Asymptote

Molecules ◽  
2020 ◽  
Vol 25 (17) ◽  
pp. 3963
Author(s):  
Jizhou Wu ◽  
Jie Ma ◽  
Yuqing Li ◽  
Wenliang Liu ◽  
Peng Li ◽  
...  
Keyword(s):  
Long Range ◽  
Spectroscopic Technique ◽  
Rigid Rotor ◽  
Simple Analysis ◽  
Rotational Constants ◽  
Vibrational Levels ◽  
Photoassociation Spectroscopy ◽  
Rotor Model ◽  
Good Agreement

This article demonstrates new observation of the high-resolution ro-vibrational bichromatic photoassociation spectra (BPAS) of Cs2 in the 0u+ long-range state below the asymptotes 6S1/2 + 6P1/2. By combining with a modulation spectroscopic technique, precise references of the frequency differences have been engineered through the BPAS, with which the rotational constants of low-lying vibrational levels of the Cs20u+ long-range state have been accurately determined by fitting the frequency differences to the non-rigid-rotor model. The rotational constants for the newly observed seven ro-vibrational levels are summarized and disagreement for the level ῦ = 498 is clarified. The rotational constants of different vibrational levels demonstrate strong perturbations of the related energy structures. A simple analysis is performed and shows good agreement with experimental results.

Nonlinear Vibration Analysis of an Elastic Rotor Supported on Angular Contact Ball Bearings Considering Six Degrees of Freedom and Waviness on Balls and Races

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
C. K. Babu ◽  
N. Tandon ◽  
R. K. Pandey
Keyword(s):  
Nonlinear Vibration ◽  
Elastic Deformation ◽  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Ball Bearings ◽  
Rigid Rotor ◽  
Six Degrees Of Freedom ◽  
Extension Work ◽  
Inner Race ◽  
Rotor Model

Nonlinear vibration analysis of an elastically deformable shaft supported on two lubricated angular contact ball bearings is reported herein considering six-degrees of freedom (6-DOF) and waviness on races and balls. This is an extension work of the investigation published by the authors Babu, C. K., Tandon, N., and Pandey, R. K., 2012, “Vibration Modeling of a Rigid Rotor Supported on the Lubricated Angular Contact Ball Bearings Considering Six Degree of Freedom and Waviness on Balls and Races,” ASME J. Vib. Acoust., 134, p. 011006. Elastic deformation of shaft, frictional moment, and waviness on races and balls have been incorporated in the model for the vibration investigations of rotor's CG. Two noded 3D Timoshenko beam element having 6-DOF has been employed in the computation of the shaft's deformation. Governing equations with appropriate boundary conditions have been solved using 4th order Runge–Kutta method. It is observed that vibration amplitude enhances considerably after incorporating the elastic deformation in comparison to the amplitude achieved using rigid rotor model approach. Moreover, the influence of outer race's radial waviness is large on the amplitudes of vibrations in comparison to radial waviness of inner race. However, it is worth noting here that in case of rigid rotor model the presence of radial waviness on inner race yields high amplitudes of vibrations.

scholarly journals Blade Loss Simulation of Multi Mass Rotor Model With Nonlinear Tilt Pad Journal Bearings

1995 ◽  
Author(s):  
R. K. Gadangi ◽  
A. B. Palazzolo
Keyword(s):  
Natural Frequency ◽  
Transient Response ◽  
Critical Speed ◽  
Journal Bearings ◽  
Rigid Rotor ◽  
Flexible Rotor ◽  
Equilibrium Location ◽  
Rotor Model ◽  
Limiting Value ◽  
Bearing System

Prediction of rotor vibrations due to large imbalance requires nonlinear solution of the supporting bearings. This paper presents a methodology and results for the effects of large, sudden imbalance on the response of a multi mass rotor model supported on tilt pad journal bearings. For a given imbalance, response is obtained for rotor speeds below, above and at the rotor natural frequency. The maximum peak to peak amplitude is larger at the critical speed than at a speed above or below the critical. The imbalance response is compared with two other methods used for predicting the transient response of a rotor bearing system. The rigid rotor and nonlinear bearing model shows a response similar in shape to that obtained with a flexible rotor and nonlinear bearing model, but the magnitude is different, which reached a limiting value as the imbalance was increased. The flexible rotor and linearized bearing model predicts a similar trend as the flexible rotor and nonlinear bearing model, with increasing speed for a given imbalance, but the shape and magnitude of the orbit is completely different. The motion of rotor to static equilibrium location for the flexible rotor and nonlinear bearing model showed oscillations which diminished with time, while the rigid rotor and nonlinear bearing model does not show any oscillations.

scholarly journals Two-parameter modified rigid rotor radial equilibrium model for field-reversed configurations

2021 ◽  
Vol 61 (3) ◽  
pp. 036046
Author(s):  
H.J. Ma ◽  
H.S. Xie ◽  
Y.K. Bai ◽  
S.K. Cheng ◽  
B.H. Deng ◽  
...  
Keyword(s):  
Equilibrium Model ◽  
Rigid Rotor ◽  
Field Reversed Configurations ◽  
Two Parameter ◽  
Radial Equilibrium

Chaos of a Flexible Rotor in Journal Bearings

1995 ◽  
Author(s):  
R. D. Brown ◽  
G. Drummond
Keyword(s):  
Theoretical Models ◽  
Journal Bearings ◽  
Rotating Machinery ◽  
Rigid Rotor ◽  
Flexible Rotor ◽  
Hydrodynamic Bearings ◽  
Stress Reversals ◽  
Oil Films ◽  
Rigid Rotors ◽  
Rotor Model

Abstract Nonlinear systems can give rise to chaotic behaviour, essentially unpredictable. Oil film forces arising from hydrodynamic bearings in rotating machinery can be extremely nonlinear under conditions of large unbalance. Chaotic response has been demonstrated in theoretical models of rigid rotors supported in hydrodynamic bearings. The behaviour of a rigid rotor can be extended by looking at a flexible rotor model supported on journal bearings and subject to large unbalance levels. The introduction of a flexible shaft yields chaotic regions which are less extensive than those obtained from a rigid rotor model. This is not surprising as the nonlinearity in the model is confined to the oil films at the end of the shaft. However if this level of unbalance is experienced in service then shaft fatigue could occur because of the sustained nature of the non-synchronous response and the effect of the resulting stress reversals.

Free rotor model or rigid rotor model for CH3F-Ne complex and comparison with other CH3F-rare gas systems

2016 ◽  
Vol 32 (5) ◽  
pp. 818-826 ◽  
Author(s):  
Yongtao Ma ◽  
Yuanyuan Zhao ◽  
Dan Hou ◽  
Hui Li
Keyword(s):  
Rare Gas ◽  
Rigid Rotor ◽  
Rotor Model

On the π-Donating Abilities of Sulfur and Oxygen. A Comparative Quantum Chemical Investigation of the Static and Dynamic Properties and Gas Phase Acidities of and

1975 ◽  
Vol 53 (8) ◽  
pp. 1144-1153 ◽  
Author(s):  
Fernando Bernardi ◽  
Imre G. Csizmadia ◽  
H. Bernhard Schlegel ◽  
Saul Wolfe
Keyword(s):  
Gas Phase ◽  
Quantum Chemical ◽  
Dynamic Properties ◽  
Population Analysis ◽  
Rigid Rotor ◽  
Linear Inversion ◽  
Overlap Population ◽  
Type Population ◽  
Methylene Group ◽  
Rotor Model

Nonempirical SCF-MO computations have been performed on CH2O, CH2S, and their protonated derivatives [Formula: see text] and [Formula: see text]. The methylene group of CH2O is strongly positive and that of CH2S is slightly negative, because oxygen in CH2O behaves towards carbon as a π-donor and σ-acceptor, but sulfur in CH2S behaves as both a π- and σ-donor. The total π-overlap in CH2O is greater than that in CH2S.The stable conformations of [Formula: see text] and [Formula: see text] correspond in each case to a structure in which all atoms lie in the same plane. In this conformation, both the C—O and C—S bond lengths are substantially shorter than those of methanol and methanethiol, indicative of conjugative interaction between the cationic center and the adjacent heteroatom. From the results of a Mulliken-type population analysis it is found that, relative to hydrogen, OH and SH behave towards an adjacent [Formula: see text] group as electron-withdrawing and electron-releasing ligands, respectively. When [Formula: see text] is considered to form from [Formula: see text] and OH fragments, π-donation from O to C amounts to 0.38 electron, but σ-donation in the opposite direction amounts to 0.35 electron; the π-overlap population is 0.1496. A similar analysis of [Formula: see text] reveals π- and σ-donation from S to C of 0.53 and 0.15 electron, respectively, and a π-overlap population of 0.1734, so that sulfurformsastronger π-bondtotheadjacentcationiccenter.Geometrical isomerization of [Formula: see text] proceeds by linear inversion at oxygen, with a barrier of 13.98 kcal/mol; but that of [Formula: see text] proceeds by rotation about the C—S bond, with a barrier of 36.47 kcal/mol. This latter value is substantially higher than that (23 kcal/mol ) computed for [Formula: see text] with a rigid rotor model, and reflects the greater strength of the π-bond between sulfur and the adjacent cationic center.

scholarly journals A Numeric Solution of the Quantum Rigid Rotor

2020 ◽  
Author(s):  
Guilherme de Souza Tavares de Morais ◽  
Rogério Custodio
Keyword(s):  
Grid Method ◽  
Integral Form ◽  
Rigid Rotor ◽  
Coordinate Systems ◽  
Numerical Techniques ◽  
Coupled Equations ◽  
Curvilinear Coordinate ◽  
Numeric Solution ◽  
Transformation Of Variables ◽  
Rotor Model

The Variable Fixed Grid Method (VFGM) combines numerical techniques of differentiation and integration to solve the Schrödinger equation in its integral form. The method is extremely simple and allows to overcome difficulties found in conventional resolutions and when coupled equations are produced. However, difficulties arise when curvilinear coordinate systems are used because there are no well-defined boundary conditions for the angular functions. Systematic numerical alternatives were performed using the rigid rotor model. A transformation of variables proved to be efficient for calculating energy and the wave function. The difficulties are located at the poles where the Jacobian of the curvilinear coordinate system is canceled. The method used in this work allows a greater application of VFGM for systems in different curvilinear coordinate systems.

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