On the Stability of Plasma in Static Equilibrium

1958 ◽  
Vol 1 (4) ◽  
pp. 275 ◽  
Author(s):  
M. D. Kruskal ◽  
C. R. Oberman
Keyword(s):  
Static Equilibrium ◽  
The Stability

On the stability of plasma in static equilibrium

1958 ◽  
Vol 7 (3-4) ◽  
pp. 278
Author(s):  
M. Kruskal ◽  
C. Oberman
Keyword(s):  
Static Equilibrium ◽  
The Stability

Modal and Stability Analysis of a Micro-Beam Structure Actuated by Electrostatic Force

2006 ◽  
Vol 505-507 ◽  
pp. 403-408 ◽  
Author(s):  
Hong Hee Yoo ◽  
Kang Sik Jung ◽  
Seung Jae Moon
Keyword(s):  
Stability Analysis ◽  
Equilibrium Position ◽  
Equilibrium Equation ◽  
Electrostatic Force ◽  
Static Equilibrium ◽  
Static Deflection ◽  
Beam Structure ◽  
Design Specification ◽  
Nonlinear Equilibrium ◽  
The Stability

For the design of a vibrating micro-beam structure, modal and stability analyses of the structure actuated by electrostatic force is performed in the present study. Static deflection of the micro-beam caused by the electrostatic force is first obtained by solving the nonlinear equilibrium equation and the modal and stability characteristics are calculated at the static equilibrium position. It is found that the amplitude and the frequency of the applied electrostatic voltage influence the stability of the structure significantly. A design specification of a vibrating micro-beam structure can be effectively determined from the modal and the stability analysis results.

Stability of the High-Speed Journal Bearing Under Steady Load: 1—The Incompressible Film

1962 ◽  
Vol 84 (3) ◽  
pp. 351-357 ◽  
Author(s):  
M. M. Reddi ◽  
P. R. Trumpler
Keyword(s):  
High Speed ◽  
Journal Bearing ◽  
Orbital Motion ◽  
Hydrodynamic Force ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Static Equilibrium ◽  
The Stability ◽  
External Loads ◽  
Steady Load

The phenomenon of oil-film whirl in bearings subjected to steady external loads is analyzed. The journal, assumed to be a particle mass, is subjected to the action of two forces; namely, the external load acting on the bearing and the hydrodynamic force developed in the fluid film. The resulting equations of motion for a full-film bearing and a 180-deg partial-film bearing are developed as pairs of second-order nonlinear differential equations. In evaluating the hydrodynamic force, the contribution of the shear stress on the journal surface is found to be negligible for the full-film bearing, whereas for the partial-film bearing it is found to be significant at small attitude values. The equations of motion are linearized and the coefficients of the resulting characteristic equations are studied for the stability of the static-equilibrium positions. The full-film bearing is found to have no stable static-equilibrium position, whereas the 180-deg partial-film bearing is found to have stable static-equilibrium positions under certain parametric conditions. The equations of motion for the full-film bearing are integrated numerically on a digital computer. The results show that the journal center, depending on the parametric conditions, acquired either an orbital motion or a dynamical path of increasing attitude terminating in bearing failure.

scholarly journals Stability Effects of Non-Circular Geometry in Floating Ring Bearings

Lubricants ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 99
Author(s):  
Giovanni Adiletta
Keyword(s):  
Equilibrium Position ◽  
Transient Analysis ◽  
Numerical Study ◽  
Theoretical Aspect ◽  
Static Equilibrium ◽  
Geometrical Parameters ◽  
Nonlinear Transient ◽  
Minor Part ◽  
The Stability ◽  
A Minor

The present study theoretically evaluates the stability potential of noncircular geometries when they are adopted in the outer bearing of floating ring bearings (FRB). A numerical study is carried out to evaluate the stability about the static equilibrium position of a balanced, symmetrical, rigid rotor, horizontally placed, and supported at both ends by identical FRBs. In the analysis, the outer bearing of these FRBs is alternatively shaped with common circular bore (CB), two lobe-wave bore (2LWB) or lemon bore (LB), assuming a linearization of the film forces. A minor part of the study consists of partially supporting the results of the above study by means of a nonlinear, transient analysis. Despite limiting to the theoretical aspect, dealt with under several simplifying hypotheses, the investigation highlights the influence of the examined non-circular geometries on the stability of the static equilibrium position, when these geometries are adopted for shaping the outer housing of the FRB. The paper shows that contrasting effects are obtained, depending on the chosen geometrical parameters. In the paper, the acronyms CB, 2LWB, and LB are used to indicate the FRB layouts respectively equipped with outer circular, wave, and lemon bearing.

Qualifications and Internal Checks versus Independent Proof of Structural Design

2017 ◽  
Author(s):  
Wolfram Jäger
Keyword(s):  
Project Scheduling ◽  
Structural Design ◽  
Structural Engineering ◽  
Self Regulation ◽  
Practical Experience ◽  
Third Party ◽  
Static Equilibrium ◽  
Construction Work ◽  
The Stability ◽  
Intense Debate

Against the background of European standardisation of structural engineering principles, there is intense debate about the extent to which self-regulation and internal inspections can replace independent inspection of calculations relating to static equilibrium, project scheduling and execution of construction work by a third party. There is also discussion about whether the likelihood of errors decreases and, to a certain extent, whether errors would be unlikely or would not have a significant effect on the stability of buildings, as engineers become better qualified. This contribution examines both questions and gives examples from the author’s practical experience.

Dynamic Relaxation Using Continuous Kinetic Damping—Part I: Basic Algorithm

2018 ◽  
Vol 13 (8) ◽  
Author(s):  
Samuel Jung ◽  
Tae-Yun Kim ◽  
Wan-Suk Yoo
Keyword(s):  
Convergence Rate ◽  
Nonlinear Models ◽  
Mass Matrix ◽  
Static Equilibrium ◽  
Stability And Convergence ◽  
Dynamic Relaxation ◽  
Basic Algorithm ◽  
Dr Method ◽  
Second Order Convergence ◽  
The Stability

Dynamic relaxation (DR) is the most widely used approach for static equilibrium analyses. Specifically, DR compels dynamic systems to converge to a static equilibrium through the addition of fictitious damping. DR methods are classified by the method in which fictitious damping is applied. Conventional DR methods use a fictitious mass matrix to increase the fictitious damping while maintaining numerical stability. There are many calculation methods for the fictitious mass matrix; however, it is difficult to select the appropriate method. In addition, these methods require a stiffness matrix of a model, which makes it difficult to apply nonlinear models. To resolve these problems, a new DR method that uses continuous kinetic damping (CKDR) is proposed in this study. The proposed method does not require the fictitious mass matrix and any tuning coefficients, and it possesses a second-order convergence rate. The aforementioned advantages are unique and significant when compared to those of conventional methods. The stability and convergence rate were analyzed by using an eigenvalue analysis and demonstrated by simulating nonlinear models of a pendulum and cable. Simple but representative models were used to clearly demonstrate the features of the proposed DR method and to enable the reproducibility of the verification results.

Nonlinear Structural Dynamic Analyses of Micro Cantilever Beams Actuated by Electrostatic Force

2006 ◽  
Vol 321-323 ◽  
pp. 1644-1648
Author(s):  
Hong Hee Yoo ◽  
Simon Song ◽  
Kang Sik Jung ◽  
Kwan Yong Kim
Keyword(s):  
Electrostatic Force ◽  
Nonlinear Modeling ◽  
Static Equilibrium ◽  
Cantilever Beams ◽  
Static Deflection ◽  
Structural Dynamic ◽  
Dynamic Analyses ◽  
Nonlinear Static ◽  
Micro Cantilever ◽  
The Stability

Nonlinear modeling method for the structural dynamic analysis of a micro cantilever beam actuated by electrostatic force is presented in this study. Static deflection is first obtained by solving nonlinear static equilibrium equation and the modal and the stability characteristics are calculated at the static equilibrium position. It is found that the amplitude and the frequency of the applied electrostatic voltage influence the stability of the structure significantly.

scholarly journals Stability of Manipulator Configuration Under External Loading

2012 ◽  
Author(s):  
Alexandr Klimchik ◽  
Anatol Pashkevich ◽  
Damien Chablat
Keyword(s):  
Equilibrium Configuration ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Static Equilibrium ◽  
Practical Significance ◽  
External Loading ◽  
Kinematic Chains ◽  
Cartesian Stiffness Matrix ◽  
The Stability ◽  
Cartesian Stiffness

The paper is devoted to the analysis of robotic manipulator behavior under internal and external loadings. The main contributions are in the area of stability analysis of manipulator configurations corresponding to the loaded static equilibrium. In contrast to other works, in addition to usually studied the end-platform behavior with respect to the disturbance forces, the problem of configuration stability for each kinematic chain is considered. The proposed approach extends the classical notion of the stability for the static equilibrium configuration that is completely defined the properties of the Cartesian stiffness matrix only. The advantages and practical significance of the proposed approach are illustrated by several examples that deal with serial kinematic chains and parallel manipulators. It is shown that under the loading the manipulator workspace may include some specific points that are referred to as elastostatic singularities where the chain configurations become unstable.

A Strategy for Characterizing the Stability of Parts Fixtured Under Three-Point Frictional Constraint

1991 ◽  
Author(s):  
K. J. Linder ◽  
R. J. Cipra
Keyword(s):  
Unstable Mode ◽  
Static Equilibrium ◽  
Assembly Systems ◽  
Clamping Force ◽  
Systematic Method ◽  
Flexible Assembly ◽  
Frictional Properties ◽  
The Stability ◽  
Fixture Configuration

Abstract Flexible assembly systems require flexible fixtures which can constrain parts in a stable fashion and will adapt quickly and easily to a change in the type of part. A fixtured part is either unstable or stable depending on whether or not it moves when the clamping force is applied. This paper gives a systematic method which uses graphical techniques to characterize the stability of parts fixtured under a particular type of three-point frictional constraint. The three inputs into this method are the location of the center of gravity of the part and the geometrical and frictional properties of the fixturing system. No information about the applied clamping force is necessary for the method to characterize stability. The method first determines if it is possible that static equilibrium will not occur when the clamping force is applied. If this possibility exists, then corresponding kinematically possible motions are determined and are tested for consistency with dynamics to determine if any of them are a possible unstable mode. Finally, the method classifies a part into one of three classifications: stable, unstable, or indeterminate. If it is determined that there are no possible unstable modes then the part is stable. But if it is determined that static equilibrium cannot occur then it is unstable. If it is discovered that static equilibrium is possible yet possible unstable motions also exist then the stability of the part is indeterminate. In spite of these stability indeterminacies, the method can determine all possible unstable motions of both unstable and indeterminate parts. This characterization of the stability of parts can provide useful feedback as to how a fixture configuration can be modified in order to either provide or improve a stable clamping arrangement.

Open discussion

1982 ◽  
Vol 99 ◽  
pp. 605-613
Author(s):  
P. S. Conti
Keyword(s):  
Buenos Aires ◽  
Large Mass ◽  
List Type ◽  
Common Phenomenon ◽  
Open Discussion ◽  
The Stability ◽  
Ring Nebulae

Conti: One of the main conclusions of the Wolf-Rayet symposium in Buenos Aires was that Wolf-Rayet stars are evolutionary products of massive objects. Some questions:–Do hot helium-rich stars, that are not Wolf-Rayet stars, exist?–What about the stability of helium rich stars of large mass? We know a helium rich star of ∼40 MO. Has the stability something to do with the wind?–Ring nebulae and bubbles : this seems to be a much more common phenomenon than we thought of some years age.–What is the origin of the subtypes? This is important to find a possible matching of scenarios to subtypes.

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