scholarly journals The universal instability in general geometry

2015 ◽  
Vol 22 (9) ◽  
pp. 090706 ◽  
Author(s):  
P. Helander ◽  
G. G. Plunk
Keyword(s):  
General Geometry

Nonlinear Corrections for Edge Bending of Shells

1980 ◽  
Vol 47 (4) ◽  
pp. 861-865 ◽  
Author(s):  
G. V. Ranjan ◽  
C. R. Steele
Keyword(s):  
Differential Equations ◽  
Spherical Shell ◽  
Asymptotic Expansions ◽  
Axial Displacement ◽  
Exponential Functions ◽  
Spherical Cap ◽  
Influence Coefficients ◽  
Edge Loading ◽  
General Geometry ◽  
Edge Influence

Asymptotic expansions for self-equilibrating edge loading are derived in terms of exponential functions, from which formulas for the stiffness and flexibility edge influence coefficients are obtained, which include the quadratic nonlinear terms. The flexibility coefficients agree with those previously obtained by Van Dyke for the pressurized spherical shell and provide the generalization to general geometry and loading. In addition, the axial displacement is obtained. The nonlinear terms in the differential equations can be identified as “prestress” and “quadratic rotation.” To assess the importance of the latter, the problem of a pressurized spherical cap with roller supported edges is considered. Results show that whether the rotation at the edge is constrained or not, the quadratic rotation terms do not have a large effect on the axial displacement. The effect will be large for problems with small membrane stresses.

scholarly journals Kinetic ballooning modes in tokamaks and stellarators

2018 ◽  
Vol 84 (6) ◽  
Author(s):  
K. Aleynikova ◽  
A. Zocco ◽  
P. Xanthopoulos ◽  
P. Helander ◽  
C. Nührenberg
Keyword(s):  
Plasma Pressure ◽  
Analytical Prediction ◽  
Ion Temperature ◽  
Ion Temperature Gradient ◽  
Large Pressure ◽  
Equilibrium Configurations ◽  
Mhd Stability ◽  
Ideal Magnetohydrodynamic ◽  
General Geometry ◽  
The Ideal

Kinetic ballooning modes (KBMs) are investigated by means of linear electromagnetic gyrokinetic (GK) simulations in the stellarator Wendelstein 7-X (W7-X), for high-$\unicode[STIX]{x1D6FD}$ plasmas, where $\unicode[STIX]{x1D6FD}$ is the ratio of thermal to magnetic plasma pressure. The analysis shows suppression of ion-temperature-gradient (ITG) and trapped particle modes (TEM) by finite-$\unicode[STIX]{x1D6FD}$ effects and destabilization of KBMs at high $\unicode[STIX]{x1D6FD}$. The results are compared with a generic tokamak case. We show that, for large pressure gradients, the frequency of KBMs evaluated by the GENE code is in agreement with the analytical prediction of the diamagnetic modification of the ideal magnetohydrodynamic limit in W7-X general geometry. Thresholds for destabilization of the KBM are predicted for different W7-X equilibrium configurations. We discuss the relation of these thresholds to the ideal magnetohydrodynamic (MHD) stability properties of the corresponding equilibria.

Closed-Form Determination of the Location of a Rigid Body by Seven In-Parallel Linear Transducers

1996 ◽  
Author(s):  
Carlo Innocenti
Keyword(s):  
Rigid Body ◽  
Linear Equations ◽  
Parallel Manipulators ◽  
Rigid Bodies ◽  
Body Location ◽  
Position And Orientation ◽  
General Geometry ◽  
Two Bodies

Abstract The paper presents an original analytic procedure for unambiguously determining the relative position and orientation (location) of two rigid bodies based on the readings from seven linear transducers. Each transducer connects two points arbitrarily chosen on the two bodies. The sought-for rigid-body location simply results by solving linear equations. The proposed procedure is suitable for implementation in control of fully-parallel manipulators with general geometry. A numerical example shows application of the reported results to a case study.

Attraction and repulsion of floating particles

1982 ◽  
Vol 60 (23) ◽  
pp. 2889-2895 ◽  
Author(s):  
M. A. Fortes
Keyword(s):  
Capillary Force ◽  
Cylindrical Symmetry ◽  
Contact Angles ◽  
Single Parameter ◽  
The Other ◽  
Horizontal Force ◽  
Wetting Properties ◽  
General Geometry ◽  
Floating Particles ◽  
Floating Cylinders

The horizontal force that has to be applied to floating cylinders to equilibrate the capillary force is calculated for a general geometry with cylindrical symmetry and for any wetting characteristics of the cylinders. The force on a cylinder can be related to a single parameter of each of the two menisci that contact the cylinder. It is found that the force between parallel vertical plates or parallelipipeds can be repulsive if one of the contact angles is acute and the other obtuse. The force on cylinders between fixed walls is also calculated and the results suggest that it may be possible to separate floating particles with different wetting properties by placing them between two walls with different contact angles.

The Workspace of a General Geometry Planar Three-Degree-of-Freedom Platform-Type Manipulator

1993 ◽  
Vol 115 (2) ◽  
pp. 269-276 ◽  
Author(s):  
G. R. Pennock ◽  
D. J. Kassner
Keyword(s):  
Degree Of Freedom ◽  
Arbitrary Orientation ◽  
End Effector ◽  
The Absolute ◽  
Position Problem ◽  
General Geometry ◽  
Three Degree Of Freedom ◽  
Insight Into

This paper focuses on the direct workspace problems of a general geometry fully-parallel-actuated, planar three-degree-of-freedom platform-type manipulator. A set of equations are presented that determine the workspace as a function of the platform orientation. The formulation is governed by the solution to the inverse position problem of the manipulator. The reachable positions of the end-effector point, for a specified platform orientation, are analyzed. To illustrate the concepts, a practical example is included where the end-effector is required to move a cup filled with water. Then the platform orientation, for a specified location of the end-effector point, is studied. If an arbitrary orientation is possible, the specified location of the end-effector point is said to be within the primary workspace. The paper includes a detailed discussion of the total primary workspaces of the manipulator. The approach adopted here is to regard the manipulator as a combination of three planar, three-revolute open chains. For the sake of completeness, the influence of special manipulator geometry on the workspace is also discussed. Finally, the paper includes the conditions that cause stationary configurations of the manipulator. Insight into these undesirable configurations is provided by a study of the location of the absolute instant center of the platform.

An Algebraic Method for Direct Position Analysis of the General Stewart Platform Manipulator Robot

2009 ◽  
Vol 626-627 ◽  
pp. 405-410
Author(s):  
Xi Guang Huang ◽  
Guang Pin He ◽  
Q.Z. Liao
Keyword(s):  
Parallel Manipulator ◽  
Algebraic Method ◽  
Stewart Platform ◽  
Mobile Platform ◽  
Analysis Problem ◽  
Position Analysis ◽  
General Geometry ◽  
Six Degree Of Freedom ◽  
Manipulator Robot ◽  
Base Platform

Stewart platform manipulator robot is a six degree of freedom, parallel manipulator, which consists of a base platform, a mobile platform and six limbs connected at six distinct points on the base platform and the mobile platform respectively. The direct position analysis problem of Stewart platform relates to the determination of the mobile platform pose for a given set of the lengths of the limbs. In this paper, we present a concise algebraic method for solving the direct position analysis problem for the fully parallel manipulator with general geometry, often referred to as General Stewart platform manipulator. Based on the presented algebraic method, we derive a 40th degree univariate polynomial from a determinant of 20×20 Sylvester’s matrix, which is relatively small in size. We also obtain a complete set of 40 solutions to the most general Stewart platform. The proposed method is comparatively concise and reduces the computational burden. Finally the method is demonstrated by a numerical example.

Resonance Calculation for Large and Complicated Geometry Using Tone’s Method by Incorporating the Method of Characteristics

2010 ◽  
Author(s):  
Yu Hao ◽  
Akio Yamamoto ◽  
Yoshihiro Yamane
Keyword(s):  
Fuel Assembly ◽  
Method Of Characteristics ◽  
Infinite Cylinder ◽  
The Method Of Characteristics ◽  
Infinite Slab ◽  
Complicated Geometry ◽  
General Geometry ◽  
Full Core

Applicability and efficiency of Tone’s method used for resonance calculations is improved by incorporating the Method of Characteristics (MOC). Verification calculations are carried out in three configurations, i.e., infinite slab, infinite cylinder, and pin-cell. The validity of the modified Tone’s method has been confirmed through the results of verification calculations. Since MOC has excellent geometric flexibility and efficiency for large and complicated configurations, the proposed method can be applied to a large, complicated, and general geometry such as a whole fuel assembly or a full core configuration.

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