scholarly journals Equilibrium configurations of a planar polygonal linkage

2014 ◽  
Vol 1 (12) ◽  
pp. 226
Author(s):  
Alena Mikhailovna Zhukova ◽  
Gaiane Yuryevna Panina
Keyword(s):  
Equilibrium Configurations ◽  
Polygonal Linkage

STABILITY OF SPATIAL ELASTICA IN A GRAVITATIONAL FIELD

2012 ◽  
Vol 12 (02) ◽  
pp. 403-421 ◽  
Author(s):  
BOONCHAI PHUNGPAINGAM ◽  
LAWRENCE N. VIRGIN ◽  
SOMCHAI CHUCHEEPSAKUL
Keyword(s):  
Gravitational Field ◽  
Elastic Equilibrium ◽  
Experimental System ◽  
Primary Control ◽  
Arc Length ◽  
Euler Parameters ◽  
Reference Analysis ◽  
Horizontal Orientation ◽  
Equilibrium Configurations ◽  
Out Of Plane

This paper considers the behavior of a spatial elastica in a gravitational field. The slenderness of the system considered is such that the weight becomes an important consideration in determining elastic equilibrium configurations. Both ends of the elastica are clamped in an initially (planar) horizontal orientation at a fixed distance apart. However, one of the ends allows an increase in arc-length, that is, it is a sleeve joint. Thus, the total arc-length is the primary control parameter. This kind of elastica typically loses stability, resulting in out-of-plane deflections, when the total arc-length is increased beyond a critical value. A small mid-length torque can used to perturb a planar equilibrium configuration in order to test for stability. The aim of this study is to assess the effect of self-weight of the elastica (which is typically ignored) on promoting or delaying the loss of stability. To this end, it is useful to compare and contrast the results of orientation, that is, the system is configured in both an initial "upright" orientation and then in an "upside-down" orientation to highlight the influence of gravity. The results of the weightless elastica are used as a reference. Analysis is based on Kirchhoff's rod theory and Euler parameters, and the resulting set of governing differential equations are solved using a shooting method. The results from an experimental system using a slender superelastic wire made from Nitinol (Nickel Titanium Naval Ordnance Laboratory) exhibit close agreement with the analytical results.

scholarly journals Two-vortex equilibrium in the flow past a flat plate at incidence

2014 ◽  
Vol 755 ◽  
pp. 50-61 ◽  
Author(s):  
Luca Zannetti ◽  
Alexandre Gourjii
Keyword(s):  
Flat Plate ◽  
Symmetric Equilibrium ◽  
Equilibrium Conditions ◽  
Kutta Condition ◽  
Vortex Pairs ◽  
Flow Past ◽  
Equilibrium Configurations ◽  
Asymmetric Flows ◽  
Asymmetric Equilibrium ◽  
Total Circulation

AbstractThe two-dimensional inviscid incompressible steady flow past an inclined flat plate is considered. A locus of asymmetric equilibrium configurations for vortex pairs is detected. It is shown that the flat geometry has peculiar properties compared to other geometries: (i) in order to satisfy the Kutta condition at both edges, which ensures flow regularity, the total circulation and the force acting on the plate must be zero; and (ii) the Kutta condition and the free vortex equilibrium conditions are not independent of each other. The non-existence of symmetric equilibrium configurations for an orthogonal plate is extended to more general asymmetric flows.

scholarly journals Equilibrium configurations of point vortices in doubly connected domains

1996 ◽  
Vol 1 ◽  
pp. 325-337
Author(s):  
Alan R. Elcrat ◽  
Chenglie Hu ◽  
Kenneth G. Miller
Keyword(s):  
Point Vortices ◽  
Equilibrium Configurations

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.

scholarly journals Curvature Dependent Electrostatic Field in the Deformable MEMS Device: Stability and Optimal Control

2020 ◽  
Vol 11 (1) ◽  
pp. 35-54
Author(s):  
Paolo Di Barba ◽  
Luisa Fattorusso ◽  
Mario Versaci
Keyword(s):  
Optimal Control ◽  
Electrostatic Field ◽  
Stable Equilibrium ◽  
Micro Electro Mechanical System ◽  
Operating Conditions ◽  
Electric Voltage ◽  
External Voltage ◽  
Device Stability ◽  
Equilibrium Configurations ◽  
Mems Device

AbstractThe recovery of the membrane profile of an electrostatic micro-electro-mechanical system (MEMS) device is an important issue because, when applying an external voltage, the membrane deforms with the consequent risk of touching the upper plate of the device (a condition that should be avoided). Then, during the deformation of the membrane, it is useful to know if this movement admits stable equilibrium configurations. In such a context, our present work analyze the behavior of an electrostatic 1D membrane MEMS device when an external electric voltage is applied. In particular, starting from a well-known second-order elliptical semi-linear di erential model, obtained considering the electrostatic field inside the device proportional to the curvature of the membrane, the only possible equilibrium position is obtained, and its stability is analyzed. Moreover, considering that the membrane has an inertia in moving and taking into account that it must not touch the upper plate of the device, the range of possible values of the applied external voltage is obtained, which accounted for these two particular operating conditions. Finally, some calculations about the variation of potential energy have identified optimal control conditions.

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