scholarly journals A perturbation analysis of the stability of long liquid bridges between almost circular supporting disks

2001 ◽  
Vol 13 (9) ◽  
pp. 2724-2727 ◽  
Author(s):  
J. Meseguer ◽  
J. M. Perales ◽  
J. I. D. Alexander
Keyword(s):  
Perturbation Analysis ◽  
Liquid Bridges ◽  
The Stability

Stability of Flexibly Supported Oil Journal Bearings Using Non-Newtonian Lubricants: Linear Perturbation Analysis

2000 ◽  
Vol 123 (3) ◽  
pp. 651-654 ◽  
Author(s):  
K. Raghunandana ◽  
B. C. Majumdar, and ◽  
R. Maiti
Keyword(s):  
Power Law ◽  
Perturbation Analysis ◽  
Perturbation Technique ◽  
Stability Margin ◽  
Journal Bearings ◽  
Diameter Ratio ◽  
Linear Perturbation ◽  
Flexible Support ◽  
The Stability ◽  
Power Law Index

The purpose of this paper is to study the effect of non-Newtonian lubricant on the stability of oil film journal bearings mounted on flexible support using linear perturbation technique. The model of non-Newtonian lubricant developed by Dien and Elrod is taken into consideration. The dynamic co-coefficients are calculated for different values of power law index and length to diameter ratio. These are then used to find stability margin for different support parameters to study the effect of the non-Newtonian lubricant.

Effects of the Interaction between Neighboring Droplets on the Stability of Nanoscale Liquid Bridges

2021 ◽  
Author(s):  
Kai-wen Tong ◽  
jian-hua Guo ◽  
Wei Zhang ◽  
Shi-chang Li ◽  
Kang Huang ◽  
...  
Keyword(s):  
Liquid Bridges ◽  
The Stability

Dynamic stability of closed plasma configurations

1970 ◽  
Vol 4 (4) ◽  
pp. 645-665 ◽  
Author(s):  
Daniel R. Wells
Keyword(s):  
Global Stability ◽  
Dynamic Stability ◽  
Perturbation Analysis ◽  
Flow Fields ◽  
Experimental Results ◽  
Plasma Confinement ◽  
Gauge Symmetries ◽  
Mhd Stability ◽  
The Stability ◽  
Dynamical Principle

The global stability of closed plasma configurations is related to the dynamical principle of least constraint and the spacetime and gauge symmetries of the flow fields. This leads to an entirely new concept of MHD stability which is more basic than stability predictions which rely on a linearized perturbation analysis. The predictions of the theory are compared to recent experimental results obtained in studies of the stability of plasma confinement geometries. The theory predicts the violent ‘instabilities’ of these systems which are currently attributed to other mechanisms. Several pertinent details of the theory which are widely misinterpreted are discussed and clarified.

Dynamic analysis of a microelectromechanical systems resonant gyroscope excited using combination parametric resonance

2006 ◽  
Vol 220 (9) ◽  
pp. 1463-1479 ◽  
Author(s):  
B J Gallacher ◽  
J S Burdess
Keyword(s):  
Perturbation Analysis ◽  
Parametric Excitation ◽  
Microelectromechanical Systems ◽  
Equations Of Motion ◽  
Multiple Time ◽  
Excitation Scheme ◽  
Electrostatically Actuated ◽  
Modes Of Vibration ◽  
The Stability ◽  
Electrostatic Coupling

This paper investigates the application of parametric excitation to a resonant microelectromechanical systems (MEMS) gyroscope. The modal equations of motion of an electrostatically actuated ring are derived and shown to be coupled via the electrostatic stiffness. Such electrostatic coupling between in-plane modes of vibration permits parametric instabilities that may be exploited in a novel excitation scheme. A multiple time scale perturbation method is used to analyse the response of the ring gyroscope to the combination parametric excitations with the principal objective of separating the drive and response frequencies of the ring gyroscope. As pairs of flexural modes of the perfect ring are degenerate, the combination excitation between distinct modes demand the ring to be analysed as a four degree of freedom system. Slight mis-tuning between the otherwise degenerate modes is incorporated in the perturbation analysis. The results of the perturbation analysis are subsequently used to determine the stability boundaries for a typical ring gyroscope when excited using a sum combination resonance between the flexural modes of order 2 and 5. In this case, the ratio of the drive and response frequencies is approximately 10:1. Drive and sense configurations that enable effective parametric excitation of a desired mode are investigated. Simulation of the oscillator scheme is achieved using MATLAB Simulink and this validates the perturbation analysis. Agreement between the models within 10 per cent is demonstrated.

scholarly journals The Perturbation Bound for the Spectral Radius of a Nonnegative Tensor

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Wen Li ◽  
Michael K. Ng
Keyword(s):  
Spectral Radius ◽  
Perturbation Analysis ◽  
Absolute Difference ◽  
Nonnegative Tensor ◽  
Backward Error ◽  
Perturbation Bound ◽  
Error Matrix ◽  
Largest Eigenvalue ◽  
The Stability ◽  
The Largest Eigenvalue

We study the perturbation bound for the spectral radius of an mth-order n-dimensional nonnegative tensor A. The main contribution of this paper is to show that when A is perturbed to a nonnegative tensor A~ by ΔA, the absolute difference between the spectral radii of A and A~ is bounded by the largest magnitude of the ratio of the ith component of ΔAxm-1 and the ith component xm-1, where x is an eigenvector associated with the largest eigenvalue of A in magnitude and its entries are positive. We further derive the bound in terms of the entries of A only when x is not known in advance. Based on the perturbation analysis, we make use of the NQZ algorithm to estimate the spectral radius of a nonnegative tensor in general. On the other hand, we study the backward error matrix ΔA and obtain its smallest error bound for its perturbed largest eigenvalue and associated eigenvector of an irreducible nonnegative tensor. Based on the backward error analysis, we can estimate the stability of computation of the largest eigenvalue of an irreducible nonnegative tensor by the NQZ algorithm. Numerical examples are presented to illustrate the theoretical results of our perturbation analysis.

Stabilization of dielectric liquid bridges by electric fields in the absence of gravity

1989 ◽  
Vol 206 ◽  
pp. 545-561 ◽  
Author(s):  
H. González ◽  
F. M. J. Mccluskey ◽  
A. Castellanos ◽  
A. Barrero
Keyword(s):  
Electric Fields ◽  
Theoretical Study ◽  
Dielectric Constants ◽  
Zero Gravity ◽  
Liquid Bridges ◽  
Two Fluids ◽  
Approximate Zero ◽  
Dimensional Parameters ◽  
The Stability ◽  
Theoretical Results

The stability of liquid bridges in zero gravity conditions under the influence of an a.c. electric field tangential to the interface is examined in this paper. For the theoretical study, a static analysis was carried out to find the bifurcation surfaces as a function of the three relevant non-dimensional parameters: Λ, the slenderness or ratio of height to diameter of the cylindrical bridge; β0, the ratio of dielectric constants of the two fluids used and Ξ, a non-dimensional quantity proportional to the applied voltage. Stable and unstable regions of Λ−βo−Ξ space were distinguished. Results indicate a strong stabilizing effect for higher values of β0. The experimental study, using silicone and ricinus oil to approximate zero gravity conditions fully confirmed quantitatively the theoretical results.

scholarly journals On the stability limits of long nonaxisymmetric cylindrical liquid bridges

2000 ◽  
Vol 12 (5) ◽  
pp. 979-985 ◽  
Author(s):  
F. Zayas ◽  
J. I. D. Alexander ◽  
J. Meseguer ◽  
J.-F. Ramus
Keyword(s):  
Liquid Bridges ◽  
The Stability ◽  
Stability Limits

Period-1 to Period-2 Motions in a Periodically Forced Nonlinear Spring Pendulum

2019 ◽  
Author(s):  
Albert C. J. Luo ◽  
Yaoguang Yuan
Keyword(s):  
Analytical Solutions ◽  
Perturbation Analysis ◽  
Mapping Method ◽  
Analytical Prediction ◽  
Pendulum System ◽  
Nonlinear Spring ◽  
Period 2 ◽  
Stability And Bifurcations ◽  
The Stability

Abstract In this paper, bifurcation trees of period-1 to period-2 motions in a periodically forced, nonlinear spring pendulum system are predicted analytically through the discrete mapping method. The stability and bifurcations of period-1 to period-2 motions on the bifurcation trees are presented as well. From the analytical prediction, numerical illustrations of period-1 and period-2 motions are completed for comparison of numerical and analytical solutions. The results presented in this paper is totally different from the traditional perturbation analysis.

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