Dynamic Stability of a Rotor Filled or Partially Filled With Liquid

1996 ◽  
Vol 63 (1) ◽  
pp. 101-105 ◽  
Author(s):  
Wen Zhang ◽  
Jiong Tang ◽  
Mingde Tao
Keyword(s):  
Dynamic Stability ◽  
Dynamic Pressure ◽  
Flow Analysis ◽  
Previous Literature ◽  
Stability Criteria ◽  
Stability Boundaries ◽  
Planar Flow ◽  
Harmonic Motion ◽  
Analytical Stability ◽  
The Stability

The dynamic stability of a high-spinning liquid-filled rotor with both internal and external damping effects involved in is investigated in this paper. First, in the case of the rotor subjected to a transverse harmonic motion, the dynamic pressure of the liquid acting on the rotor is extracted through a planar flow analysis. Then the equation of perturbed motion for the liquid-filled rotor is derived. The analytical stability criteria as well as the stability boundaries are given. The results are extensions of those given by previous literature.

Influence of Gravity and Taper on the Vibration of a Standing Column

2012 ◽  
Vol 4 (04) ◽  
pp. 483-495 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Cross Section ◽  
Numerical Stability ◽  
Natural Vibration ◽  
Vibration Frequencies ◽  
Stability Criteria ◽  
Initial Value ◽  
Vertical Column ◽  
Stability Boundaries ◽  
Section Shape ◽  
The Stability

AbstractThe stability and natural vibration of a standing tapered vertical column under its own weight are studied. Exact stability criteria are found for the pointy column and numerical stability boundaries are determined for the blunt tipped column. For vibrations we use an accurate, efficient initial value numerical method for the first three frequencies. Four kinds of columns with linear taper are considered. Both the taper and the cross section shape of the column have large influences on the vibration frequencies. It is found that gravity decreases the frequency while the degree of taper may increase or decrease frequency. Vibrations may occur in two different planes.

scholarly journals A Three Species Ecological Model with a Prey, Predator and Competitor to the Predator and Optimal Harvesting of the Prey

2012 ◽  
Vol 1 ◽  
pp. 21-32
Author(s):  
A.V. Papa Rao ◽  
K. Lakshmi Narayan ◽  
Shahnaz Bathul
Keyword(s):  
Ecological Model ◽  
Equilibrium Points ◽  
Single Species ◽  
Analytical Investigation ◽  
Optimal Harvesting ◽  
Stability Criteria ◽  
Linear Ordinary Differential Equations ◽  
First Order ◽  
Analytical Stability ◽  
The Stability

The present paper is devoted to an analytical investigation of three species ecological model with a Prey (N1), a predator (N2) and a competitor (N3) to the Predator without effecting the prey (N1). in addition to that, the species are provided with alternative food. The model is characterized by a set of first order non-linear ordinary differential equations. All the eight equilibrium points of the model are identified and local and global stabilitycriteria for the equilibrium states except fully washed out and single species existence are discussed. Further exact solutions of perturbed equations have been derived. The analytical stability criteria are supported by numerical simulations using mat lab. Further we discussed the effect of optimal harvesting on the stability.

Dynamic Stability of Nonlinear Antisymmetrically-Laminated Cross-Ply Rectangular Plates

1989 ◽  
Vol 56 (2) ◽  
pp. 375-381 ◽  
Author(s):  
Andrzej Tylikowski
Keyword(s):  
Asymptotic Stability ◽  
Dynamic Stability ◽  
Material Properties ◽  
Stability Problem ◽  
Large Deflection ◽  
Direct Method ◽  
Rectangular Plates ◽  
Stability Criteria ◽  
The Stability ◽  
Liapunov's Direct Method

The dynamic stability problem is solved for rectangular plates that are laminated antisymmetrically about their middle plane and compressed by time-dependent deterministic or stochastic membrane forces. Moderately large deflection equations taking into account a coupling of in-plane and transverse motions are used. The asymptotic stability and almost-sure asymptotic stability criteria involving a damping coefficient and loading parameters are derived using Liapunov’s direct method. A relation between the stability of nonlinear equations and linearized ones is analyzed. An influence on the number of orthotropic layers, material properties for different classes of parametric excitation on stability domains is shown.

Online Combustor Stability Margin Assessment Using Dynamic Pressure Data

2004 ◽  
Author(s):  
Tim Lieuwen
Keyword(s):  
Dynamic Stability ◽  
Environmental Changes ◽  
Dynamic Pressure ◽  
Stability Boundary ◽  
Stability Margin ◽  
Operating Conditions ◽  
Margin Assessment ◽  
Pressure Oscillations ◽  
Acoustic Damping ◽  
The Stability

This paper describes a strategy for determining a combustor’s dynamic stability margin. Currently, when turbines are being commissioned or simply going through day to day operation, the operator has no idea how the dynamic stability of the system is affected by changes to fuel splits/operating conditions unless, of course, pressure oscillations are actually present. We have developed a methodology for ascertaining stability margin from passive monitoring of the acoustic pressure. This method consists of signal processing and analysis that determines a real-time measure of combustor damping. When the calculated damping is positive, the combustor is stable. When the damping goes to zero, the combustor approaches its stability boundary. Changes in the stability margin of each of the combustor’s stable modes due to tuning, aging or environmental changes can then be monitored through online analysis of the pressure signal. This paper outlines the basic approach used to quantify acoustic damping and demonstrates the technique on combustor test data.

scholarly journals Stability Criterion for Dynamic Gaits of Quadruped Robot

2018 ◽  
Vol 8 (12) ◽  
pp. 2381 ◽  
Author(s):  
Yan Jia ◽  
Xiao Luo ◽  
Baoling Han ◽  
Guanhao Liang ◽  
Jiaheng Zhao ◽  
...  
Keyword(s):  
Dynamic Stability ◽  
Stability Criterion ◽  
Quadruped Robot ◽  
Stability Criteria ◽  
Irregular Terrain ◽  
Quadruped Robots ◽  
Simulation Results ◽  
Zero Moment ◽  
The Stability ◽  
Dynamic Gait

Dynamic-stability criteria are crucial for robot’s motion planning and balance recovery. Nevertheless, few studies focus on the motion stability of quadruped robots with dynamic gait, none of which have accurately evaluated the robots’ stability. To fill the gaps in this field, this paper presents a new stability criterion for the motion of quadruped robots with dynamic gaits running over irregular terrain. The traditional zero-moment point (ZMP) is improved to analyze the motion on irregular terrain precisely for dynamic gaits. A dynamic-stability criterion and measurement are proposed to determine the stability state of the robot and to evaluate its stability. The simulation results show the limitations of the existing stability criteria for dynamic gaits and indicate that the criterion proposed in this paper can accurately and efficiently evaluate the stability of a quadruped robot using such gaits.

Dynamic Stability of Poroelastic Columns

1999 ◽  
Vol 67 (2) ◽  
pp. 360-362 ◽  
Author(s):  
G. Cederbaum
Keyword(s):  
Dynamic Stability ◽  
Multiple Scales ◽  
Transversely Isotropic ◽  
Axial Direction ◽  
Periodic Force ◽  
Stability Boundaries ◽  
Coupled Equations ◽  
Column Material ◽  
The Stability ◽  
Fluid Diffusion

The dynamic stability of a poroelastic column subjected to a longitudinal periodic force is investigated. The column material is assumed to be transversely isotropic with respect to the column axis, and the pore fluid flow is possible in the axial direction only. The motion of the column is governed by two coupled equations, for which the stability boundaries are determined analytically by using the multiple-scales method. It is shown that due to the fluid diffusion the stability regions are expanded, relative to the elastic (drained) case. The critical (minimum) loading amplitude, for which instability occurs, is also given. [S0021-8936(00)00902-8]

Dynamic Stability of a Pendulous Missile Suspension System

1962 ◽  
Vol 29 (2) ◽  
pp. 276-282
Author(s):  
V. Chobotov
Keyword(s):  
Differential Equations ◽  
Dynamic Stability ◽  
Periodic Coefficient ◽  
Suspension System ◽  
Second Order ◽  
Stability Criteria ◽  
Parametrically Excited ◽  
Second Order Differential Equations ◽  
The Stability

The stability criteria for a missile on a pendulous support are derived for the case of parametrically excited motions of the support. The suspension system is described by two linear second-order differential equations with a periodic coefficient. The analysis is carried out by means of the first method of Liapunov. The results are somewhat modified, however, to obtain greater generality without which the technique is too laborious to be useful.

Dynamic Stability of a Flexible Spinning Cylinder Partially Filled With Liquid

2002 ◽  
Vol 69 (5) ◽  
pp. 708-710 ◽  
Author(s):  
M. Tao ◽  
W. Zhang
Keyword(s):  
Dynamic Stability ◽  
Three Dimensional ◽  
Dynamic Force ◽  
Two Dimensional ◽  
Euler Beam ◽  
Dimensional Flow ◽  
Analytical Stability ◽  
Two Dimensional Flow ◽  
Spinning Cylinder ◽  
The Stability

Dynamic stability of a flexible spinning cavity cylinder partially filled with liquid is discussed in the paper. The cylinder is assumed to be slender. Choosing characteristic quantities and estimating the orders of magnitude of all terms in the governing equations and boundary conditions, the three-dimensional flow in the slender cylinder is reduced to a quasi-two-dimensional flow. Using the known formulas of a two-dimensional dynamic force acting on the rotor and regarding the slender cylinder as a Bernoulli-Euler beam, the perturbed equations of the liquid-filled beam-wise cylinder are derived. The analytical stability criteria as well as the stability boundaries are obtained. The results further the study of this problem.

Stability Analysis of the Rocking Block: Numerical Investigations on Analytical Stability Boundaries

2003 ◽  
Author(s):  
Alessio Ageno ◽  
Anna Sinopoli
Keyword(s):  
Initial Conditions ◽  
General Procedure ◽  
Dynamic Responses ◽  
Stability Range ◽  
Stability Boundaries ◽  
Strong Discontinuities ◽  
Rocking Block ◽  
Analytical Stability ◽  
The Stability ◽  
Characteristic Multipliers

The present paper illustrates some recently developed techniques to evaluate stability features, such as characteristic multipliers and Lyapunov’s exponents, for a problem with strong discontinuities. The problem analyzed concerns the plane dynamics of a rigid block simply supported on a harmonically moving rigid ground. In previous papers [1–3] many aspects have been investigated and the following results have been carried out: 1. the general procedure to approach numerically the problem has been outlined; 2. a rigorous method has been established to calculate characteristic multipliers and Lyapunov’s exponents at the instants of discontinuities; 3. the stability boundaries of symmetric sub-harmonic responses have been drafted by means of closed-form analytical methods based on various hypotheses of linearization. In this paper the new capacities allowed by the techniques and methods pointed out at the previous points 1., 2. and 3. are exploited with the aims: • to investigate numerically in the occurrence of dissipative impacts the features of dynamic responses across the upper boundary of a stability range (i.e. that of the (1,3) sub-harmonic response) included in a larger one (i.e. that of the (1,1) response); • to analyze the responses attainable with a value of the restitution coefficient equal to 1 to describe the impulsive phases (namely for non-dissipative impacts); in previous works, these responses have been classified as quasi-periodic or chaotic [4]. By means of the new techniques proposed and implemented, it has been possible to classify and analyze more deeply such presumed quasi-periodic or chaotic responses and at the same time to clarify the role played by the initial conditions.

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