A Generalized Hill’s Method for the Stability Analysis of Parametrically Excited Dynamic Systems

1982 ◽  
Vol 49 (1) ◽  
pp. 217-223 ◽  
Author(s):  
S. T. Noah ◽  
G. R. Hopkins
Keyword(s):  
Stability Analysis ◽  
Dynamic Systems ◽  
Absolute Convergence ◽  
General System ◽  
Closed Form Expression ◽  
Form Expression ◽  
Null Solution ◽  
Hill’S Method ◽  
The Stability ◽  
Pulsating Fluid

A method is described for investigating the stability of the null solution for a general system of linear second-order differential equations with periodic coefficients. The method is based on a generalization of Hill’s analysis and leads to a generalized Hill’s infinite determinant. Following a proof of its absolute convergence, a closed-form expression for the characteristic infinite determinant is obtained. Methods for the stability analysis utilizing different forms of the characteristic determinant are discussed. For cases where the instabilities are of the simple parametric type, a truncated form of the determinant may be used directly to locate the boundaries of the resonance regions in terms of appropriate system parameters. The present generalized Hill’s method is applied to a multidegree-of-freedom discretized system describing pipes conveying pulsating fluid. It is demonstrated that the method is a flexible and efficient computational tool for the stability analysis of general periodic systems.

Influence of Nonlinearities on the Behavior of Parametrically Excited Articulated Pipes Conveying Fluid

1978 ◽  
Vol 5 (1) ◽  
pp. 31-38 ◽  
Author(s):  
J. Rousselet ◽  
G. Herrmann
Keyword(s):  
Fluid Flow ◽  
Stability Analysis ◽  
Dynamic Systems ◽  
Linear Formulation ◽  
Fluctuating Pressure ◽  
The Past ◽  
Pipes Conveying Fluid ◽  
Critical Velocities ◽  
The Stability ◽  
Conveying Fluid

This paper presents the analysis of a system of articulated pipes hanging vertically under the influence of gravity. The liquid, driven by a slightly fluctuating pressure, circulates through the pipes. Similar systems have been analysed in the past by numerous authors but a common feature of their work is that the behavior of the fluid flow is prescribed, rather than left to be determined by the laws of motion. This leads to a linear formulation of the problem which can not predict the behavior of the system for finite amplitudes of motion. A circumstance in which this behavior is important arises in the stability analysis of the system in the neighbourhood of critical velocities, that is, flow velocities at which the system starts to flutter. Hence, the purpose of the present study was to investigate in greater detail the region close to critical velocities in order to find by how much these critical velocities would be affected by the amplitudes of motion. This led to a set of three coupled-nonlinear equations, one of which represents the motion of the fluid. In the mathematical development, use is made of a scheme which permits the uncoupling of the modes of motion of damped nonconservative dynamic systems. Results are presented showing the importance of the nonlinearities considered.

Concept Of The Decomposition And Aggregation Method With Example: Part 1

1988 ◽  
pp. 27-40
Author(s):  
Dr. Zainol Anuar Mohd. Sharif ◽  
Ng Boon Choong
Keyword(s):  
Stability Analysis ◽  
Dynamic Systems ◽  
Basic Concept ◽  
Large Scale ◽  
Direct Method ◽  
Aggregation Method ◽  
Control Engineering ◽  
Large Scale Systems ◽  
Engineering Economics ◽  
The Stability

This paper describes the basic concept of the decomposition and aggregation method. It shows the feasibility of the method and its advantages when applied, particularly to large scale systems. This method is extensively used in solving problems related to control engineering, economics, optimization and stability. This paper also illustrates specifically the application of the method of decomposition and aggregation in the analysis of dynamic systems. It is divided into two important parts, namely; the decomposition part which involves breaking up a large system into subsystems and the aggregation part which is obtained through a reformulation of the Liapunov's second method (direct method). The relation between the decomposition and the aggregation methods is also shown. The procedure for checking the stability based on this concept is also outlined.For further illustration, an example of a dynamic system has been included. It shows how the system is decomposed and aggregated to suit the requirement for stability analysis.

scholarly journals ON THIN-SHELL WORMHOLES EVOLVING IN FLAT FRW SPACETIMES

2011 ◽  
Vol 26 (12) ◽  
pp. 857-863 ◽  
Author(s):  
M. LA CAMERA
Keyword(s):  
Stability Analysis ◽  
Equation Of State ◽  
Perfect Fluid ◽  
Dynamic Systems ◽  
Spherical Symmetry ◽  
Thin Shell ◽  
Time Dependent ◽  
State Formula ◽  
Thin Shell Wormholes ◽  
The Stability

We analyze the stability of a class of thin-shell wormholes with spherical symmetry evolving in flat FRW spacetimes. The wormholes considered here are supported at the throat by a perfect fluid with equation of state [Formula: see text] and have a physical radius equal to aR, where a is a time-dependent function describing the dynamics of the throat and R is the background scale factor. The study of wormhole stability is done by means of the stability analysis of dynamic systems.

Regions of asymptotic stability of dynamic systems by the combination of Lyapunov techniques and digital simulation

SIMULATION ◽  
1965 ◽  
Vol 5 (6) ◽  
pp. 384-391 ◽  
Author(s):  
Thomas Z. Fahidy
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Dynamic Systems ◽  
Digital Simulation ◽  
Systematic Search ◽  
Function Technique ◽  
Lyapunov Techniques ◽  
Machine Interference ◽  
The Stability

The usefulness of the combination of the Lyapunov function technique and digital simulation for the stability analysis of dynamic systems is illustrated in two examples where the region of asymptotic sta bility is estimated by the analytical Lyapunov ap proach and established by a systematic search via digital simulation of the Lyapunov function. The ad vantage of the PACTOLUS simulator, with particular regard to man-to-machine interference, is empha sized.

Stability of Isolators at Large Horizontal Displacements

1997 ◽  
Vol 13 (3) ◽  
pp. 415-430 ◽  
Author(s):  
Maura Imbimbo ◽  
James M. Kelly
Keyword(s):  
Horizontal Displacement ◽  
Vertical Displacement ◽  
Closed Form Expression ◽  
Elastic Analysis ◽  
Form Expression ◽  
Elastomeric Bearings ◽  
Post Buckling ◽  
Link Model ◽  
The Stability ◽  
Horizontal Displacements

Elastomeric bearings used as seismic isolators are susceptible to a buckling type of instability similar to that of structural columns. The buckling load and buckling behaviour can be determined from an elastic analysis of the isolator modelled as a continuous composite column with bending and shear flexibility; this analysis cannot be used, however, to assess the post-buckling behaviour or the stability of the isolator at large horizontal displacements. By using a two-spring rigid link model that considers large angles without using linear approximations, it is possible to predict the post-buckling behaviour of an isolator. Using the simple closed form expression, this paper will model three aspects of post-buckled isolator behaviour: the dependence of horizontal stiffness on vertical load, the stability at large horizontal displacements, and the increase of horizontal displacement with respect to axial load and vertical displacement.

Stability Analysis of Control Systems with the Asymmetric Controllers using Frequency Domain Criterion

1970 ◽  
Vol 111 (5) ◽  
pp. 63-66 ◽  
Author(s):  
V. Zlosnikas ◽  
A. Baskys ◽  
V. Gobis
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Frequency Domain ◽  
Control Systems ◽  
Dynamic Systems ◽  
Simulation Software ◽  
Nonlinear Element ◽  
The Stability ◽  
The One ◽  
Systems Simulation

The stability of control systems with the linear plants using asymmetric Proportional and Proportional-asymmetric Integral controllers is analyzed in this work. The methods of nonlinear systems stability analysis based on the frequency domain criterion proposed by Popov and modified by the Cho and Narendra were employed. They are dedicated for the systems with the one nonlinear element. The investigation has been performed using Off-Axis and Circle criterions by employing graphical-analytical analysis methods, which were realized using software Mathcad. The obtained analysis results were verified using dynamic systems simulation software Matlab/Simulink. Ill. 6, bibl. 13 (in English; abstracts in English and Lithuanian).http://dx.doi.org/10.5755/j01.eee.111.5.358

Optimization of the Control Function for a Footless Biped in a Stationary, Upright Posture

1987 ◽  
Author(s):  
M. S. Hsu ◽  
M. De Spain ◽  
J. Shaw ◽  
M. Mulder ◽  
N. Wagner
Keyword(s):  
Optimal Control ◽  
Closed Form ◽  
Sagittal Plane ◽  
Control Function ◽  
Closed Form Expression ◽  
Upright Posture ◽  
Numerical Techniques ◽  
Form Expression ◽  
Stability Range ◽  
The Stability

Abstract The stability of a footless biped in a stationary, upright posture is studied on the sagittal plane using two and three link models. Closed form expression of the stability range for the control gains is derived from Routh-Hurwitz criteria. Evaluation and optimization of the multiple gain systems are realized using statistical and numerical techniques. The optimal control gains are obtained and the gain-locus is derived. The algorithm for optimizing the control function is provided and several numerically derived examples are illustrated.

Collocated Position Control of Oscillatory System in Presence of Delay

2020 ◽  
Author(s):  
Bence Szaksz ◽  
Gabor Stepan
Keyword(s):  
Time Delay ◽  
Position Control ◽  
Critical Time ◽  
Oscillatory System ◽  
Constant Time Delay ◽  
Closed Form Expression ◽  
Pd Controller ◽  
Governing Equations ◽  
Form Expression ◽  
The Stability

Abstract The stability of the collocated position control of a mass is studied when a pendulum is attached to it. The simplest proportional-derivative (PD) controller is applied, but the relevant constant time delay is taken into account. The linearized governing equations of the system are investigated. Stability charts are constructed for different pendulum parameters. Closed form expression is derived for the critical time delay; for delay values larger than the critical one, the PD controller cannot stabilize the desired position of the mass. The frequencies of the self-excited vibrations at the stability boundaries have essential role in identifying the types of loss of stability.

Maneuvering Model for FPSOs and Stability Analysis of the Offloading Operation

2002 ◽  
Vol 124 (4) ◽  
pp. 196-202 ◽  
Author(s):  
Sergio H. Sphaier ◽  
Antonio C. Fernandes ◽  
Sylvio H. S. Correa ◽  
Gustavo A. V. Castro
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Classical Theory ◽  
Deep Water ◽  
Experimental Test ◽  
Dynamic Systems ◽  
Scale Effects ◽  
Local Analysis ◽  
Floating System ◽  
The Stability

The discovery of new fields in deep water brought back the use of large ships such as FPSOs. This seems to be the trend toward ultra deep water units at least in offshore Brazil. At about the same time, VLCCs (very large crude carriers) have been converted to work as FPSOs. However, working as a stationary unit a VLCC presents directional stability problems. In the present paper a methodology is discussed to develop a mathematical model for the simulation and the verification of the stability of a VLCC working as a FPSO. To express the forces and moments acting on the ship hull the results of a group of experiments are described in the classical sense of the maneuverability theory, although they concern large angles of attack and low advance velocity. Besides, a procedure to determine the stability of the floating system is also presented. This is based on local analysis and follows the classical theory of dynamic systems. Further, the use of stabilization devices for a floating unit and the offloading operation are discussed. Finally, an experimental test is proposed, in order to take into account scale effects.

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