Impulsive Parametric Excitation: Theory

1972 ◽  
Vol 39 (2) ◽  
pp. 551-558 ◽  
Author(s):  
C. S. Hsu
Keyword(s):  
Stability Analysis ◽  
General Theory ◽  
Parametric Excitation ◽  
Periodic Systems ◽  
Stability Criteria ◽  
Dirac Delta ◽  
Special Cases ◽  
Delta Functions ◽  
Analytic Stability ◽  
The Stability

Given in this paper is the development of a theory for dynamical systems subjected to periodic impulsive parametric excitations. By periodic impulsive parametric excitation we mean those excitations representable by periodic coefficients which consist of sequences of Dirac delta functions. It turns out that for this class of periodic systems the stability analysis can be carried out in a remarkably simple and general manner without approximation. In the paper, after giving the general theory, many special cases are examined. In many instances simple and closed-form analytic stability criteria can be easily established.

Stability of time-dependent rotational Couette flow Part 2. Stability analysis

1971 ◽  
Vol 48 (2) ◽  
pp. 365-384 ◽  
Author(s):  
C. F. Chen ◽  
R. P. Kirchner
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Kinetic Energy ◽  
Initial Value Problem ◽  
Basic Flow ◽  
The Other ◽  
Time Dependent ◽  
Stability Criteria ◽  
Initial Value ◽  
The Stability

The stability of the flow induced by an impulsively started inner cylinder in a Couette flow apparatus is investigated by using a linear stability analysis. Two approaches are taken; one is the treatment as an initial-value problem in which the time evolution of the initially distributed small random perturbations of given wavelength is monitored by numerically integrating the unsteady perturbation equations. The other is the quasi-steady approach, in which the stability of the instantaneous velocity profile of the basic flow is analyzed. With the quasi-steady approach, two stability criteria are investigated; one is the standard zero perturbation growth rate definition of stability, and the other is the momentary stability criterion in which the evolution of the basic flow velocity field is partially taken into account. In the initial-value problem approach, the predicted critical wavelengths agree remarkably well with those found experimentally. The kinetic energy of the perturbations decreases initially, reaches a minimum, then grows exponentially. By comparing with the experimental results, it may be concluded that when the perturbation kinetic energy has grown a thousand-fold, the secondary flow pattern is clearly visible. The time of intrinsic instability (the time at which perturbations first tend to grow) is about ¼ of the time required for a thousandfold increase, when the instability disks are clearly observable. With the quasi-steady approach, the critical times for marginal stability are comparable to those found using the initial-value problem approach. The predicted critical wavelengths, however, are about 1½ to 2 times larger than those observed. Both of these points are in agreement with the findings of Mahler, Schechter & Wissler (1968) treating the stability of a fluid layer with time-dependent density gradients. The zero growth rate and the momentary stability criteria give approximately the same results.

An Approximate Analysis of Quasi-Periodic Systems Via Floquét Theory

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Ashu Sharma ◽  
S. C. Sinha
Keyword(s):  
Parametric Excitation ◽  
Periodic System ◽  
Floquet Theory ◽  
Picard Iteration ◽  
Periodic Systems ◽  
Transition Matrices ◽  
Frequency Spectra ◽  
Periodic Coefficients ◽  
Stability Diagrams ◽  
The Stability

Parametrically excited linear systems with oscillatory coefficients have been generally modeled by Mathieu or Hill equations (periodic coefficients) because their stability and response can be determined by Floquét theory. However, in many cases, the parametric excitation is not periodic but consists of frequencies that are incommensurate, making them quasi-periodic. Unfortunately, there is no complete theory for linear dynamic systems with quasi-periodic coefficients. Motivated by this fact, in this work, an approximate approach has been proposed to determine the stability and response of quasi-periodic systems. It is suggested here that a quasi-periodic system may be replaced by a periodic system with an appropriate large principal period and thus making it suitable for an application of the Floquét theory. Based on this premise, a systematic approach has been developed and applied to three typical quasi-periodic systems. The approximate boundaries in stability charts obtained from the proposed method are very close to the exact boundaries of original quasi-periodic equations computed numerically using maximal Lyapunov exponents. Further, the frequency spectra of solutions generated near approximate and exact boundaries are found to be almost identical ensuring a high degree of accuracy. In addition, state transition matrices (STMs) are also computed symbolically in terms of system parameters using Chebyshev polynomials and Picard iteration method. Stability diagrams based on this approach are found to be in excellent agreement with those obtained from numerical methods. The coefficients of parametric excitation terms are not necessarily small in all cases.

Stability Criteria and Analysis of a Monocolumn Concept

2004 ◽  
Author(s):  
Felipe Cruz Rodrigues de Campos ◽  
Marcos Cueva ◽  
Kazuo Nishimoto ◽  
Ana Paula Dos Santos Costa
Keyword(s):  
Stability Analysis ◽  
Offshore Structures ◽  
Oil Fields ◽  
Stability Criteria ◽  
Offshore Drilling ◽  
Steel Catenary Risers ◽  
Special Concern ◽  
The Stability ◽  
Almost All ◽  
Classification Society

To be classified and approved by a classification society, all offshore structures shall be submitted and analyzed according to standard rules. The stability criteria are based on the IMO–MODU (International Maritime Organization–Mobile Offshore Drilling Units) Code which has reference to almost all types of floating units such as surface, column-stabilized and self elevating, but problems were found when dealing with monocolumn concept due to differences between this concept and those presented by the rules. The monocolumn studied is a floating production system (FPS) platform designed to handle steel catenary risers (SCR) in a depth of 1800 m in Brazilian oil fields. In this project, special concern was given to sea keeping behavior, constructability and security. This paper discusses the last item, focusing on subdivision and stability analysis. In order to overcome difficulties in finding the appropriate criteria, the work was developed using a special criteria, discussed with Det Norske Veritas (DNV) and PETROBRAS, which could be implanted in future classifications for this type of hull.

G-INFLATION: INFLATION WITH THE MOST GENERAL SECOND-ORDER FIELD EQUATIONS

2012 ◽  
Vol 10 ◽  
pp. 77-84
Author(s):  
TSUTOMU KOBAYASHI ◽  
MASAHIDE YAMAGUCHI ◽  
JUN'ICHI YOKOYAMA
Keyword(s):  
Power Spectra ◽  
Second Order ◽  
Stability Criteria ◽  
Cosmological Perturbations ◽  
Field Equations ◽  
Special Cases ◽  
Single Field ◽  
The Stability

In this talk, we have discussed generalized Galileons as a framework to develop the most general single-field inflation models ever, (Generalized) G-inflation, containing previous examples such as k-inflation, extended inflation, and new Higgs inflation as special cases. We have also investigated the background and perturbation evolution in this model, calculating the most general quadratic actions for tensor and scalar cosmological perturbations to give the stability criteria and the power spectra of primordial fluctuations.

scholarly journals The Stability Analyze of KM. Rejeki Baru Kharisma of Tarakan – Tanjung Selor Route

Teknik ◽  
2021 ◽  
Vol 42 (1) ◽  
pp. 52-62
Author(s):  
Alamsyah Alamsyah ◽  
Zen Zulkarnaen ◽  
Suardi Suardi
Keyword(s):  
Stability Analysis ◽  
Stability Criteria ◽  
Load Case ◽  
Ship Stability ◽  
Intact Stability ◽  
Ship Capsize ◽  
The Stability ◽  
Stability Area ◽  
The Ideal

Ship stability that is not according to the IMO standard will make the ship capsize when operating. The purpose of this research is to determine the cause of the overturn in terms of the stability criteria of the ship. The method used is software  of simulation. Stability analysis is carried out with the load case that occurs in the field when an accident occurs and the ideal loadcase according to PM 104 2017 standards about’s the transportation of operation. The results showed is cargo of goods placed on the roof top (loadcase 1) based on the criteria of Intact Stability; area of the stability arm curve at heeling 0° ~ 30° = 0.9417 m.deg, area 0° ~ 40° = 1,0200 m.deg, 30° ~ 40° = 0.0783 m.deg, GZ value at heeling 30° = 0.029 m, angle of occurrence of maximum GZ = 21.8°, and the initial GMt value = 0.135 m, the results stated that all did not meet the Intact Stability code A.749 criteria, while in it was obtained cargo of goods placed in the hull (loadcase 2) based on Intact Stability; area of the stability arm curve at heeling 0° ~ 30° = 4.5338 m.deg, area 0° ~ 40° = 7.1643 m.deg, area 30° ~ 40° = 2.6305 m.deg, GZ value at heeling 30° = 0.265 m, angle of occurrence of maximum GZ = 34.5°, and the initial GMt value = 0.621 m, the results stated that all met the Intact Stability code A.749 criteria

An Approximate Analysis of Quasi-Periodic Systems via Floquét Theory

2017 ◽  
Author(s):  
Ashu Sharma ◽  
Subhash C. Sinha
Keyword(s):  
Parametric Excitation ◽  
Periodic System ◽  
Floquet Theory ◽  
Periodic Systems ◽  
Frequency Spectra ◽  
Periodic Coefficients ◽  
Approximate Approach ◽  
Varying Coefficients ◽  
P Transformation ◽  
The Stability

Parametrically excited systems are generally represented by a set of linear/nonlinear ordinary differential equations with time varying coefficients. In most cases, the linear systems have been modeled by Mathieu or Hill equations (periodic coefficients) because their stability and response can be determined by Floquét theory. However, in many cases the parametric excitation is not periodic but consists of frequencies that are incommensurate, making them quasi-periodic. Unfortunately, there is no complete theory for linear dynamic systems with quasi-periodic coefficients. Motivated by this fact, in this work, an approximate approach has been proposed to determine the stability and response of quasi-periodic systems. Although Floquét theory is applicable only to periodic systems, it is suggested here that a quasi-periodic system may be replaced by a periodic system with an appropriate large principal period and thus making it suitable for an application of the Floquét theory. Based on this premise, a systematic approach has been developed and applied to two typical quasi-periodic systems. The approximate boundaries in stability charts obtained from the proposed method are extremely close to the exact boundaries of the original quasi-periodic equations. The exact boundaries are detected by computing the maximal Lyapunov exponents. Further, the frequency spectra of solutions generated near approximate and exact boundaries are found to be almost identical ensuring a high degree of accuracy. The coefficients of the parametric excitation terms are not necessarily small in all cases. ‘Instability loops’ or ‘Instability pockets’ that appear in the stability diagram of Meissner’s equation are also observed in one case presented here. The proposed approximate approach would allow one to construct Lyapunov-Perron (L-P) transformation matrices that reduce quasi-periodic systems to systems whose linear parts are time-invariant. The L-P transformation would pave the way for controller design and bifurcation analysis of quasi-periodic systems.

scholarly journals Stability Analysis of Pulse-Width-Modulated Feedback Systems with Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Zhong Zhang ◽  
Huahui Han ◽  
Qiling Zhao ◽  
Lixia Ye
Keyword(s):  
Stability Analysis ◽  
Stability Problem ◽  
Pulse Width ◽  
Time Varying ◽  
Stability Criteria ◽  
Feedback Systems ◽  
Stochastic Perturbations ◽  
Pulse Width Modulated ◽  
The Stability ◽  
Moment Exponential Stability

The stability problem of pulse-width-modulated feedback systems with time-varying delays and stochastic perturbations is studied. With the help of an improved functional construction method, we establish a new Lyapunov-Krasovskii functional and derive several stability criteria aboutpth moment exponential stability.

scholarly journals A framework for linear stability analysis of finite-area vortices

2013 ◽  
Vol 469 (2152) ◽  
pp. 20120709 ◽  
Author(s):  
Alan Elcrat ◽  
Bartosz Protas
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Singular Integrals ◽  
Numerical Approach ◽  
Perturbation Equation ◽  
Constant Vorticity ◽  
Special Cases ◽  
Euler Flows ◽  
The Stability

In this investigation, we revisit the question of linear stability analysis of two-dimensional steady Euler flows characterized by the presence of compact regions with constant vorticity embedded in a potential flow. We give a complete derivation of the linearized perturbation equation which, recognizing that the underlying equilibrium problem is of a free-boundary type, is carried out systematically using methods of shape-differential calculus. Particular attention is given to the proper linearization of contour integrals describing vortex induction. The thus obtained perturbation equation is validated by analytically deducing from it stability analyses of the circular vortex, originally due to Kelvin, and of the elliptic vortex, originally due to Love, as special cases. We also propose and validate a spectrally accurate numerical approach to the solution of the stability problem for vortices of general shape in which all singular integrals are evaluated analytically.

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