Influence of a variable time lag on the stability of oscillations of a pendulum with a vibrating suspension point

1985 ◽  
Vol 37 (1) ◽  
pp. 112-114 ◽  
Author(s):  
A. Yu. Shvets
Keyword(s):  
Time Lag ◽  
Suspension Point ◽  
Variable Time ◽  
The Stability

scholarly journals Nonlinear analysis of low-frequency combustion instabilities in liquid rocket engines

2019 ◽  
Author(s):  
M. Leonardi ◽  
F. Di Matteo ◽  
J. Steelant ◽  
F. Nasuti ◽  
M. Onofri
Keyword(s):  
Characteristic Frequency ◽  
Stability Boundary ◽  
Time Lag ◽  
Low Frequency ◽  
Fuel Injector ◽  
Combustion Instabilities ◽  
Variable Time ◽  
Lag Model ◽  
Double Time ◽  
The Stability

Low-frequency combustion instabilities are here studied taking advantage of the software EcosimPro. A specific module has been implemented based on the double time lag model and the coupling of combustion chamber and feed line oscillations were investigated by using a complete set of nonlinear equations. The characteristic time lags have been identified following two approaches: (i) a constant time lag approach; and (ii) a variable time lag approach based on correlations available in open literature. To prove the module capabilities, an experimental setup was reproduced and a stability map was generated, comparing the obtained results with literature data from both experiments and a linear double time lag model. The stability boundaries obtained with the chugging module are in good agreement with those obtained in open literature and the first characteristic frequency of the engine is well predicted. Furthermore, the model proves its capability in reconstructing the reversal in the slope of the stability boundary at low fuel injector pressure drops and in detecting the high-frequency content typically observed in presence of multimode oscillations. However, in the calculations, the higher frequency does not dominate the instabilities, that is, in the unstable regime, the model diverges with a frequency equal to the first characteristic frequency. In the last part of the paper, the variable time lag approach is used to investigate a portion of the aforementioned stability map. Thanks to the semiempirical correlations, the present authors managed to improve the prediction of the first characteristic frequency, whereas the stability boundary does not change significantly and remains comparable with the one predicted by the constant double time lag approach.

Braucht die EU einen flexibleren Stabilitätspakt?

2004 ◽  
Vol 53 (1) ◽  
Author(s):  
Carsten Hefeker ◽  
Friedrich Heinemann ◽  
Klaus F. Zimmermann
Keyword(s):  
Public Awareness ◽  
Time Lag ◽  
Fiscal Rules ◽  
External Control ◽  
Public Expenditures ◽  
Stability And Growth Pact ◽  
Consolidation Process ◽  
Growth Pact ◽  
Long Run ◽  
The Stability

AbstractIn his contribution Carsten Hefeker points out that most of the official arguments concerning the necessity of the Stability and Growth Pact are not convincing. Nevertheless, a mechanism that credibly avoids excessive debts and deficits is needed in most member states. It would be more useful, however, if such rules would focus on overall debt rather than on deficits. In addition, he advocates to create an external control for such fiscal rules, independent from the Commission and ECOFIN. He concludes that the Pact does not need to become more flexible, but more credible.Friedrich Heinemann states that much of the recent reform debate on the Stability Pact is based on a fundamental misconception: The Pact has not been established as a guiding tool for welfare - maximising politicians, but in order to limit detrimental incentives from fiscal short-sightedness. “Stupid” elements like the three-per-cent deficit ceiling have a clear and beneficial strategic function as boundary within the national budgetary process. Furthermore, simple rules are superior to smart ones in increasing the political costs of high deficits in terms of public awareness. The critique on the pact′s missing flexibility is correct mainly regarding its lose logical link to long-run sustainability. Increasing flexibility in a cyclical sense, however, is not a reform priority. Already today the Pact leaves sufficient leeway for responsible politicians. Instead, the reform focus must be on depoliticising the pact in the sense of limiting Council power in the deficit procedure. More flexibility must not come without depoliticising. He recommends that any reform should only be carried into effect with a significant time lag in order to limit the reputation damage which would be the consequence of any quick institutional response to the Pact′s recent crisis.In his paper Klaus F. Zimmermann argues that the Stability and Growth Pact (SGP) has been subject to criticism ever since its inception. He points out that it overlooks business cycle developments within the framework of the consolidation process; it adopts a too short-term view of the stabilisation target which is also hardly under control of policy-makers; and it deals with policy imperfections in a sub-optimal way. Therefore, a reform of the SGP is urgent. The author suggests that the rules must be handled more flexibly. In his opinion, a mediumterm budgetary target and a focus on public expenditures to tackle the pro-cyclical bias is needed. To restore credibility, the task of supervision should be transferred to an independent European institution.

A note on the stability of uncertain time-lag systems

1995 ◽  
Vol 332 (6) ◽  
pp. 773-782
Author(s):  
Yeong-Jeu Sun ◽  
Jer-Guang Hsieh
Keyword(s):  
Time Lag ◽  
The Stability ◽  
Uncertain Time

scholarly journals Managing cost uncertainties in transportation and assignment problems

1998 ◽  
Vol 2 (1) ◽  
pp. 65-104 ◽  
Author(s):  
V. Adlakha ◽  
H. Arsham
Keyword(s):  
Time Lag ◽  
Real Life ◽  
Optimal Solution ◽  
Global Market ◽  
Solution Algorithm ◽  
Assignment Problems ◽  
The Stability ◽  
Order Assignment ◽  
Cost Parameters ◽  
The Cost

In a fast changing global market, a manager is concerned with cost uncertainties of the cost matrix in transportation problems (TP) and assignment problems (AP).A time lag between the development and application of the model could cause cost parameters to assume different values when an optimal assignment is implemented. The manager might wish to determine the responsiveness of the current optimal solution to such uncertainties. A desirable tool is to construct a perturbation set (PS) of cost coeffcients which ensures the stability of an optimal solution under such uncertainties.The widely-used methods of solving the TP and AP are the stepping-stone (SS) method and the Hungarian method, respectively. Both methods fail to provide direct information to construct the needed PS. An added difficulty is that these problems might be highly pivotal degenerate. Therefore, the sensitivity results obtained via the available linear programming (LP) software might be misleading.We propose a unified pivotal solution algorithm for both TP and AP. The algorithm is free of pivotal degeneracy, which may cause cycling, and does not require any extra variables such as slack, surplus, or artificial variables used in dual and primal simplex. The algorithm permits higher-order assignment problems and side-constraints. Computational results comparing the proposed algorithm to the closely-related pivotal solution algorithm, the simplex, via the widely-used pack-age Lindo, are provided. The proposed algorithm has the advantage of being computationally practical, being easy to understand, and providing useful information for managers. The results empower the manager to assess and monitor various types of cost uncertainties encountered in real-life situations. Some illustrative numerical examples are also presented.

Modeling the Vibratory Drilling Process

1999 ◽  
Author(s):  
Stephen A. Batzer ◽  
Alexander M. Gouskov ◽  
Sergey A. Voronov
Keyword(s):  
Rotational Velocity ◽  
Time Lag ◽  
Chip Thickness ◽  
Cutting Conditions ◽  
Model Parameters ◽  
Drilling Process ◽  
Workpiece Material ◽  
Velocity Amplitude ◽  
The Stability

Abstract The dynamic behavior of deep-hole vibratory drilling is analyzed. The mathematical model presented allows the determination of axial tool and workpiece displacements and cutting forces for significant dynamic system behavior such as the entrance of the cutting tool into workpiece material and exit. Model parameters include the actual rigidity of the tool and workpiece, time-varying chip thickness, time lag for chip formation due to tool rotation and possible disengagement of drill cutting edges from the workpiece due to tool and/or workpiece axial vibrations. The main features of this model are its nonlinearity and inclusion of time lag differential equations which require numeric solutions. The specific cutting conditions (feed, tool rotational velocity, amplitude and frequency of forced vibrations) necessary to obtain discontinuous chips and reliable removal are determined. The stability conditions of excited vibrations are also investigated. Calculated bifurcation diagrams make it possible to derive the domain of system parameters along with the determination of optimal cutting conditions.

Dynamic Behavior of an SIR Epidemic Model along with Time Delay; Crowley–Martin Type Incidence Rate and Holling Type II Treatment Rate

2019 ◽  
Vol 20 (7-8) ◽  
pp. 757-771 ◽  
Author(s):  
Abhishek Kumar ◽  
Nilam
Keyword(s):  
Incidence Rate ◽  
Time Lag ◽  
Type Ii ◽  
Functional Type ◽  
Sir Epidemic Model ◽  
Treatment Rate ◽  
Nonlinear Incidence Rate ◽  
Sir Epidemic ◽  
The Stability ◽  
Disease Free

Abstract In this article, we propose and analyze a time-delayed susceptible–infected–recovered (SIR) mathematical model with nonlinear incidence rate and nonlinear treatment rate for the control of infectious diseases and epidemics. The incidence rate of infection is considered as Crowley–Martin functional type and the treatment rate is considered as Holling functional type II. The stability of the model is investigated for the disease-free equilibrium (DFE) and endemic equilibrium (EE) points. From the mathematical analysis of the model, we prove that the model is locally asymptotically stable for DFE when the basic reproduction number {R_0} is less than unity ({R_0} \lt 1) and unstable when {R_0} is greater than unity ({R_0} \gt 1) for time lag \tau \ge 0. The stability behavior of the model for DFE at {R_0} = 1 is investigated using Castillo-Chavez and Song theorem, which shows that the model exhibits forward bifurcation at {R_0} = 1. We investigate the stability of the EE for time lag \tau \ge 0. We also discussed the Hopf bifurcation of EE numerically. Global stability of the model equilibria is also discussed. Furthermore, the model has been simulated numerically to exemplify analytical studies.

Variation of uplift pressure of debris flow on the dam bottom

2020 ◽  
Author(s):  
Xingzhang Chen ◽  
Hui Chen
Keyword(s):  
Debris Flow ◽  
Time Lag ◽  
Temporal Variations ◽  
Flow Density ◽  
Flume Experiments ◽  
Fine Content ◽  
Dam Foundation ◽  
Uplift Pressure ◽  
Average Value ◽  
The Stability

<p>Abstract: Uplift pressure is crucial for the stability of debris flow dam because of its reducing the effective pressure on the dam foundation and the anti-slide force of the dam. This study investigates the spatial and temporal variations of the uplift pressures during the debris flow impact processes, through a series of flume experiments. Before the debris flow impacting on the dam, the uplift pressure keeps stable due to the steady water level, and then it decreases slightly at the instant of debris flow impacting on the dam which lasts for no more than 1 s, and then increases sharply within a time lag no more than 2 s, and then decreases sharply soon afterwards. The maximal increasing ratio is 6.4 and the average value is 3, comparing with the uplift pressure before the impacting. The peak pressure occurs before the dam and decreases with the distance from the dam with a nearly linear tendency. The increment of uplift pressure also presents a similar tendency with the distance from the dam. In addition, the uplift pressure is found to be strongly influenced by the permeability of debris flow deposits, especially by the fine content of grain composition, and by the properties of the flow, such as the flow density, runoff volume and hydraulic gradient, and the pressure rises in a nearly linear form with the properties.</p><p>Keywords: debris flow, uplift pressure, check dam, flume experiments</p>

scholarly journals Qualitative Analysis of a Retarded Mathematical Framework with Applications to Living Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Carlo Bianca ◽  
Massimiliano Ferrara ◽  
Luca Guerrini
Keyword(s):  
Qualitative Analysis ◽  
Carrying Capacity ◽  
Time Lag ◽  
Sufficient Conditions ◽  
Logistic Equation ◽  
Living Systems ◽  
Hopf Bifurcations ◽  
Economic Systems ◽  
Mathematical Framework ◽  
The Stability

This paper deals with the derivation and the mathematical analysis of an autonomous and nonlinear ordinary differential-based framework. Specifically, the mathematical framework consists of a system of two ordinary differential equations: a logistic equation with a time lag and an equation for the carrying capacity that is assumed here to be time dependent. The qualitative analysis refers to the stability analysis of the coexistence equilibrium and to the derivation of sufficient conditions for the existence of Hopf bifurcations. The results are of great interest in living systems, including biological and economic systems.

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