Domains and Types of Aeroelastic Instability of Slender Beam

2007 ◽  
Author(s):  
Jirˇi´ Na´prstek
Keyword(s):  
Stability Boundary ◽  
Stability Loss ◽  
Stability Domain ◽  
Theoretical Explanation ◽  
Point Of View ◽  
System Response ◽  
Physical Point ◽  
Model Response ◽  
Gyroscopic Forces ◽  
The Stability

Slender structures exposed to a cross air flow are prone to vibrations of several types resulting from aeroelastic interaction of a flowing medium and a moving structure. Aeroelastic forces are the origin of nonconservative and gyroscopic forces influencing the stability of a system response. Conditions of a dynamic stability loss and a detailed analysis of a stability domain has been done using a linear mathematical model. Response properties of a system located on a stability boundary together with tendencies in its neighborhood are presented and interpreted from physical point of view. Results can be used for an explanation of several effects observed experimentally but remaining without theoretical explanation until now.

scholarly journals Singularities in Structural Optimization of the Ziegler Pendulum

10.14311/1400 ◽  
2011 ◽  
Vol 51 (4) ◽  
Author(s):  
O. N. Kirillov
Keyword(s):  
Structural Optimization ◽  
Degrees Of Freedom ◽  
Optimization Problems ◽  
Stability Boundary ◽  
Research Area ◽  
Stability Domain ◽  
Conservative Systems ◽  
The Stability ◽  
Flutter Load ◽  
The Masses

Structural optimization of non-conservative systems with respect to stability criteria is a research area with important applications in fluid-structure interactions, friction-induced instabilities, and civil engineering. In contrast to optimization of conservative systems where rigorously proven optimal solutions in buckling problems have been found, for nonconservative optimization problems only numerically optimized designs have been reported. The proof of optimality in non-conservative optimization problems is a mathematical challenge related to multiple eigenvalues, singularities in the stability domain, and non-convexity of the merit functional. We present here a study of optimal mass distribution in a classical Ziegler pendulum where local and global extrema can be found explicitly. In particular, for the undamped case, the two maxima of the critical flutter load correspond to a vanishing mass either in a joint or at the free end of the pendulum; in the minimum, the ratio of the masses is equal to the ratio of the stiffness coefficients. The role of the singularities on the stability boundary in the optimization is highlighted, and an extension to the damped case as well as to the case of higher degrees of freedom is discussed.

scholarly journals On the stability of waves in classically neutral flows

2020 ◽  
Vol 85 (2) ◽  
pp. 309-340
Author(s):  
Colin Huber ◽  
Meaghan Hoitt ◽  
Nathaniel S Barlow ◽  
Nicole Hill ◽  
Kimberlee Keithley ◽  
...  
Keyword(s):  
Stability Boundary ◽  
Fractional Power ◽  
Single Mode ◽  
Fourier Integral ◽  
Linear Stability Theory ◽  
System Response ◽  
Neutral Stability ◽  
Complex Frequency ◽  
The Stability ◽  
Dispersive Flows

Abstract This paper reports a breakdown in linear stability theory under conditions of neutral stability that is deduced by an examination of exponential modes of the form $h\approx{{e}^{i(kx-\omega t)}}$, where $h$ is a response to a disturbance, $k$ is a real wavenumber and $\omega (k)$ is a wavelength-dependent complex frequency. In a previous paper, King et al. (2016, Stability of algebraically unstable dispersive flows. Phys. Rev. Fluids, 1, 073604) demonstrates that when Im$[\omega (k)]=0$ for all $k$, it is possible for a system response to grow or damp algebraically as $h\approx{{t}^{s}}$ where $s$ is a fractional power. The growth is deduced through an asymptotic analysis of the Fourier integral that inherently invokes the superposition of an infinite number of modes. In this paper, the more typical case associated with the transition from stability to instability is examined in which Im$[\omega (k)]=0$ for a single mode (i.e. for one value of $k$) at neutral stability. Two partial differential equation systems are examined, one that has been constructed to elucidate key features of the stability threshold, and a second that models the well-studied problem of rectilinear Newtonian flow down an inclined plane. In both cases, algebraic growth/decay is deduced at the neutral stability boundary, and the propagation features of the responses are examined.

Numerical Research on Machining Stability Subject to Delayed PID Control

2018 ◽  
Author(s):  
Mingjie Li ◽  
Xiaojian Zhang ◽  
Yakun Xie
Keyword(s):  
Pid Control ◽  
Production Efficiency ◽  
Stability Boundary ◽  
Stability Domain ◽  
Integral Parameter ◽  
Controlled System ◽  
Critical Boundary ◽  
Numerical Research ◽  
The Stability ◽  
Delay Differential

Machining stability analysis is important for chatter avoiding and production efficiency improvement. This paper conducts the numerical research on machining stability subject to delayed PID active control which is used to avoid chatter in machine milling. This control strategy is introduced into a two-degree-of-freedom milling system for illustration, the resulting hybrid system with both regenerative and feedback delays is represented as a delay-differential equation with time-periodic coefficients. From the comparison of stability region, it is found that the delayed PID control with proper parameters can lift the stability boundary largely compared with the case without control. To evaluate the stabilizability of the controlled system in cutting, the sensitivity of the stability boundary with respect to the PID parameters is analyzed. The numerical simulation of critical axial depth to PID parameters indicate that the milling stability critical boundary varies drastically with the derivative parameter. It also demonstrates that the stability critical boundary is strongly influenced by the proportional parameter, but it is less effected by the integral parameter. Hence, the stability domain can be expanded drastically with appropriate PID parameters based on the analysis above.

Electrohydrostatic instability in electrically stressed dielectric fluids. Part 2

1975 ◽  
Vol 72 (1) ◽  
pp. 95-112 ◽  
Author(s):  
D. H. Michael ◽  
J. Norbury ◽  
M. E. O'Neill
Keyword(s):  
Electric Field ◽  
Point Of View ◽  
Dielectric Fluid ◽  
Sufficient Information ◽  
Physical Point ◽  
Dielectric Fluids ◽  
A Value ◽  
Asymmetric Equilibria ◽  
The Stability ◽  
Loading Parameter

The paper is the second part of a study of the failure of the insulation of a layer of dielectric fluid of arbitrary volume, occupying a hole in a solid dielectric sheet, when stressed by an applied electric field. In part 1 symmetric and asymmetric equilibria were found for the two-dimensional problem, using an approximation given by Taylor (1968) for the electric field, which is valid for large holes. In this paper axisymmetric equilibria are given for a circular hole, under the same conditions. In addition the points of bifurcation of asymmetric solutions have been found, and provide sufficient information to give the stability characteristics. It is found that when the volume-excess fraction δ exceeds a value of approximately −0·3 instability occurs in an asymmetric form reported earlier for large holes by Michael, O'Neill & Zuercher (1971) in the case δ = 0. For δ < −0·3 the nature of the instability changes to an axisymmetric form of failure associated with a maximum of the loading parameter.The analysis given shows that axisymmetric displacements of ‘sausage’ mode type, that is, symmetric about a centre-plane, are associated with small changes in the static pressure in the dielectric layer. Such modes have not previously been examined in this context, and in an appendix to this paper Michael & O'Neill give an analysis of them when δ = 0, valid for all hole sizes, by extending the small perturbation analysis of Michael, O'Neill & Zuercher. These modes however do not provide the most unstable displacements for any configuration, and do not therefore affect the stability from a physical point of view.

Abandonment in Danger, Resulting in the Death of the Victim: Problems of Theory and Judicial Practice

2021 ◽  
pp. 82-92
Author(s):  
Vladimir N. Safonov ◽  
Keyword(s):  
Law Enforcement ◽  
Research Methods ◽  
Criminal Law ◽  
Criminal Behavior ◽  
Theoretical Explanation ◽  
Point Of View ◽  
Criminal Cases ◽  
Dialectical Approach ◽  
Judicial Practice ◽  
The Stability

Problem Statement. The inconsistency of judicial practice in criminal cases of abandonment in danger remains an urgent theoretical, legal and practical problem that needs doctrinal coverage. The second premise of the study is the inconsistency of the established judicial practice in cases of this category with the principles of the criminal law-legality, justice, guilt. Goals and Objectives of the Study, Research Methods. The goal is to provide a theoretical explanation and practical suggestions for optimizing judicial practice in cases of this category. The study is carried out in the tradition of a dialectical approach to the content and essence of any social phenomenon, in the coordinates of which the state of the phenomenon under consideration is determined by the content and the ratio of the factors forming this phenomenon. From this point of view, the current practice of reviewing criminal cases on the most dangerous type of abandonment of an unauthorized person in danger, which resulted in his death, is subjected to research. The research methods are systematic, historical, logical, comparative, and proper – legal. Results and Summary Conclusions. The article presents a picture of the contradictory judicial practice in criminal cases of abandonment in danger, and provides a cross-section of theoretical views on the problem under consideration. The main focus is on the consideration of leaving the victim in danger, resulting in his death. It is argued that the reason for the different qualifications of abandonment in danger, associated with the onset of serious consequences (causing harm to the health or death of the victim), is due to the disregard by law enforcement officers of the understanding of this act as a single mechanism of criminal behavior, including the uniqueness of the objective signs of the act with their reflection in the consciousness of the perpetrator. The conclusion is made about the need for a systematic approach to the legal assessment of the phenomenon of abandonment in danger with the subsequent causing of death. In addition to the stability of judicial practice, the author believes that this would lead to a more precise adherence to the principles of criminal law: legality, justice, and guilt. The same principles would be more consistent with the qualification activities of law enforcement entities as a component of the State’s criminal law policy.

scholarly journals Stabilizing and destabilizing perturbations of PT -symmetric indefinitely damped systems

2013 ◽  
Vol 371 (1989) ◽  
pp. 20120051 ◽  
Author(s):  
O. N. Kirillov
Keyword(s):  
Tangent Cone ◽  
Symmetric Matrix ◽  
Stability Boundary ◽  
Stability Domain ◽  
Exceptional Point ◽  
Damped System ◽  
Whitney Umbrella ◽  
The Stability ◽  
Damped Systems ◽  
Pure Imaginary Eigenvalues

Eigenvalues of a potential dynamical system with damping forces that are described by an indefinite real symmetric matrix can behave as those of a Hamiltonian system when gain and loss are in a perfect balance. This happens when the indefinitely damped system obeys parity–time ( ) symmetry. How do pure imaginary eigenvalues of a stable -symmetric indefinitely damped system behave when variation in the damping and potential forces destroys the symmetry? We establish that it is essentially the tangent cone to the stability domain at the exceptional point corresponding to the Whitney umbrella singularity on the stability boundary that manages transfer of instability between modes.

GROUNDWATER TIME SERIES

1970 ◽  
Vol 1 (3) ◽  
pp. 181-205 ◽  
Author(s):  
ERIK ERIKSSON
Keyword(s):  
Time Series ◽  
Point Of View ◽  
Hydrologic Models ◽  
Physical Point ◽  
Run Off ◽  
Fort Collins ◽  
Statistical Sense ◽  
Full Benefit ◽  
Future Work ◽  
Prediction Problems

The term “stochastic hydrology” implies a statistical approach to hydrologic problems as opposed to classic hydrology which can be considered deterministic in its approach. During the International Hydrology Symposium, held 6-8 September 1967 at Fort Collins, a number of hydrology papers were presented consisting to a large extent of studies on long records of hydrological elements such as river run-off, these being treated as time series in the statistical sense. This approach is, no doubt, of importance for future work especially in relation to prediction problems, and there seems to be no fundamental difficulty for introducing the stochastic concepts into various hydrologic models. There is, however, some developmental work required – not to speak of educational in respect to hydrologists – before the full benefit of the technique is obtained. The present paper is to some extent an exercise in the statistical study of hydrological time series – far from complete – and to some extent an effort to interpret certain features of such time series from a physical point of view. The material used is 30 years of groundwater level observations in an esker south of Uppsala, the observations being discussed recently by Hallgren & Sands-borg (1968).

Stability of Ring-Type MEMS Gyroscopes Subjected to Stochastic Angular Speed Fluctuation

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Samuel F. Asokanthan ◽  
Soroush Arghavan ◽  
Mohamed Bognash
Keyword(s):  
Angular Velocity ◽  
Degrees Of Freedom ◽  
Microelectromechanical Systems ◽  
Damping Ratio ◽  
Operating Conditions ◽  
System Stability ◽  
System Response ◽  
Ring Type ◽  
Mems Gyroscopes ◽  
The Stability

Effect of stochastic fluctuations in angular velocity on the stability of two degrees-of-freedom ring-type microelectromechanical systems (MEMS) gyroscopes is investigated. The governing stochastic differential equations (SDEs) are discretized using the higher-order Milstein scheme in order to numerically predict the system response assuming the fluctuations to be white noise. Simulations via Euler scheme as well as a measure of largest Lyapunov exponents (LLEs) are employed for validation purposes due to lack of similar analytical or experimental data. The response of the gyroscope under different noise fluctuation magnitudes has been computed to ascertain the stability behavior of the system. External noise that affect the gyroscope dynamic behavior typically results from environment factors and the nature of the system operation can be exerted on the system at any frequency range depending on the source. Hence, a parametric study is performed to assess the noise intensity stability threshold for a number of damping ratio values. The stability investigation predicts the form of threshold fluctuation intensity dependence on damping ratio. Under typical gyroscope operating conditions, nominal input angular velocity magnitude and mass mismatch appear to have minimal influence on system stability.

scholarly journals Suboptimal Disturbance Observer Design Using All Stabilizing Q Filter for Precise Tracking Control

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1434 ◽  
Author(s):  
Wonhee Kim ◽  
Sangmin Suh
Keyword(s):  
Design Method ◽  
Industrial Applications ◽  
Point Of View ◽  
Observer Design ◽  
Linear Matrix ◽  
External Disturbances ◽  
Closed Loop Systems ◽  
Control Target ◽  
The Stability ◽  
Unified Index

For several decades, disturbance observers (DOs) have been widely utilized to enhance tracking performance by reducing external disturbances in different industrial applications. However, although a DO is a verified control structure, a conventional DO does not guarantee stability. This paper proposes a stability-guaranteed design method, while maintaining the DO structure. The proposed design method uses a linear matrix inequality (LMI)-based H∞ control because the LMI-based control guarantees the stability of closed loop systems. However, applying the DO design to the LMI framework is not trivial because there are two control targets, whereas the standard LMI stabilizes a single control target. In this study, the problem is first resolved by building a single fictitious model because the two models are serial and can be considered as a single model from the Q-filter point of view. Using the proposed design framework, all-stabilizing Q filters are calculated. In addition, for the stability and robustness of the DO, two metrics are proposed to quantify the stability and robustness and combined into a single unified index to satisfy both metrics. Based on an application example, it is verified that the proposed method is effective, with a performance improvement of 10.8%.

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