Effects of Flexibility on the Stability of Flying Aircraft

2004 ◽  
Vol 127 (1) ◽  
pp. 41-49 ◽  
Author(s):  
Ilhan Tuzcu ◽  
Leonard Meirovitch
Keyword(s):  
Feedback Control ◽  
Eigenvalue Problem ◽  
Rigid Body ◽  
Flight Dynamics ◽  
Flight Path ◽  
The Other ◽  
Flexible Aircraft ◽  
First Case ◽  
Rigid Body Motions ◽  
The Stability

Traditionally, flying aircraft have been treated within the confines of flight dynamics, which is concerned, for the most part, with rigid aircraft. On the other hand, flexible aircraft fall in the domain of aeroelasticity. In reality all aircraft possess some measure of flexibility and carry out rigid body maneuvers, so that the question arises as to whether rigid body motions and flexibility in combination can affect adversely the stability of flying aircraft. This paper addresses this question by solving the eigenvalue problem for the following three cases: (i) the flight dynamics of a flexible aircraft regarded as rigid and whose perturbations about the flight path are controlled by feedback control, (ii) the aeroelasticity of a corresponding flexible aircraft prevented from undergoing rigid body translations and rotations, and (iii) the control of the actual flexible aircraft using the control gains derived in the first case by regarding the aircraft as rigid. This investigation demonstrates that it is not always safe to treat separately rigid body and flexibility effects in a flying flexible aircraft.

Effects of Flexibility on the Stability of Flying Aircraft

2003 ◽  
Author(s):  
Ilhan Tuzcu ◽  
Leonard Meirovitch
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Flight Dynamics ◽  
Flight Path ◽  
The Other ◽  
Feedback Controls ◽  
Flexible Aircraft ◽  
Other Hand ◽  
First Case ◽  
The Stability

Traditionally, flying aircraft have been treated within the confines of flight dynamics, which is concerned for the most part with rigid aircraft. On the other hand, flexible aircraft fall in the domain of aeroelasticity. Although some attempts have been made to include aircraft rigid body degrees of freedom, aeroelasticity is concerned mostly with the vibration and flutter instability of wings fixed at the root. In reality all aircraft possess some measure of flexibility and carry out rigid body maneuvers, so that the question arises as to whether flexibility can have adverse effects on the stability of flying aircraft. This paper addresses the question of flexibility effects on the stability of flying aircraft by solving the eigenvalue problem associated with the following three cases: 1) the flight dynamics of a flexible aircraft regarded as rigid and whose perturbations about the flight path are controlled by feedback control, 2) the aeroelasticity of a corresponding flexible aircraft prevented from undergoing rigid body translations and rotations and 3) the control of the actual flexible aircraft using the same control gains as in the first case. This investigation demonstrates that it is not always safe to treat separately rigid body effects and flexibility effects in a flying flexible aircraft. Indeed, it is shown that on the one hand the flight of a flexible aircraft treated as rigid can be stabilized by means of feedback controls and on the other hand that the motion of the same flexible aircraft prevented from undergoing rigid body motions tends to consist of damped oscillation. But, when the flying flexible aircraft is treated as it actually is, namely, a single system, the elastic vibration and the perturbations from the flight path can be rendered unstable by feedback controls designed by ignoring the elastic variables.

Über Actin-Nucleotide und die Funktion und Bindung der Nucleotidphosphate im G- und F-Actin

1961 ◽  
Vol 16 (7) ◽  
pp. 435-444 ◽  
Author(s):  
N. Grubhofer ◽  
Hans H. Weber
Keyword(s):  
Half Life ◽  
Equilibrium Concentration ◽  
Special Kind ◽  
The Other ◽  
Mechanical Destruction ◽  
Reversible Dissociation ◽  
First Case ◽  
The Difference ◽  
The Stability ◽  
The Individual

1. If pure F-actin-ADP * which is free of enzymes is depolymerized G-actin-ATP * arises in the presence of 10-4 M ATP, G-actin-ITP * in the presence of 10-4 M ITP, and G-actin-ADP in the presence of 10-4 M ADP. If the depolymerization takes place in the absence of free nucleotide phosphate G-actin-ADP also arises. If G-actin-ADP is added to a solution containing 10-4 M ITP or ATP the bound ADP is exchanged with ATP respectively with ITP (Section II).2. G-actin-ATP and G-actin-ITP polymerize to F-actin-ADP and to F-actin-IDP respectively by splitting off the γ-phosphate of the ATP or ITP. G-actin-ADP polymerizes to F-actin-ADP without splitting off phosphate. The polymerization of G-actin-ADP is as complete as the polymerization of G-actin-ATP; but the process is perceptibly shower (Section II).3. G-actin that is not bound to a nucleotide phosphate does not polymerize (Section II).4. G-actin-ADP in the absence of free ADP spontaneously disintegrates in a half-life of 70 minutes to yield G-actin and ADP. If the dissociating ADP is continuously removed by being bound to Dowex 1 × 10 the half life drops to 7 to 8 minutes. In the presence of Dowex G-actin-ATP disintegrates in a half life of 240 minutes (Section III).5. The disintegration of G-actin-ADP takes place in two stages. A reversible dissociation into ADP and G-actin I is followed by an irreversible denaturation of G-actin I to G-actin II in a half life ~ 12 minutes. Contrary to actin I G-actin II even on the addition of ATP no longer polymerizes. The difference in the half life of pure G-actin-ADP on the hand and of G-actin-ADP+ADP as well as G-actin-ATP on the other must be attributed to the relatively high equilibrium concentration of G-actin I in the first case and of the relatively slight equilibrium concentration of G-actin I in the second case (Section IV).6. If the alkaline earth of G-actin is blocked by 10-3 M EDTA G-actin-ATP disintegrates in a half life ∼ 3 minutes and G-actin-ADP in a half life ∼ 0,3 minutes. On the other hand, the stability of F-actin-ADP is not noticeably affected (Section V).7. Through a two hour rapid dialysis in the presence of 10-4 M ATP the KCl-content of an F-actin-ADP solution drops to 5 × 10-4 M KCl. In spite of this the depolymerization and exchange of ADP with ATP is finished not before 40 hours if the solution remains at rest. If, however, the actin solution containing 5 × 10-4 M KCl is treated with the Teflon homogenizer for about 30 sec. depolymerization and ADP-ATP-exchange occur immediately. On the contrary, F-actin-ADP in 10–1 M KCl solution is not affected at all by a treatment with the Teflon-homogenizer. Apparently the decrease of the KClconcentration from 10-1 M to 5 × 10-4 M considerably diminishes the strength of the bond between the actin monomers without immediately destroying the F-actin arrangement. The immediate ADP-ATP-exchange after the mechanical destruction of the F-actin arrangement proves that this exchange in F-actin does not take place only because of steric hindrance. ADP is present in F-actin apparently between the individual monomers so that EDTA, ATP and enzymes affecting ATP cannot approach ADP. Consequently it is not necessary to assume that the extraordinary stability of F-actin-ADP is due to a special kind of bond between actin monomers and nucleotide phosphate (Section V).8. In the appendix it is shown that G-actin-ADP does not polymerize 15′ after preparation if the aceton dried muscle powder is prepared at pH 8 to 9 instead of pH ∼ 7.

Dynamic absorption in a vibrating beam

2003 ◽  
Vol 217 (2) ◽  
pp. 187-197 ◽  
Author(s):  
A N Singh ◽  
Y M Ram
Keyword(s):  
Feedback Control ◽  
Spectral Data ◽  
Single Point ◽  
The Other ◽  
Controlled System ◽  
Numerical Examples ◽  
Harmonic Response ◽  
Control Gain ◽  
The Stability

The paper deals with dynamic absorption in a harmonically excited beam. It is shown that the harmonic response of vibration at a desired position can be made to vanish by applying a feedback control at a single point. Two expressions for the control gain are given. One is based on deformation and the other is based on spectral data. The stability of the controlled system is analysed. Numerical examples demonstrate the various results.

On the stability of the dynamical system ‘rigid body + inviscid fluid’

1999 ◽  
Vol 386 ◽  
pp. 43-75 ◽  
Author(s):  
V. A. VLADIMIROV ◽  
K. I. ILIN
Keyword(s):  
Dynamical System ◽  
Rigid Body ◽  
Translational Motion ◽  
Sufficient Conditions ◽  
The Body ◽  
Inviscid Fluid ◽  
Rigid Boundary ◽  
First Case ◽  
Fixed Axis ◽  
The Stability

In this paper we study a dynamical system consisting of a rigid body and an inviscid incompressible fluid. Two general configurations of the system are considered: (a) a rigid body with a cavity completely filled with a fluid and (b) a rigid body surrounded by a fluid. In the first case the fluid is confined to an interior (for the body) domain and in the second case it occupies an exterior domain, which may, in turn, be bounded by some fixed rigid boundary or may extend to infinity. The aim of the paper is twofold: (i) to develop Arnold's technique for the system ‘body + fluid’ and (ii) to obtain sufficient conditions for the stability of steady states of the system. We first establish an energy-type variational principle for an arbitrary steady state of the system. Then we generalize this principle for states that are steady either in translationally moving in some fixed direction or rotating around some fixed axis coordinate system. The second variations of the corresponding functionals are calculated. The general results are applied to a number of particular stability problems. The first is the stability of a steady translational motion of a two-dimensional body in an irrotational flow. Here we have found that (for a quite wide class of bodies) the presence of non-zero circulation about the body does not affect its stability – a result that seems to be new. The second problem concerns the stability of a steady rotation of a force-free rigid body with a cavity containing an ideal fluid. Here we rediscover the stability criterion of Rumyantsev (see Moiseev & Rumyantsev 1965). The complementary problem – when a body is surrounded by a fluid and both body and fluid rotate with constant angular velocity around a fixed axis passing through the centre of mass of the body – is also considered and the corresponding sufficient conditions for stability are obtained.

Uniformity of Magnification from Different Electron Microscopes

1967 ◽  
Vol 25 ◽  
pp. 32-33
Author(s):  
Godfrey C. Hoskins ◽  
V. Williams ◽  
V. Allison
Keyword(s):  
Diffraction Grating ◽  
The Other ◽  
Carbon Replica ◽  
Electron Microscopes ◽  
The Stability

The method demonstrated is an adaptation of a proven procedure for accurately determining the magnification of light photomicrographs. Because of the stability of modern electrical lenses, the method is shown to be directly applicable for providing precise reproducibility of magnification in various models of electron microscopes.A readily recognizable area of a carbon replica of a crossed-line diffraction grating is used as a standard. The same area of the standard was photographed in Phillips EM 200, Hitachi HU-11B2, and RCA EMU 3F electron microscopes at taps representative of the range of magnification of each. Negatives from one microscope were selected as guides and printed at convenient magnifications; then negatives from each of the other microscopes were projected to register with these prints. By deferring measurement to the print rather than comparing negatives, correspondence of magnification of the specimen in the three microscopes could be brought to within 2%.

A NEW APPROACH TO THE STUDY OF COORDINATIVE CONSTRUCTIONS

2019 ◽  
pp. 175-187
Author(s):  
Anna Varnayeva
Keyword(s):  
Characteristic Property ◽  
Mathematical Concept ◽  
The Other ◽  
New Approach ◽  
Logical Aspect ◽  
First Case

Coordinative constructions are traditionally opposed to subordinative constructions. However, this opposition comes down to denial of dependence in coordinative constructions. Thereby the parity of these two constructions does not come to light: subordinative construction can be described without coordinative one. This situation is not improved by detection of a coordinative triangle in all coordinative constructions. The article shows a new approach in the study of coordinative constructions: a coordinative construction is a system; there are not only specific relations – a coordinative triangle, – but also specific elements. Novelty of the study consists in the address to extralinguistic facts, viz. a mathematical concept of a set and its elements. There are a lot of similarities between them. A set in mathematics includes generalizing elements and the composed row in coordinative constructions; in the first case the set is not partitioned, in the second case it is partitioned. In mathematics equivalent components in coordinative constructions correspond to the set elements. A characteristic property in mathematics is homogeneity in coordinative constructions and etc. It is firstly demonstrated, that coordinative and subordinative constructions are correlative and the study of one construction is impossible without the study of the other one. Their parity is shown in coordinative constructions with elements of one set, in subordinative ones with elements of different sets. Cf.: roses and tulips –red roses. In the coordinatiму construction elements of one set are called: «flowers »; in the subordinative construction there are elements of different sets: «flowers » and «colors». It should be noted that the mathematical concept of a set relates to so called logical aspect in linguistics or thinking about reality.

Applications of random graphs

2017 ◽  
Author(s):  
A.C.C. Coolen ◽  
A. Annibale ◽  
E.S. Roberts
Keyword(s):  
Social Networks ◽  
Random Graphs ◽  
Interaction Network ◽  
Power Grids ◽  
Protein Protein Interaction ◽  
Topological Features ◽  
First Case ◽  
The Stability ◽  
Protein Protein Interaction Network

This chapter reviews graph generation techniques in the context of applications. The first case study is power grids, where proposed strategies to prevent blackouts have been tested on tailored random graphs. The second case study is in social networks. Applications of random graphs to social networks are extremely wide ranging – the particular aspect looked at here is modelling the spread of disease on a social network – and how a particular construction based on projecting from a bipartite graph successfully captures some of the clustering observed in real social networks. The third case study is on null models of food webs, discussing the specific constraints relevant to this application, and the topological features which may contribute to the stability of an ecosystem. The final case study is taken from molecular biology, discussing the importance of unbiased graph sampling when considering if motifs are over-represented in a protein–protein interaction network.

scholarly journals Black Hole Algorithm for Sustainable Design of Counterfort Retaining Walls

2020 ◽  
Vol 12 (7) ◽  
pp. 2767 ◽  
Author(s):  
Víctor Yepes ◽  
José V. Martí ◽  
José García
Keyword(s):  
Black Hole ◽  
Sustainable Design ◽  
Retaining Walls ◽  
The Other ◽  
Trade Off ◽  
Construction Company ◽  
Geometric Variables ◽  
The Stability ◽  
The Cost ◽  
Black Hole Algorithm

The optimization of the cost and CO 2 emissions in earth-retaining walls is of relevance, since these structures are often used in civil engineering. The optimization of costs is essential for the competitiveness of the construction company, and the optimization of emissions is relevant in the environmental impact of construction. To address the optimization, black hole metaheuristics were used, along with a discretization mechanism based on min–max normalization. The stability of the algorithm was evaluated with respect to the solutions obtained; the steel and concrete values obtained in both optimizations were analyzed. Additionally, the geometric variables of the structure were compared. Finally, the results obtained were compared with another algorithm that solved the problem. The results show that there is a trade-off between the use of steel and concrete. The solutions that minimize CO 2 emissions prefer the use of concrete instead of those that optimize the cost. On the other hand, when comparing the geometric variables, it is seen that most remain similar in both optimizations except for the distance between buttresses. When comparing with another algorithm, the results show a good performance in optimization using the black hole algorithm.

scholarly journals Explicit parallel co-simulation approach: analysis and improved coupling method based on H-infinity synthesis

2021 ◽  
Author(s):  
Weitao Chen ◽  
Shenhai Ran ◽  
Canhui Wu ◽  
Bengt Jacobson
Keyword(s):  
Frequency Domain ◽  
Wide Frequency Range ◽  
Coupling Method ◽  
Sampled Data ◽  
H Infinity ◽  
First Case ◽  
Communication Step ◽  
Coupling Variables ◽  
The Stability ◽  
Stability And Accuracy

AbstractCo-simulation is widely used in the industry for the simulation of multidomain systems. Because the coupling variables cannot be communicated continuously, the co-simulation results can be unstable and inaccurate, especially when an explicit parallel approach is applied. To address this issue, new coupling methods to improve the stability and accuracy have been developed in recent years. However, the assessment of their performance is sometimes not straightforward or is even impossible owing to the case-dependent effect. The selection of the coupling method and its tuning cannot be performed before running the co-simulation, especially with a time-varying system.In this work, the co-simulation system is analyzed in the frequency domain as a sampled-data interconnection. Then a new coupling method based on the H-infinity synthesis is developed. The method intends to reconstruct the coupling variable by adding a compensator and smoother at the interface and to minimize the error from the sample-hold process. A convergence analysis in the frequency domain shows that the coupling error can be reduced in a wide frequency range, which implies good robustness. The new method is verified using two co-simulation cases. The first case is a dual mass–spring–damper system with random parameters and the second case is a co-simulation of a multibody dynamic (MBD) vehicle model and an electric power-assisted steering (EPAS) system model. Experimental results show that the method can improve the stability and accuracy, which enables a larger communication step to speed up the explicit parallel co-simulation.

scholarly journals A Fractional SAIDR Model in the Frame of Atangana–Baleanu Derivative

2021 ◽  
Vol 5 (2) ◽  
pp. 32
Author(s):  
Esmehan Uçar ◽  
Sümeyra Uçar ◽  
Fırat Evirgen ◽  
Necati Özdemir
Keyword(s):  
Existence And Uniqueness ◽  
Laplace Transformation ◽  
Cell Phones ◽  
Mobile Network ◽  
The Other ◽  
Banach Fixed Point Theorem ◽  
Propagation Models ◽  
Computer Worms ◽  
Computer Viruses ◽  
The Stability

It is possible to produce mobile phone worms, which are computer viruses with the ability to command the running of cell phones by taking advantage of their flaws, to be transmitted from one device to the other with increasing numbers. In our day, one of the services to gain currency for circulating these malignant worms is SMS. The distinctions of computers from mobile devices render the existing propagation models of computer worms unable to start operating instantaneously in the mobile network, and this is particularly valid for the SMS framework. The susceptible–affected–infectious–suspended–recovered model with a classical derivative (abbreviated as SAIDR) was coined by Xiao et al., (2017) in order to correctly estimate the spread of worms by means of SMS. This study is the first to implement an Atangana–Baleanu (AB) derivative in association with the fractional SAIDR model, depending upon the SAIDR model. The existence and uniqueness of the drinking model solutions together with the stability analysis are shown through the Banach fixed point theorem. The special solution of the model is investigated using the Laplace transformation and then we present a set of numeric graphics by varying the fractional-order θ with the intention of showing the effectiveness of the fractional derivative.

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