Dynamic Stability Criteria Research Articles

Controversy Associated With the So-Called “Follower Forces”: Critical Overview

This paper is inspired by two articles on the title subject, namely by Koiter and by Sugiyama, Langthjem and Ryu. The former warned the engineering community to beware of the above forces. The latter maintained that these forces are realistic. It is hoped that this review sheds some additional light on an issue that seems to perplex many students of dynamic stability. The paper does not contain any new information unknown to researchers; it represents a critical review of pertinent papers dedicated to the topic of dynamic stability of structures under so called “follower” forces. The attempt here is to present an account of the literature in a manner that is both objective and humble. This paper reviews both the theoretical and experimental contributions to the theory of nonconservative problems with a single objective in mind, to attempt to answer a nagging question “Is the model of the statically applied follower forces useful?,” that arose due to the papers by Koiter and Sugiyama, Langthjem and Ryu. This article explores the static and dynamic stability criteria as pertaining to the nonconservative problems; the experimental side of the problem; the results pertaining to Beck’s column placed on homogenous or inhomogeneous elastic foundations; and criticisms expressed in the literature about the result on the immunity of the instability load to the Winkler foundation modulus: The paper then discusses Koiter’s ideas on nonconservative instability problems, and attempts to provide insights on the abovementioned question. Special emphasis is placed on pipes conveying fluid with or without an elastic foundation. It then summarizes the literature on the “follower forces.” Such a summary is inevitably incomplete because of the huge literature accumulated so far on the nonconservative problems in the theory of elastic stability. There are 202 references cited in this review article, and a supplementary bibliography is provided.

An improved energy stability margin for walking machines subject to dynamic effects

Several static and dynamic stability criteria have been defined in the course of walking-robot history. Nevertheless, previous work on the classification of stability criteria for statically stable walking machines (having at least four legs) reveals that there is no stability margin that accurately predicts robot stability when inertial and manipulation effects are significant. In such cases, every momentum-based stability margin fails. The use of an unsuitable stability criterion yields unavoidable errors in the control of walking robots. Moreover, inertial and manipulation effects usually appear in the motion of these robots when they are used for services or industrial applications. A new stability margin that accurately measures robot stability considering dynamic effects arising during motion is proposed in this paper. The new stability margin is proven to be the only exact stability margin when robot dynamics and manipulation forces exist. Numerical comparison has been conducted to support the margin's suitability. Stability-level curves are also presented on the basis of a suitable stability margin to control the trajectory of the center of gravity during the support phase.

A Design Criterion for Dynamic Stability of Eccentric Tainter-Gates

Tainter gates used for regulating the back water level of dam may be designed so that the skinplate center is kept under the trunnion pin. Such gates may be called an “eccentric Tainter-gate”, which is statically stably but dynamically unstable. This study presents a design criterion for dynamic stability of eccentric Tainter gates, which is theoretically derived in a practical form, that is, in a non-dimensional expression of the Scruton number representing the mass-damping parameter vs. the Froude number representing the dynamic similarity of fluctuating flow in the back water. In addition, in-air and in-water free vibration tests are made for two of Tainter-gate models with different size and eccentricity, and the measured data of Scruton number is plotted over the tested Froude number, and the design criterion for dynamic stability of the eccentric Tainter gates is verified for its practical validity.

Dynamic Stability of Long Cylindrical Sandwich Shells and Panels Subject to Periodic-in-Time Lateral Pressure

The paper presents an analysis of dynamic stability of long cylindricalsandwich shells and shallow panels subject to a uniform periodic lateral pressure.The solution is obtained using the Sanders shell theory by assumption that the shellor panel remains in the state of plane strain during both steady-state and perturbedmotion. The steady-state motion of a shell is axisymmetric, while perturbedvibrations superimposed on the steady response are asymmetric. The analysis ofperturbed motion is reduced to specifying the conditions of stability of the Mathieuequation. Subsequently, the criteria of dynamic stability and the boundaries of theregions of unstable motion in the pressure amplitude–pressure frequency planeare immediately available. A shallow panel subjected to hydrodynamic pressureexperiences forced vibrations. However, these vibrations can become unstable.Dynamic stability of such vibrations is investigated through the solution of thelinearized equations for perturbed motion. It is shown that these equations can bereduced to a system of Mathieu equations.

Effect of microstructural complexity on the hot deformation behavior of aluminum alloy 2024

Abstract Powder metallurgy (P/M) aluminum alloy 2024 (Al-2024) reinforced with SiC whiskers is difficult to shape-form because of microstructural complexities introduced by rapid solidification and whisker additions. In the present investigation, four forms of Al-2024, viz. ingot, wrought, P/M, and P/M with 20 v/o silicon-carbide whiskers (SiC w ) were examined to understand the influence of structural complexity on the hot deformation microstructural mechanisms. The analyses using the concepts of activation energy and dynamic stability criteria revealed that the safe hot working window of Al-2024 narrows as the microstructural complexity increases. This experimental observation was also explained on the basis of information theory. Safe processing window identified for the composite was validated using scaled-up extrusion experiments and the influence of processing conditions on microstructural control was demonstrated.

The dynamic stability analysis of guyed masts under random wind loads

On the basis of the first Lyapunov stability theory, this paper develops a dynamic stability criterion for elastic structural systems under arbitrary dynamic loads, and shows the stability criterion using energy variation. After the dynamic stability criterion is validated through a classic example, it is used for the dynamic stability investigation of practical guyed masts under random wind loads. The criterion is reliable, simple and of advantage for structures with large number of elements and nodes. The slack guys and internal resonance between guys and mast are two main factors which induces the dynamic instability of guyed masts, at the same time, some dynamic stability characteristics of guyed masts are found.

Control of ball-racket interactions in rhythmic propulsion of elastic and non-elastic balls.

Ball-racket interactions were investigated in a task where participants propelled a ball rhythmically into the air. The study contrasted two ball-racket conditions: (1) an elastic impact where the ball was able to rebound due to the elasticity of the colliding objects and participants bounced the ball, and (2) a non-elastic impact where the coefficient of restitution was zero and the ball did not rebound such that the participants had to throw the ball. The goal of the study was to contrast the situations where haptic information about the ball-racket interactions is either secondary (elastic bouncing) or becomes a primary factor for control (non-elastic propulsion). In the elastic condition, the performers controlled the parameters for ball-racket contact prior to contact: In agreement with the criteria for dynamical stability defined by a model, racket accelerations immediately before the contacts were negative, racket positions and velocities at the instant of the initial contact correlated negatively, contact durations were short (30+/-9 ms), and during the collision interval racket velocity and acceleration decreased monotonically. In the non-elastic condition, the parameters of ball release were primarily controlled during the collision phase: Racket accelerations before contact were positive, racket positions and velocities at initial contact showed weak correlations, and the contact intervals were significantly longer (116+/-15 ms) with a clear segmentation into two segments. Negative correlations were observed between the integrals of the velocity and acceleration computed over the two consecutive segments, giving evidence that in the non-elastic condition the CNS is able to introduce corrections during the very short collision interval. The results are discussed with respect to physiological mechanisms of movement corrections available during such short time intervals.

Incremental behaviour of hyperelastic dielectrics and piezoelectric crystals

The equations describing the behaviour of a hyperelastic dielectric under pre-existing mechanical and electrical fields are derived. The associated differential system is shown to be self-adjoint. This property, in turn, is used to establish the equivalence of linear static and dynamic stability criteria.

A comparative study of stability margins for walking machines

Several static and dynamic stability criteria have been defined in the course of walking robot history. Nevertheless, different applications may require different stability criteria and, to the authors' best knowledge, there is no qualitative classification of such stability measurements. Using the wrong stability criterion to control a robot gait may prevent the task from succeeding. Furthermore, if the optimum criterion is found, the robot gait can also be optimized. In this paper, the stability criteria that have been applied to walking robots with at least four legs are examined in terms of their stability margins in different static and dynamic situations. As a result, a qualitative classification of stability criteria for walking machines is proposed so that the proper criterion can be chosen for every desired application.

Longitudinal stability and dynamic motions of a small passenger WIG craft

The longitudinal stability characteristics of a Wing-In-Ground (WIG) effect craft are quite different from those of the conventional airplane due to the existence of force and moment derivatives with regard to height. These stability characteristics play an important role in designing a safe and efficient WIG due to its potential danger in sea surface proximity. The static and dynamic stability criteria are derived from the motion equations of WIG in the framework of small disturbance theory and discussed in this paper. The static and dynamic stability analyses of a 20-passenger WIG are conducted based on wind tunnel test data, and dynamic motion behaviors are investigated for changes in design parameters. Finally, the flying quality of the 20-passenger WIG is analyzed at cruising conditions according to the military regulations.

INCREASING STABILITY IN DYNAMIC GAITS USING NUMERICAL OPTIMIZATION

Optimal gait planning is applied in this work to the problem of improving stability in quadruped locomotion. In many settings, it is desired to operate legged machines at high performance levels where rapid velocities and a changing environment make stability of utmost concern. Since gait planning still remains a vital component of legged system control design, an efficient method of determining periodic paths is presented which optimize a dynamic stability criterion. Efficient recursive multibody algorithms are used with numerical optimal control software to solve the minimax performance stability criteria.

Dynamic stability of shallow arch with elastic supports—application in the dynamic stability analysis of inner winding of transformer during short circuit

In this paper, the dynamic stability of a shallow arch with elastic supports subjected to impulsive load is used as a theoretical model to investigate the dynamic stability problem of inner windings of power transformer under short-circuit condition. Firstly, the series solution representing the equilibrium configurations of a shallow arch is obtained by solving the corresponding non-linear integration-differential equation. The local stability of each equilibrium configuration is discussed, and the sufficient condition for stability of the shallow arch system as well as the critical load against snap-through is obtained. Secondly, the equivalent relation between short-circuit load and impulsive one, and the electrical forces transferred pattern between the coils of inner windings are assumed. Then the results of the shallow arch model are applied to the case of the inner winding of transformer and the formulas for computing critical electromagnetic force and the dynamic stability criterion of the inner windings are established. Finally, examples are offered and the theoretical results are shown to agree well with the experimental ones.

Short wavelength spectrum and Hamiltonian stability of vortex rings.

We compare dynamical and energetical stability criteria for vortex rings. It is argued that vortex rings will be intrinsically unstable against perturbations with short wavelengths below a critical wavelength because the canonical vortex Hamiltonian is unbounded from below for these modes. To explicitly demonstrate this behavior, we derive the oscillation spectrum of vortex rings in incompressible, inviscid fluids within a geometrical cutoff procedure for the core. The spectrum develops an anomalous branch of negative group velocity and approaches the zero of energy for wavelengths that are about six times the core diameter. We show the consequences of this dispersion relation for the thermodynamics of vortex rings in superfluid 4He at low temperatures.

Magnetothermal instabilities in cylindrical melt-textured Y-Ba-Cu-O

The magnetothermal flux jump instabilities of the critical state in cylindrical melt-textured Y-Ba-Cu-O samples are investigated during the magnetization process. The flux jumps result in a drastic reduction of the magnetization accompanied by a strong heating of the sample. We determine the first flux jump field as function of the parameters, which influence the stability, such as the heat transfer coefficient between the surface of the sample and the surrounding, the sweep rate of the external field and the temperature of the sample. The comparison of the thermal and magnetic diffusivity of the melt-textured material indicates isothermal behavior of the flux jump scenario, supporting a dynamic stability criterion.

Mass distribution management & dynamic balancing of aircraft mass

A new methodology has been proposed to control the distribution of mass in an aircraft during the design and development process. Having estimated the total mass, the aircraft is considered to be composed of different segments each with an unknown mass and the equations of motion are derived based on this discritized mass model. A suitable mass distribution is then found based on the desired dynamic and static stability criterion. Using this methodology the aircraft static margin can be controlled by changing the external shape (Xac) as well as mass distribution (Xcg). By relating all applicable mass moments of inertia to the frequencies and damping ratios of longitudinal and lateral-directional dynamic modes, the chance of designing a well dynamically balanced aircraft in a variety of flight phases is increased. The mathematical procedure can explicitly be derived only for rigid airplanes where two-dimensional approximations are valid. However, numerical algorithms must be used for elastic and/or rigid aircraft with coupled equations of motion. The proposed methodology has been used to find suitable mass distributions for a B-747-100 in a cruising flight while satisfying the Level-I flying quality requirements.

Nonclassical Stability Problems: Instability of Slender Tubes under Pressure

Several nonclassical stability problems dealing with simple cantilever columns of practical engineering importance are comprehensively presented. The salient feature of these rather peculiar problems is that column instability with a tubular cross section filled with a liquid or subjected to gas pressure may occur while its cross section remains axially unstressed. Interesting subcases are also discussed where the static stability criterion of existence of two adjacent equilibria fails to predict the actual critical load. This leads to the erroneous conclusion that the undeformed configuration is the only equilibrium position, being stable irrespective of the level of external loading. Hence, the dynamic stability criterion which is of general validity must be employed for establishing the critical load. It has also been clarified that the hydrostatic pressure load, although nonconstant-directional, cannot be identified as nonconservative.

Critical Loading Parameters for Plates

A perturbation technique is used to study the critical loading of flexible plates subjected to small buckling with mechanical or thermal fields in their middle planes which create prior stresses. The application of a dynamic stability criterion is examined. The original problem is reduced to a recurrence sequence of static bending problems. Some numerical calculations are presented for plates containing a concentrated heat source.

Stability of Equilibria in Games with Procedurally Rational Players

One approach to the modeling of bounded rationality in games is based on the dynamics of evolution and learning. An alternative static and equilibrium-based approach has been developed recently by Osborne and Rubinstein. This paper formalizes Osborne and Rubinstein's dynamic interpretation of their equilibrium concept, uses the criterion of dynamic stability as an equilibrium refinement, and shows that stable equilibria can involve the playing of strictly dominated actions while dominant strategy equilibria can be unstable. These effects cannot occur under standard evolutionary game dynamics. Sufficient conditions for the instability of equilibria are provided for symmetric and asymmetric games. Journal of Economic Literature Classification Number: C72.

Selection of the dynamically stable regime of rapid solidification front motion in an isothermal binary alloy

On the basis of local nonequilibrium approach the dynamics of a motion of the rapid solidification front in a binary alloy is considered. Asymptotic expansion for concentration of solute and its diffusion flux at the front is found in the limit of large times t→∞. A selection criterion for dynamic stability of the front motion in a steady-state regime (V=V0≡const) is formulated. An expression for the definition of a nonstationary time during the transition to the steady-state regime is obtained. The front motion regimes with decreasing velocity in time are investigated. In these regimes the velocity decreases in time as V(t)∼t−1/2 and V(t)∼t−1/3.

Stability of standing matter waves in a trap

We discuss excited Bose-condensed states and find the criterion of dynamical stability of a kinkwise state, i.e., a standing matter wave with one nodal plane perpendicular to the axis of a cylindrical trap. The dynamical stability requires a strong radial confinement corresponding to the radial frequency larger than the mean-field interparticle interaction. We address the question of thermodynamic instability related to the presence of excitations with negative energy.