bluuebunny/crossref_metadata_2025 huggingface dataset:
An Extended Liapunov Approach to the Stability Assessment of Marine Risers
Authors: Köhl M.
Published: May 2007

Liapunov's direct method in an extended version suitable, for spatially continuous systems is used to derive sufficient conditions for the stability of marine risers. The method has its origin in considering the system energy and represents a dynamic extension of Lagrange's static stability approach which relates the existence of a positive definite potential energy to stability. Since the direct method utilizes only the differential equation and the boundary conditions to construct energy‐like functions from which stability statements are deduced, it is not necessary to solve the system equations. The applicability of the method to nonlinear systems makes it possible to include the nonlinear hydrodynamic drag force due to the sea water in the stability analysis. As an example, the dynamic stability of the vertical riser equilibrium position is analysed here for pinned‐pinned boundary conditions, resulting in a confirmation of the “stability limit” already known through purely static stability analysis.
Subharmonic Vibrations and Chaos in Forced Nonlinear Oscillators
Authors: Schmidt G. , Seisl M.
Published: May 2007

For forced nonlinear oscillators, different subharmonic vibrations are investigated analytically by higher approximations, checked by computer algebra, and numerically by a damped Newton procedure combined with a continuation algorithm (BIFPACK package by R. Seydel). Especially for a damping value which leads to a frequency region with chaotic behaviour, second subharmonic vibrations appear with amplitudes of the same size as for the harmonic vibrations, whereas third subharmonic vibrations appear only for lower frequencies. This gives an explaination for the existence of second and later on of third subharmonic periodic windows in the period doubling route to chaos.
On Optimal Including Circular Approximation for the Range of a Complex Exponential Function
Authors: Petković Lj. D.
Published: May 2007

For a given disk Z circular including approximation of the range of the complex exponential function ez = {ez: z ∈ Z} is considered. The optimal covering disk {ζ: |ζ — w| ≦ D/2} ⊇ ez, with the diameter D which is equal to the diameter of the closed range ez, is determined.
On the Relation of Static to Dynamic Bifurcation in Nonlinear Autonomous Dissipative or Nondissipative Structural Systems
Authors: Mahrenholtz O. , Kounadis A. N.
Published: May 2007

Dynamical dissipative or nondissipative discrete systems under constant directional (conservative) step loading described by nonlinear autonomous Ordinary Differential Equations (ODEs) are considered. Attention is restricted on gradient structural systems which under the same loading applied statically exhibit a branching point critical response bifurcating from a trivial prebuckling path. The connection of static bifurcations and stability with the corresponding dynamic bifurcations and stability are comprehensively discussed after a thorough investigation of the structural form of the Jacobian matrix and its characteristic equation. The relation of the eigenvalues of the statical system with those of the dynamical system associated with the Jacobian matrix is examined at the precritical, critical and postcritical stage. This enables us to establish very simple stability conditions (related basically to the sign of second variation of the total potential energy) compared to those of Routh‐Hurwitz.
Ermittlung modaler Parameter aus Übertragungsfrequenzgängen — Auswerteverfahren zur experimentellen Modalanalyse an Werkzeugmaschinen
Authors: Milberg J. , Kirchknopf P.
Published: May 2007

Die Aufgabenstellung der experimentellen Modalanalyse liegt in der Identifikation der Eigenschwingungsgrößen eines meßtechnisch untersuchten Objekts. Im Rahmen eines Konzepts zur Durchführung experimenteller Modalanalysen an Werkzeugmaschinen mit leicht transportierbarer Hardware wird ein Algorithmus zur Identifikation modaler Parameter anhand gemessener Übertragungsfrequenzgänge vorgestellt.
Models for Constrained Motion and d'Alembert's Principle
Authors: Schmidt H.‐J.
Published: May 2007

A theorem of Arnol'd and Gallavotti states that by a suitable potential of increasing rigidity a mechanical system with conservative forces can be constrained to a hypersurface of the configuration space and its motion approaches a solution of the reduced Lagrangian equation. In this paper the theorem will be generalized to time‐ and velocity‐dependent forces including time‐dependent constraints and proved with the aid of the method of averaging. This technique also allows us to identify the constraint force as the averaged negative gradient of the constraint potential.
On the Existence of Plasma Corners
Authors: Kaiser R. , Lortz D.
Published: May 2007

The free‐boundaryMHDequilibrium is considered for plane symmetry and constant current profile. It is shown that there are solutions with an x‐point at the plasma‐vacuum interface, such that the plasma fills one of the four sectors formed by the separatrix. Such “plasma corners” are a common feature of modern fusion devices.
Stability of the Numerical Solution of Transonic Potential Flow
Authors: Maršík F. , Danêk V.
Published: May 2007

The influence of an artificial viscosity on the stability of numerical solution of transonic flows with shock waves is investigated. The variational principle with dissipation introduced through a physical viscosity is derived, and a simplified relation describing the stabilizing influence of the dissipative process is presented. The numerical solution of the potential equation by FEM is examined and compared with the formulation using the variational principle. The correspondence between physical viscosity μ and artificial viscosity μnum is shown both qualitatively and quantitatively. The necessary amount of artificial viscosity is investigated analytically and the results are compared with numerical experiments.
ARMAX Modelling in Structural Dynamics – Numerical Integration of the Integral Representations
Authors: Natke H. G. , Zamirowski M.
Published: May 2007

A review of ARMAX modelling and the approximations of the differential equations of motion are given in previous publications. Here ARMAX modelling based on integral equations in structural dynamics using direct numerical integration equations is investigated. The result is an ARMAX representation for a pre‐given accuracy for numerical purposes. Various integration methods lead to various ARMAX models. Taking into account the resulting estimation errors several ARMAX representations are also compared. It is shown that the inverse problem, the determination of physical parameters from the AR and MA coefficients leads to a unique solution.
L∞ Estimates of Optimal Order for Galerkin Methods to Second Order Hyperbolic Differential Equations
Authors: Ohm M.‐R.
Published: May 2007

Using weighted norms L∞‐error estimates of the Galerkin method for second order hyperbolic differential equations are derived.
On the Algebra of Two‐Point Tensors on Manifolds with Applications in Nonlinear Solid Mechanics
Authors: Kollmann F. G. , Hackenberg H.‐P.
Published: May 2007

In this paper we consider the algebra of two‐point tensors on manifolds. A new way to define transposition is suggested. Further, we consider orthogonal two‐point tensors. Finally, we investigate symmetry of two‐point and ordinary tensors. We demonstrate applications of our results to examples from nonlinear solid mechanics.
Existence of Solutions for Some Singular Higher Order Boundary Value Problems
Authors: Eloe P. W. , Henderson J.
Published: May 2007

Solutions are obtained for the boundary value problem, yn + Ψ(x) f(x, y, y′, …,yn−1 − 0, yi(0) ‐ 0, 0, ≦ i ≦ k − 1, and yj(1) ‐ 0, k ≦ j ≦ n − 1, where Ψ(x) is singular at x ‐ 0, 1, and f(x, y1, …, yn) is singular at yi =; 0, 1 ≦ i ≦ n. The techniques involve topological transversality methods.
Vibrations of Arches and Onset of Chaos
Authors: Schmidt G. , Yu J. S.
Published: May 2007

For non‐shallow arches, an internal resonance of symmetrical and antisymmetrical vibrations is the most important phenomenon. It is shown by higher analytical iteration that the nonlinear coupling between the two vibration modes yields maximum amplitudes and an onset of chaotic motions in dependence of the detuning. The results on the onset of chaos correspond to numerical results found by J. J. Thomsen [6].
The Stress Conjugate to Logarithmic Strain In V
Authors: Lehmann Th. , Liang Haoyun
Published: May 2007

In this paper a certain generalization of the concept of conjugate stress and strain is given particularly with respect to strain measures of Eulerian type. According to this interpretation the stress conjugate to logarithmic strain In V is determined.
Transient Flow of a Compressible Viscous Fluid Near an Infinite Disk
Authors: Bhattacharyya S. , Nath G.
Published: May 2007

We have considered the transient motion of an electrically conducting viscous compressible fluid which is in contact with an insulated infinite disk. The initial motion is considered to be due to the uniform rotation of the disk in an otherwise stationary fluid or due to the uniform rigid rotation of the fluid over a stationary disk. Different cases of transient motion due to finite impulse imparted either to the disk or to the distant fluid have been investigated. Effects of the imposed axial magnetic field and the disk temperature on the transient flow are included. The nonlinear partial differential equations governing the motion are solved numerically using an implicit finite‐difference scheme along with the Newton's linearisation technique.
Das Reduktionsverfahren für Polynommatrizen
Authors: Falk S.
Published: May 2007

Für eine quadratische Polynommatrix F(λ), deren Eigenwerte bekannt sein müssen, wird eine Methode entwickelt, die eine sukzessive Abspaltung von Eigenwerten einzeln oder in Gruppen ermöglicht, wobei der Grad der aktuellen reduzierten Polynommatrix Fred(λ) laufend erniedrigt wird.
Attitude Drift of a Dissipative, Torquefree, Radially Deformable Gyro
Authors: Romrott F. P. J. , Semenov G.
Published: May 2007

The present investigation is concerned with the behaviour of a dissipative, originally axisymmetric, torquefree model gyro, that has deformation in the body‐fixed equatorial plane only. This model gyro has been devised to pick up deformations due to the centrifugal forces in the equatorial plane, and serves to describe the resulting motion.
A Unified Approach to Enclosure Methods for Eigenpairs
Authors: Mayer G.
Published: May 2007

We consider a class of methods for verifying and enclosing eigenpairs of real and complex matrices. The class is based on a Taylor expansion which allows to derive properties holding for each member of the class. We generalize these results to the case of enclosing simultaneously eigenpairs for all matrices which vary between given bounds.
Nichtlineare Schwingungen mechanischer Strukturen mit Füge‐oder Kontaktstellen
Authors: Popp K.
Published: May 2007

No Abatract.
On the Consideration of the Geometric and Physical Fractality in Solid Mechanics. I: Theoretical Results
Authors: Panagiotopoulos P. D. , Panagouli O. , Mistakidis E.
Published: May 2007

The aim of the present paper is to investigate the influence which the behaviour of solids and structures has on the possible fractality of their geometry or of their material behaviour. To this end certain methods are proposed for the theoretical investigation of this influence, based on the consideration of the fractal as attractor of a deterministic or a random iterated function system. First the mechanical notions and the mechanical laws are extended to fractal geometries. Then certain calculation methods are proposed and their results are investigated.
Eine energetische Variante der Theorie des Kriechens und der Langzeitfestigkeit für isotrope Werkstoffe mit komplizierten Eigenschaften
Authors: Altenbach H. , Zolochevsky A. A.
Published: May 2007

Es wird die Formulierung von Konstitutivgleichungen zur Beschreibung des stationären (sekundären) und des beschleunigten (tertiären) Kriechstadiums von isotropen Materialien mit komplizierten Eigenschaften dargelegt. Die vorgeschlagenen Beziehungen enthalten drei Invarianten des Spannungstensors und sechs Parameter. Weiterhin werden Grundversuche erörtert und Sonderfälle abgeleitet. Für zwei leichte legierungen wird ein Vergleich von theoretischen und experimentellen Ergebnissen für den Fall mehrachsiger Beanspruchung durchgeführt.
Axisymmetric Natural Frequencies of a Rotating Infinitely Long Viscous Liquid Column
Authors: Bauer H. F.
Published: May 2007

The axisymmetric damped natural frequencies have been determined for a solidly spinning infinitely long viscous liquid column in zerogravity environment. The column ist held together by the surface tension of the free liquid surface, which acts as the restoring force. The damped natural frequencies depend on the surface tension parameter σa/ϱv2, the wave length in axial direction λz/2πa and the spin parameter λz/2Ωoa2/v. Instability appears from an aperiodic mode for the axial wave length λz > 2πa/√1+ We, We = ϱa3Ω2o/σ being the Webernumber.
Response of an Anchored Viscous Liquid Layer to Axial Excitation in Zero‐Gravity
Authors: Bauer H. F.
Published: May 2007

Das Antwortverhalten einer viskosen Flüssigkeitsschicht wurde analytisch behandelt, wobei die Flüssigkeit am Rand der oberen und unteren Scheibe gefesselt ist. Die gedämpften Frequenzen, die Vergrößerungsfunktionen der freien Oberflächenauslenkung, die radiale und axiale Geschwindigkeitsverteilung wurden als Funktion von ω für verschiedene Oberflächenspannungsparameter νa/ Streckungsverhältnisse h/a an verschiedenen Stellen der Flüssigkeitssäule dargestellt. Dabei Konnte eine endliche, aber scharfe erste Resonanzerhöhung festgestellt werden.
On the Secondary Forces in a Semi‐Infinite Medium Containing an Edge Dislocation, a Circular Cut and a Circular Hole
Authors: Shioya S. , Yamaguchi H.
Published: May 2007

Die Wechselwirkung zwischen einer halbkreisförmigen Einkerbung, einer kreisförmigen Öffnung und einer Stufenversetzung (auf der Symmetrieachse) in einem halbunendlich ausgedehnten Medium wird mit Hilfe der Airyschen Spannungsfunktion untersucht. Die Lösung wird mit der Grund‐Spannungsfunktion und Hilfs‐Spannungsfunktionen konstruiert. Die zwei Hilfs‐Spannungsfunktionen werden aus den 6 Grundspannungsfunktionen, die für diesen Zweck konstruiert werden, gebildet. Die Resultate, die für die numerische Berechnung erhalten werden, zeigen, daß –‐ für das Gebiet nahe der Grenzfläche –‐ die Wechselwirkungen durch geometrische Beziehungen stark beeinflußt werden. Es ist interessant, daß die Stufenversetzung instabile Gleichgewichtslagen hat in einer Zwischenentfernung von de Einkerbung bei der Anordnung Einkerbung‐Stufenversetzung‐Öffnung.
Non‐Linear and Iterative Mechanics for the Investigation of Multi‐Body Systems with Friction
Authors: Klepp H. J.
Published: May 2007

Von den Reibungskräften und Reibungsmomenten in Schub‐ und Drehgelenken wird angenommen, daß sie durch geschwindigkeitsabhängige Reibungskoeffizienten und durch lage‐, geschwindigkeits‐ und beschleunigungsabhängige Reaktionskräfte bestimmt sind. Solche Reibungsmodelle führen auf nichtlineare Bewegungsdifferentialgleichungen und auf nichtlineare algebraische Gleichungen und können in der Regel nur numerisch und iterativ gelöst werden. Für ein System mit einem Freiheitsgrad werden diese Gleichungen mit der Lagrangeschen Methode und aus den kinetischen Gleichgewichtsbedingungen der Teile des Systems bestimmt. Besonderheiten, die bei der Untersuchung solcher Systeme zu berücksichtigen sind, werden aufgezeigt, und repräsentative Eigenschaften der Bewegungen und der Reaktionskräfte werden durch numerische Simulation für ein Mehrkörpersystem mit zwei Gleit‐ und zwei Drehlagern bei harmonischen Erregungen bestimmt.
Differential‐Algebraic Equations in Riemannian Spaces and Applications to Multibody System Dynamics
Authors: Jungnickel U.
Published: May 2007

Für Mehrkörpersysteme mit eventuell anholonomen oder rheonomen Bindungen wird eine Riemannsche Metrik des erweiterten Zustandsraums in Abhängigkeit von den Massen und Zwangsbedingungen konstruiert. Dies gestattet die Anwendung allgemeiner Prinzipien zur Transformation von Differentialgleichungen mit Invarianten in Riemannschen Räumen. Enge Verbindungen zu Projektionsmethoden in der Mehrkörper‐Dynamik werden aufgezeigt.
A Discretization Theory for Monotone Semicoercive Problems and Finite Element Convergence for p‐Harmonic Signorini Problems
Authors: Gwinner J.
Published: May 2007

Es wird eine Erweiterung der Diskretisierungstheorie von Glowinski auf nichtlineare monotone, semikoerzitive Variationsungleichungen vorgestellt. Als eine Anwendung wird die Finite‐Element‐Diskretisierung von p‐harmonischen Signorini‐Problemen untersucht. Ohne Regularitätsannahmen wird Normkonvergenz für stückweise lineare und stückweise quadratische Ansatzfunktionen gezeigt, was im letzteren Fall auf ein nichtkonformes Approximationsverfahren führt.
On the Convergence of Time‐Discrete Processes
Authors: Bohl E.
Published: May 2007

We prove a general convergence result for a multistep time‐discrete process

equation image

under very mild conditions on the function V. We discuss the application to boundary value‐ and boundary layer problems. Our proof is a straight‐forward argument without any concepts for stability or consistency.
Construction of Outwards Impermeable Surface Systems by Means of Comparison Systems
Authors: Koksch N.
Published: May 2007

For the determination of positive invariant sets for a dynamical system, in general surfaces without contact with the vector field of the system are used. The main objective of the paper is to present a method for the construction of an auxiliary system of differential equations. (comparison system), such that the system of surfaces defined by means of the solutions of this auxiliary system is impermeable to the solutions of the original system in a desired direction and has the property of contactlessness with respect to the vector field of the original system. The above described procedure makes it possible to determine all the comparison systems of the paper [6]. The Lorenz system is considered as an example here, too.
On the Observability and Controllability of Vibrating Structures
Authors: Niedbal N. , Klusowski E.
Published: May 2007

The realization of observability and controllability are basic requirements for experimental modal analysis. Since highly sophisticated modal analysis testing techniques and multiple input/multiple output equipment are availabel today, the realization of observability and controllability is no longer regarded as an unsolved problem. Based on a selection criterion for optimal observability and controllability, the influence of both parameters on the accuracy of test data results is presented.
Analysis of Anisotropic Elasticity by Means of Internal Stress in a Reference Isotropic Elastic Body
Authors: Armitsu Y. , Nishioka K. , Senda T.
Published: May 2007

A method of anisotropic elasticity problems is proposed which employs superposition of the analytic solution for an isotropic elastic body and the suitable internal stress determined by the boundary condition. Employing the incompatibility tensor and Kröner's stress functions, we can establish a simple formulation for the anisotropic elasticity. The difference of the stress fields in an isotropic material and an anisotropic material can be considered as an internal stress field caused by the incompatibility which can be evaluated from the solution of the isotropic material by use of its curl curl operations for the incompatibility tensor. Though it is difficult to get the analytic solution for general cases, some special cases with Airy's stress function are analyzed as simple examples. Since the internal stress can be expressed by the dislocations distributed continuously in the isotropic body, we can gain further physical insight into the anisotropy.
Numerical Computation of Vortical Flow Fields of Double‐Delta Wings Moving in a Compressible Viscous Medium
Authors: Das A. , Longo J. M. A.
Published: May 2007

Detailed study of the flows around double‐delta wings is undertaken by performing numerical simulation of the Navier‐Stokes equations in finite‐volume formulation. The turbulent viscous stresses are accounted for by means of eddy viscosity model. For the discretization of the space around the sings 0‐0 grid topologies have been used. The analysis includes the study of the spiraling vortices in the cross‐flow fields comprising velocity and pressure distributions yield further essential results, including total forces and moments of the wings. The computation method is applicable for subsonic, transonic and supersonic onflow Mach numbers. The numerical results are well validated with experimental data.
The Jumping Tippe Top
Authors: Kuypers F. , Meyer G. P. , Freihart J. , Friedl C. , Gerisch M. , Kraus H. J. , Seidel R.
Published: May 2007

Nach unseren Experimenten und numerischen Berechnungen hebt der Stehaufkreisel in vielen Läufen einige Millimeter vom Boden ab und fliegt ein kurzes Stück durch die Luft. Die Aufschläge auf den Boden können nur mit einem weichen Boden realistisch beschrieben werden. Unser Modell enthält aber nicht nur einen weichen Boden mit linearer Rückstellkraft, Sondern berücksichtigt auch den Stift, so daß vier Bewegungsphasen möglich sind: (1) Die Hauptkugel rutscht über den Boden. (2) Freier Flug (kein Bodenkontakt). (3) Doppelkontakt von Stift und Hauptkugel mit dem Boden. (4) Der Stift rutscht über den Boden.
The Behaviour of the Etching Rate in a Model of Plasma Etching
Authors: Kern M. , Koksch N.
Published: May 2007

Diese Arbeit ist sowohl der Modellierung einiger Oberflächen‐ und Volumenprozesse beim Plasmaätzen durch gewöhnliche Differentialgleichungen als auch der qualitativen Untersuchung des resultierenden Systems gewidmet. Die explizite Konstruktion von Attraktoreinhüllenden erlaubt, die Ätzrate des Prozesses durch eine Folge von Schranken einzugrenzen.
Some Tests for Determining the Number of Effective Modes
Authors: Zamirowski M.
Published: May 2007

In der Arbeit werden Probleme betrachtet die mit Identifikationsverfahren zusammenhängen und als ein Schritt in der Theorie der Modellierung linearer Strukturen behandelt werden können. Beginnend mit einem mathematischen Modell für ein mechanisches System wird der Einfluß der effektiven Anzahl der Moden auf die dynamische Modellantwort entwickelt. Für die Abschätzung der effektiven Moden‐Anzahl innerhalb der gemessenen dynamischen Antworten werden numerische Algebra und statistische Theorien verwendet. Die theoretischen Ergebnisse werden an einem Beispiel erläutert. Es kann gezeigt werden, daß die vorgeschlagenen Verfahren effektiv effektiv arbeiten.
Folge‐Wöhlerlinien und Miner‐Regel in einen Stochastischen Ermüdungsmodell
Authors: Nawrotzki K.
Published: May 2007

In der Arbeit wird ein stochastisches Ermüdungsmodell angegeben, das eine Beschreibung der Schadensakkumulation bei stückweise konstanter Belastung durch Folge‐Wöhlerlinien und die Formulierung einer Miner‐Regel für zufällige Lebensdauern ermöglicht.
Flow and Heat Transfer in a Saturated Porous Medium over a Stretching Surface
Authors: Vajravelu K.
Published: May 2007

Eine Untersuchung wird durchgeführt, die Strömungs‐ und Wärmeübergangseigenschaften in einem durchtränkten, porösen Medium über einer impermeable sich ausdehnenden Schicht mit Reibungswärme und innerer Wärmeerzeugung oder Absorption zu studieren. Zwei Fälle werden untersucht, nämlich (i) die Schicht mit vorgeschriebener Oberflächentemperatur (PST‐Fall) und (ii) die Schicht mit vorgeschriebener Wandwärmeströmung (PHF‐Fall). Exakte Lösungen für das Geschwindigkeitsfeld und die Oberflächenreibung werden erhalten. Auch die Lösungen für die Temperatur, die Wärmeübergangseigenschaften und ihre asymptotischen Grenzwerte für große und kleine Prandtl‐Zahlen werden in Termen der Kummerschen und parabolischen Zylinderfunktionen erhalten. Für große Prandtl‐Zahlen (σ) wird eine thermische Grenzschichtdicke von √1/sigma; für die PST‐und PHF‐Fälle bestimmt. Weiter wird gezeigt, daß es keine Lösung vom Grenzschichttyp für kleine Prandtl‐Zahlen gibt.
An Existence and Inclusion Method for Two‐Point Boundary Value Problems with Turning Points
Authors: Plum M.
Published: May 2007

Für parameterabhängige Zweipunkt‐Randwertprobleme wird eine Methode zum nachweis der Existens und zur Berechnung von Schranken für Lösungen vorgestellt, die auch in Umgebungen (einfacher) Nachweispunkte erfolgreich angewendet werden kann, wo „direkte”︁ Existens‐ und Einschließungsverfahren infolge der Singularität des linearisierten Problems versagen. Diese Singularität wird durch Umparametrisierung beseitigt.
Error Estimates for Galerkin Approximations to the Periodic Schrödinger‐Poisson System
Authors: Bohun S. , Illner R. , Lange H. , Zweifel P. F.
Published: May 2007

We establish convergence rates for a Galerkin approximation to the periodic Schrödinger‐Poisson problem in the unit cube [0, 1]3. The error estimates transform into corresponding L∞‐error estimates for the Wigner distribution function.
Dynamik hybrider Mehrkörpersysteme aus kontinuumsmechanischer Sicht
Authors: Maisser P.
Published: May 2007

Die Dynamik von Mehrkörpersystemen, die auch elastisch deformierbare Körper enthalten, wird mittels globalem Ritz‐Ansatz für das Verschiebungsfeld der elastischen Deformation im Rahmen der Lagrangeschen Mechanik auf eine Punktdynamik auf einer endlich‐dimensionalen Reimannschen Mannigfaltigkeit zurückgeführt. Metrik und Christoffelsymbole dieser Mannigfaltigkeit sowie generalisierte Kräfte auf dem entsprechenden Tangentialbündel können unabhängig voneinander und rein algebraisch computergestützt generiert werden, ebenso diverse Zwangsbedingungen geometrisch gekoppelter elastisch deformierbarer Körper. Elastisch deformierbare Körper werden ihrerseits als glatte, von einem Parameter abhängige Mannigfaltigkeiten betrachtet, auf denen Metriken und Zusammenhangsobjekte definiert sind, mit deren Hilfe Zwangsbedingungen in jeder aktuellen Lage korrekt formuliert werden Können.
Solution of the Thermoelastic Problem for a Cylinder in the Case of a Two‐Dimensional Nonaxisymmetric Temperature Field
Authors: Vihak V. M.
Published: May 2007

A new method of the construction of an analytical solution of a thermoelastic problem for a homogeneous isotropic cylinder in the case of an arbitrary two‐dimensional nonaxisymmetric temperature field is proposed in this paper. The integral relations between separate components of the stress tensor, and also the integral conditions of equilibrium for stress tensor components and integral conditions of material continuity of the cylinder for displacement vector components are additionally found.
Transient Pressure Variation of a Fluid in a Gravity‐Free Environment
Authors: Schieber D.
Published: May 2007

The paper deals with a simple model of a mechanically excited column of a highly viscous fluid. Its transient oscillations are calculated via the theory of functions. The excess pressure is obtained in the form of an infinite series. An estimate of the natural frequencies under the influence of very high viscosity, in a gravity‐free environment, is put forward in graphical form.
Fluid‐Structural Coupling of Vibrating Bodies in a Surrounding Confined Liquid
Authors: Seemann W. , Wauer J.
Published: May 2007

The dynamic characteristics of elastically supported rigid bodies in contact with a compressible viscous fluid are studied. In particular, the complex eigenvalues of the coupled system are determined. Reference cases are the corresponding elastically supported rigid body vibrating in vacuum and the compressible viscous fluid confined between rigid walls. The effects of the fluid‐body density ratio and the fluid‐foundation stiffness ratio as the governing coupling parameters are analyzed in detail. To obtain analytical results, a simple one‐dimensional piston problem and a more complicated two‐dimensional generalization in form of an elastically supported rigid cylinder in a cylindrically bounded fluid‐filled duct are considered.
Nonsimilar MHD Boundary Layer Flow Near in Asymmetric Plane Stagnation Point
Authors: Lawrence P. Sam , Rao B. Nageswara
Published: May 2007

The nonsimilar boundary layer equations of the title problem are solved using a reliable numerical scheme for obtaining the coefficient of skin‐friction. It is found that the normal surface velocity gradient increases with the magnetic interaction parameter.
Tensorgeneratoren bei Systemen von Tensoren zweiter und vierter Stufe
Authors: Betten J. , Helisch W.
Published: May 2007

Tensorgeneratoren spielen in der Theorie der Tensorfunktionen eine wichtige Rolle bei der Aufstellung tensorwertiger Funktionen mit einem oder mehreren Argumenttensoren (im allgemeinen) unterschiedlicher Stufenzahlen (s. [1] – [7]). Im folgenden Aufsatz werden nach einer kombinatorischen Methode irreduzible Systeme von Tensorgeneratoren für Systeme symmetrischer Tensoren zweiter und vierter Stufe im zwei‐, drei‐ und vierdimensionalen Raum aufgestellt.
The Existence and Uniqueness of Solutions by the Covering Domain Method in Linear Elastostatics
Authors: Lin X. , Ballmann J.
Published: May 2007

The paper deals with problems of linear elastostatics with multiply connected solution domains. Generally, a multiply connected domain can be represented in a non‐unique way by the intersection set of n > 1 domains, each of which covering completely the original solution domain. If exact analytical solutions can be found in the covering domains, then, making use of the superposition principle, the solution of the original problem can be constructed by summation of the n solutions of the covering domains. Following this idea, the “covering Domain Method” is developed, by which the original problem is transformed into a system of Fredholm integral equations which finally offers the solution of the problem. In this paper we consider the existence and uniqueness of the solutions for different choice of covering domains. Two theorems are presented, which are useful for the application of the covering domain method in elasticity.
Lösung linearer Differentialgleichungen beliebiger Ordnung mit Polynomkoeffizienten und Anwendung auf ein baustatisches Problem
Authors: Rubin H.
Published: May 2007

Aufbauend auf das in [1], [2] angegebene Lösungskonzept für lineare Differentialgleichungen mit konstanten Koeffizienten wird eine Erweiterung auf den Fall nichtkonstanter Koeffizienten (Polynome beliebigen Grades) vorgenommen. Sowohl das allgemeine Integral der homogenen Differentialgleichung als auch das partikuläre Integral wird mit Hilfe der Lösungsfunktionen bj beschrieben, wobei letztere mittels Reihenformeln bestimmt werden. Beliebige Sonderfälle (z. B. einzelne Koeffizienten sind konstant oder Null) werden durch den allgemeinen Fall erfaßt. Anhand des angegebenen Struktogramms kann das Verfahren leicht programmiert werden. Die praktische Anwendung wird schließlich mit der Berechnung eines schlanken Turmes nach der Theorie II. Ordnung gezeigt, wobei sowohl Querschnitt als auch Normalkraft veränderlich sind.
On Integral Equations for Wave Diffraction Problems
Authors: Umek A.
Published: May 2007

The conditions, under which the partial differential equations of the linear, time harmonic elastodynamics can be replaced by the corresponding boundary integral equation, are investigated. It is found by an example that this is the case, whenever the domains are normal in the simple or extended sense. Further, a counter‐example known in the literature is examined and is proven to be erroneous, thus corroborating our findings.
Diffraktion von Wasserwellen am horizontalen Zylinder
Authors: Dorfmann A.
Published: May 2007

Die analytische Lösung einer ebenen Aufgabe von Diffraktion der Wasserwellen am Zylinder mit kreisförmigem Querschnitt, der sich in unendlich tiefer Flüssigkeit befindet, so daß Wasser‐ und Zylinderoberfläche sich berühren, wurde im Rahmen der linearen dispersiven Theorie gebildet. Dabei wurden krummlinige Koordinaten und Integraltransformationsverfahren verwendet. Betrachtet worden ist auch die Aufgabe der Aufgabe der Ausstrahlung der Wasserwellen, die von der Pulsation oder Bewegung des Zylinders verursacht wurden.
A Parallel Newton Multigrid Method for High Order Finite Elements and Its Application to Numerical Existence Proofs for Elliptic Boundary Value Equations
Authors: Wieners Chr.
Published: May 2007

We describe a parallel algorithm for the numerical computation of guaranteed bounds for solutions of elliptic boundary value equations of second order. We use C2‐Hermite‐elements and a parallel Newton multigrid method to produce approximations of high accuracy. Then, we compute upper bounds for the defect and enclosures for the eigenvalues of the linearization. In order to obtain verified bounds, these computations are realized in interval arithmetic. The application of the Newton‐Kantorovich‐theorem yields the existence of a solution and error bounds for the approximation. The method is implemented on a 256 processor transputer grid and tested for the Bratu problem – Δu = λ exp(u).
On Isotropic Extension of Anisotropic Tensor Functions
Authors: Xiao H.
Published: May 2007

The present paper indicates that through some simple vector‐valved and 2nd‐order‐tensor‐valued invariant tensor functions anisotropic functions can be extended to isotropic functions merely with vectors and 2nd‐order tensors as extended variables. This result enables us to obtain representations of anisotropic functions using the much well‐known representations of isotropic functions. The thirty‐two crystal classes and almost all noncrystal classes are considered.
On the Cauchy Problem for the Lamé System
Authors: Shlapunov A.
Published: May 2007

Solvability conditions and Carleman formula for the Cauchy problem for Lamé type systems in ℝn n ≧ 2, are obtained. In particular, for given displacement and strain on an open connected part of the boundary of the domain of a special type, the formula for the reconstruction of solutions of the Lamé system in the domain is derived.
Modelling of Nonstationary Heat Conduction Problems in Micro‐periodic Composites
Authors: Woźaniak C. , Baczyński Z. F. , Woźniak M.
Published: May 2007

In this contribution an averaged refined model of a rigid heat conductor with micro‐periodic structure is formulated. The proposed model describes the effect of a microstructure length dimension on the time‐dependent heat transfer processes. It is shown that this effect plays a crucial role in the analysis of nonstationary problems and hence the known effective modulus theories of heat conduction (where the microstructure is scaled down), have the range of applicability restricted to steady‐state problems.
On the Plane Potential Flow Through the Inhomogeneous Porous Line
Authors: Keglević I.
Published: May 2007

The plane stationary potential flow of an inviscid incompressible fluid through the porous straight line or porous straight segment is considered. On the porous line the normal velocity is assumed to be linearly proportional to the pressure difference. With given velocity at infinity, we give the formula of the solution of the problem and the proof of the uniqueness of the solution, except in the case, when the velocity at infinity is perpendicular to the porous line. In this case we do not have any solutions.
On the Discretization of van Roosbroeck's Equations with Magnetic Field
Authors: Gajewski H. , Gärtner K.
Published: May 2007

We investigate qualitative properties of the drift‐diffusion model of carrier transport in semiconductors when a magnetic field is present. At first the spatially continuous problem is studied. Essentially, global stability of the thermal equilibrium is shown using the free energy as a Lyapunov function. This result implies exponential decay of any perturbation of the thermal equilibrium. Next, we introduce a time discretization that preserves the dissipative properties of the continuous system and assumes not more than the naturally available smoothness of the solution. Finally, we present a space discretization scheme based on weak and consistent definitions of discrete gradients and currents. Starting with a fundamental result on global stability (dissipativity) of the classical Scharfetter‐Tummel scheme (without magnetic field), we adapt this scheme with respect to magnetic fields and study the M‐property o the associated matrix. For two dimensional applications explicit conditions on the smallest inner angle and the modulus of the magnetic field are derived.
On a Class of Winkler‐Type Contact Problems
Authors: Angelov T. A.
Published: May 2007

A class of Winkler‐type contact problems is considered. Existence and uniqueness results are obtained and an a priori finite element error estimate is derived. An algorithm is proposed by which an example problem with different Winkler‐type boundary conditions is solved.
Similarity Solutions for the Squeezed Film Flow between Two Rotating Naturally Permeable Discs
Authors: Bhatt B. S. , Hamza E. A.
Published: May 2007

A Newtonian fluid film squeezed between two rotating discs which are made up of naturally permeable (porous) materials and of finite thicknes has been considered. Similarity solution has been obtained when the discs at time t are separated by a distance H (1–αt)1/2, rotating with angular velocities proportional to Ωi(1–αt)−1 and of permeabilities ki(1–αt) (i – 1, 2 for lower, upper disc) where H, α−1, Ωi and ki denote a representative length, time, angular velocities, and permeabilities of the discs, respectively. The effects of rotation and permeabilities have been studied on velocity profiles, the load capacity, and the torques which the fluid exerts on the discs. If we take the discs of same permeability, there exists a critical value of permeability above and below which the behaviour of various physical quantities changes.
Practical Approximate Turbulent Boundary Layer Calculation into the Divergent Rectangular Channel
Authors: Askovic R.
Published: May 2007

Both plane and axially symmetrical turbulent boundary layers are analysed in the sense of the well‐known phenomenologic semi‐empiric boundary‐layer theory. The analysis is based on an analogy with the rheologic power‐laws widely used in the study of non‐linear viscous flows. A simple “one layer method” to calculate both plane and axisymmetric turbulent boundary layers is first derived and after that tested on the model of a rectangular channel, used for the hydraulic machines for instance. The model is composed of an annular disc and two perpendicular radial plates in the flow produced by a linear source. Neglecting the interaction between the disc and two plates, both boundary layers are considered separately: the plane boundary layer between two divergent plates and the axially symmetrical boundary layer on the disc (even in the presence of a funnel above the disc to vary the slowing down of the flow).
Problems of Hydrofoil Design for a Given Range of Angles of Attack
Authors: Elizarov A. M. , Fokin D. A. , Galyavieva M. S.
Published: May 2007

This paper is an attempt to pose the universal inverse problem for two angles to attack, when the initial data are given as a function of a generalized coordinate, and to indicate the common way of its solving.
Growth and Decay of Acceleration Waves in Incompressible Saturated Poroelastic Solids
Authors: De Boer R. , Liu Z.
Published: May 2007

In the present paper the evolution of the amplitudes of acceleration waves in incompressible saturated poroelastic solids within the framework of the geometrically linear theory is examined. The incompressible porous media model by Bowen is adopted to describe the mechanical behaviour of an incompressible two‐phase system. The underlying assumption made is that the amplitudes do not change tangentially to the wave fronts. The differential equations governing the amplitudes of acceleration waves are derived and the explicit solutions are obtained. The results indicate that the amplitudes of acceleration waves may either decay to vanish or grow to infinity in finite time, which depends on the geometrical property of the initial shapes of the wave fronts and the diffusion effect between the two phases. In particular, the longitudinal acceleration waves in the liquid are completely carried by the solid skeleton. The behaviour of acceleration waves in the porous medium is similar to that in isotropic elastic non‐porous solids.
A Reduction Principle for ω‐Limit Sets
Authors: Schropp J.
Published: May 2007

Characterizing the ω‐limit sets of evolutions is one of the central taks in dynamical systems theory. In some cases, one can assure a‐priori that the ω‐limit set of an evolution lives in a certain subset of the phase space. Assuming now that the global dynamics of the system on this subset is known, we prove a theorem which determines the ω‐limit set of the given trajectory. Furthermore, we apply this theorem to a chemostat model, which describes the degradation of organic substrate governed by some organisms.
Shape Preserving C3 Data Interpolation and C3 Histopolation with Splines on Threefold Refined Grids
Authors: Walter Hess , Schmidt J. W.
Published: May 2007

This paper is concerned with the convex C3 interpolation of univariate data sets. An algorithm based on the use of quartic splines on threefold refined girds is presented which is always successful for data sets in strictly convex position. These splines are suitable also for monotone as well as positive C3 interpolation. Further, the derived algorithms apply to the monotone and positive C2 histopolation with cubic splines on grids refined as before.
On Mathematical Aspects of Dual Variables in Continuum Mechanics. Part 2: Applications in Nonlinear Solid Mechanics
Authors: van der Giessen Erik , Kollmann F. G.
Published: May 2007

Continuing the approach of Part 1 of this paper we apply our results to dual variables appearing in continuum mechanics. We investigate the kinematics and dynamics of continuous bodies. As a consequence, this leads to a mixed variant formulation of kinematics and Cauchy's law for the stress tensor. The mixed variant formation of kinematics is advantageous, for instance, in finite deformation plasticity. Finally, we give some examples of constitutive equations which demonstrate in an exemplaric manner the additional mathematical structure gained through our approach.
Analyse selbsterregter Drehschwingungen in Torsionsstäben
Authors: Kreuzer E. , Kust O.
Published: May 2007

Torsionsstränge bilden in vielen technischen Anwendungen das Kraftübertragungselement zwischen An und Abtrieb. Es werden die Systemgleichungen eines allgemeinen Torsionsstranges unter Berücksichtigung von Nichtlinearitäten angegeben. die Stabilität wird anhand der Eigenwertverteilung und mit der Poincaré‐Abbildung untersucht. Ursache für die zu beobachtenden selbsterregten Drehschwingungen ist eine superkritische Hopf‐Verzweigung. Mit Hilfe des Antriebes ist eine aktive Dämpfung möglich, und die Schwingungen werden damit minimiert. Es wird ein Reglerentwurf für das nichtlineare System vorgestellt. Dabei wird die Bestimmung der Reglerparameter über die Optimierung eines Gütekriteriums vorgenommen. Nach den theoretischen Grundlagen werden die Berechnungen an einem Anwendungsbeispiel vorgestellt. Es handelt sich um einen Bohrstrang zur Förderung von Öl und Gas. Solche Bohrstränge weisen ein extrem kleines Durchmesser‐Längenverhältnis auf. durch das nichtlineare Drehmoment am Bohrkopf können selbsterregte Drehschwingungen auftreten.
On Nonstationary von Kármán Equations
Authors: Bock I.
Published: May 2007

In der vorliegenden Arbeit wird ein Anfangswert‐ und Randwertproblem für eine visko‐elastische dünne Platte mit großen Biegungen formuliert und studiert. Es wird ein System nichtlinearer pseudoparabolischer und Volterrascher Integro‐Differential Gleichungen für die Biegungs‐ und die Airy‐Spannungs‐Funktion formuliert. Das vorliegende System ist eine Verallgemeinerung der von Kármá‐Gleichungen für den elastischen Fall. Die schwache Formulierung in Sobolev‐Räumen und das kanonische Anfangswertproblem für die Biegungsfunktion werden betrachtet. Die Existenz einer Lösung wird mittels elliptischer Regularisierung bewiesen.
On Well‐Posedness for Non‐Linear Problems in the Theory of Elastic Materials with Voids
Authors: Scarpetta E.
Published: May 2007

In the context of a well known theory for finite deformations of porous elastic materials, some theorems on uniqueness and continuous dependence on data are proved for both the dynamic and the static (nonlinear) problems. A possibly unbounded domain of the physical space is considered for the material in concern.
Vortices and Heat Transfer
Authors: Fiebig M.
Published: May 2007

For internal flow the influence of vortices on heat transfer is studied mainly numerically. Laminar channel flows with two types of periodic vortex generators (VGs), transverse ribs and rectangular winglets, are considered. The transverse ribs generate transverse vortices (TVs), and the rectangular winglets at 45° angle of attack generate longitudinal vortices (LVs). Velocity and temperature fields, local and global friction, flow losses, and heat transfer are computed from the full unsteady, three‐dimensional conservation equations. Point comparisons with experimental results are given. For steady flow the TVG configuration strongly influences heat transfer locally, but not globally. The stationary TVs don't provide an additional mechanism for convective thermal energy transport, but cause additional flow losses for their generation. The LVG configuration enhances local and global heat transfer for both steady and unsteady flow. For steady flow the LVs generate swirl which is an additional mode of convective thermal energy transport. When the flow reaches a critical Re‐number, which is more than an order of magnitude lower than the normal transition Re‐number, self‐sustained oscillations set in. They provide an additional heat transfer mode due to “Reynolds” averaged transport which further increases the heat transfer. For the same heat transfer increase the LVG configuration causes only half the flow losses of the TVG configuration. For practical applications, where high heat transfer and low flow losses are important, LVG configurations are better suited than TVG configurations.
The Nonlinear Stability of Mass and Heat Transfer in Magnetic Fluids
Authors: Elhefnawy A. R. F.
Published: May 2007

The nonlinear analysis of the Rayleigh‐Taylor stability of two superposed magnetic fluids with interfacial transfer of mass and heat is presented for two layers each of finite thickness. The system is subjected to a tangential magnetic field. The method of multiple scale expansion is employed for the analysis. It is shown that the evolution of the amplitude is governed by a nonlinear Ginzburg‐Landau equation. There is also obtained a nonlinear diffusion equation describing the evolution of wave packets near the marginal state. Further, the nonlinear Schrödinger equation is obtained when the influence of mass and heat transfer is neglected. The various stability criteria are discussed both analytically and numerically and the stability diagrams are obtained. It is found that, in the linear theory, the stability criterion is independent of mass and heat transfer coefficient. While in the nonlinear theory it is found that, when this coefficient is large enough, the system which would be unstable classically, can be stabilized for finite amplitude disturbances.
On the Existence and Uniqueness in Linear Thermoviscoelasticity
Authors: Foutsitzi G. , Kalpakidis V. K. , Massalas C. V.
Published: May 2007

Es wird ein Anfangs‐Randwertproblem aus der Theorie der linearen Thermoviskoelastizität betrachtet. Nach Formulierung des zugeordneten Variationsproblems werden Existenz und Eindeutigkeit seiner Lösung in einem geeigneten funktionalanalytischen Rahmen studiert.
A Bifurcation Theory for a Nonconvex Unilateral Laminated Plate Problem Formulated as a Hemivariational Inequality Involving a Potential Operator
Authors: Goeleven D.
Published: May 2007

The present paper concerns the hemivariational inequality approach to the laminated plate theory under abstract subdifferential conditions. The mechanical problem is formulated as a nonlinear eigenvalue problem for hemivariational inequalities and a corresponding bifurcation theory is given.