bluuebunny/crossref_metadata_2025_split huggingface dataset:
On Boundary Layer and Interior Equations for Higher‐Order Theories of Plates
Authors: Nosier A. , Reddy J. N. 
Published: May 2007

AbstractSeveral shear‐deformation plate theories of symmetric laminated plates with transversely isotropic layers are reviewed and the governing equations of these theories are then recast into two equations: one for the interior of the domain and the other for the edge‐zone or the boundary layer. For the first time it si shown that the governing equations of the third‐order shear‐deformation theory of Reddy result in a sixth‐order interior equation and a second‐order edge‐zone equations. It is also demonstrated that in bending and stability problems, and under certain conditions in dynamic problems, the contribution of the edge‐zone equation is identically zero for a simply‐supported plate. The pure‐shear frequencies of a plate according to different theories are determined and compared.
On the Method of Characteristics in Rate‐Type Viscoelasticity with Non‐Monotone Equilibrium Curve
Authors: Mihâilescu‐Suliciu M. , Suliciu I. 
Published: May 2007

AbstractThe standard method of characteristics is applied to a hyperbolic system of partial differential equations describing the motion of a viscoelastic body. The equilibrium curve can be of the van der Waals type such that the system may describe phase transition phenomena. For isolated body problems, sufficient conditions are given on the time integration steps of the first and second numerical approximations such that the total energy of the numerical solution be a nonincreasing function of the number of time integration steps. This property is required since the total energy of the exact solution is a nonincreasing function of time as required by the second law of thermodynamics. Numerical examples of nonisolated body problems when the violations of the above conditions lead to numerical instabilities are presented elsewhere (see Introduction).
Steady Plane Orthogonal MHD Flows
Authors: Chandna O. P. , Nguyen P. V. 
Published: May 2007

AbstractComplex variable technique is used to study steady plane orthogonal magnetohydrodynamic flows of a viscous incompressible fluid of infinite electrical conductivity. The equations of motion are recast in variables z = x + iy and z̄ = x − iy. Four exact integrals for four different flow geometries and Hamel's problem are considered to illustrate the developed theory.
Über die Anwendung der Randelementmethoden auf Probleme der Wellendiffraktion
Authors: Triantafyllidis Th. 
Published: May 2007

AbstractBei der Anwendung der Randelement‐ oder Randintegralmethode auf Gebiete, bei denen sog. „Schattenzonen”︁ entstehen, wird die Kausalität der Lösung verletzt. Da es hierüber bereits Veröffentlichungen mit gegensätzlichen Positionen gibt, wird in dieser Arbeit das Problem auf analytischem Weg behandelt. Für den Fall einer einfallenden SH‐ (shear horizontal) Welle auf eine zylindrische Inhomogenität im Vollraum wird sowohl die Randintegralmethode analytisch angewendet als auch die analytische Lösung des Problems angegeben. Beim Vergleich der beiden Lösungen stellt man fest, daß sie nicht identisch sind. Die Gründe für die Unstimmigkeiten zwischen den beiden Lösungen werden in dieser Arbeit diskutiert, und es wird die Möglichkeit einer korrekten Anwendung der Randelementmethode für solche Gebiete aufgezeigt.
The Poisson Processes of Actions and their Combinations
Authors: Murzewski J. W. 
Published: May 2007

AbstractFour parameters characterize a random action process: the point‐in‐time mean value and its standard deviation, the rate of occurences and their mean duration. A cumulative distribution function of extreme values in a reference time is derived for a filtered Poisson process. A combination of two independent processes of actions is also analyzed and the overlapping effect is taken into account. The final formulae differ from those of Der Kiureghian and Wen. Characteristic and design values are determined in terms of the parameters of the action processes.
On the Nonlinear Stability of the Magnetic Bénard Problem with Rotation
Authors: Mulone G. , Rionero S. 
Published: May 2007

AbstractThe nonlinear stability of the magnetic Bénard problem with rotation is studied through the Lyapunov direct method. It is shown that, in the stress‐free case and for vanishing stress at the boundaries, the nonlinear critical Rayleigh number has the same behaviour as in the linear case. In particular, for a stationary convection, it shows an initial decrease with the Chandrasekhar number Q2 and for large Q2 it goes to infinity as Q.
Creeping Flow Past a Porous Spherical Shell
Authors: Qin Yu. , Kaloni P. N. 
Published: May 2007

AbstractAn exact solution for the creeping flow past a porous spherical shell has been obtained using the Stokes & Brinkman equations. Expressions for the velocities and pressure fields both inside and outside of porous spherical shell are obtained and the force acting on the shell is also determined. It is found that the drag on a porous spherical shell is smaller as compared to the shell with solid core. Several limiting cases of the solution are also discussed. In particular it is shown that the solution obtained using Darcy's law can be derived easily with the appropriate choice of boundary conditions.
An Extended Liapunov Approach to the Stability Assessment of Marine Risers
Authors: Köhl M. 
Published: May 2007

AbstractLiapunov'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

AbstractFor 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

AbstractFor 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

AbstractDynamical 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

AbstractDie 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

AbstractA 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

AbstractThe 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

AbstractThe 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

AbstractA 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.
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

AbstractIn 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

AbstractSolutions 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

AbstractFor 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].
Transient Flow of a Compressible Viscous Fluid Near an Infinite Disk
Authors: Bhattacharyya S. , Nath G. 
Published: May 2007

AbstractWe 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

AbstractFür 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

AbstractThe 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

AbstractWe 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.
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

AbstractThe 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

AbstractEs 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

AbstractThe 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

AbstractDas 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

AbstractDie 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

AbstractVon 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

AbstractFür 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

AbstractEs 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.
Construction of Outwards Impermeable Surface Systems by Means of Comparison Systems
Authors: Koksch N. 
Published: May 2007

AbstractFor 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

AbstractThe 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.