bluuebunny/crossref_metadata_2025_split huggingface dataset:
On Nonstationary von Kármán Equations
Authors: Bock I. 
Published: May 2007

AbstractIn 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

AbstractIn 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

AbstractFor 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

AbstractThe 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

AbstractEs 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

AbstractThe 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.
A General View of Minimally Extended Systems for Simple Bifurcation Points
Authors: Allgower E. L. , Schwetlick H. 
Published: May 2007

AbstractA simple bifurcation point y* of the nonlinear equation F(y) = 0 with a function F : ℝn + 1 → ℝn can be characterized by a so‐called minimally extended system G(z) = 0 where G : ℝn + 2 → ℝn + 2 is chosen such that z* = (y*, 0) is a regular solution of this system in the sense that the Jacobian ∂zG(z*) is nonsingular. Hence, y* can be computed by applying superlinearly convergent Newton type methods. A general principle for obtaining such minimally extended systems is described which, as special cases, yields the systems proposed in the literature by Griewank and Reddien [5], Pönisch [9], and Janovský [7]. Moreover, an improvement of Pönisch's method is given, and some numerical aspects of implementing the methods and optimally choosing free parameters are discussed.
Transporting and Mixing Gasses with Different Qualities
Authors: Ten Kate H. , van Der Hoeven T. , Sierksma G. 
Published: May 2007

AbstractThe Dutch gas company “Gasunie” has as one of its main policies, always meeting fluctuating demands, even in case of sudden changes of temperature. Gas originates roughly from three locations which have different gas qualities. A fast and flexible algorithm is needed to determine the quantities of gasses to be mixed and transported. In this paper the advantages of piecewise linear and network programming are combined to a simplex‐like algorithm, that speeds up the recently used algorithms with at least a factor 50.
Time Estimation of Disturbance Occurrences in Monitoring Systems
Authors: Banek T. , Batko W. 
Published: May 2007

AbstractThe paper presents a method of estimating the exit time of vibratory signals in monitoring systems into areas assigned to emergency states. It refers to the methods of the analysis of dynamic systems' stochastic trajectories, including the method of “functionals supporting the availability areas”. A simple model of a system “rotorbearing” was accepted as the basis for the derivation of the estimation dependencies of the time of the disturbance occurrences in a monitored bearing nod. The system is given by a model of an elastic, symmetrical rotor with the mass concentrated in the centre, and supported by two identical slide bearings.
Transmission Loss in the Far Field over a One‐layer Seabed Assuming the Biot Sediment Model
Authors: Buchanan J. L. , Gilbert R. P. 
Published: May 2007

AbstractA system of differential equations is derived from Biot's constitutive and motion equations for a poroelastic material and a model for a one‐layer seabed is constructed. A normal modes representation for pressure in the far field is found in the case of constant parameters. The model's prediction for transmission loss is examined for five different types of sediments and compared to the predictions of a solid elastic halfspace model.
Geometric Aspects of the Co‐Rotational Derivative of a Continuous Motion
Authors: Kadianakis N. 
Published: May 2007

AbstractIn this work we use a frame‐independent version of the co‐rotational derivative of a motion, and study the geometry defined by this derivative on classical space‐time. This is done in the general framework of derivatives, called Spins, which define a rigid parallel translation of space‐like vectors. We express the Spin itself in terms of this translation, and show that for a non‐uniform Spin this translation depends on the path. Since the co‐rotational derivative is a Spin, its geometry is studied in this context. After showing that the relative vorticity of two motions is the difference of their co‐rotational derivatives, we prove that the translation defined by the co‐rotational derivative of a motion is path‐independent, if and only if the motion is homogeneous.
On the Stabilization of a Parametrically Driven Inverted Double Pendulum
Authors: Schiele K. 
Published: May 2007

AbstractThe stability of a two state process periodically driven inverted double pendulum is considered by Floquet's theory. A stability criterion is derived and numerically analysed. For some values of the excitation a stabilization is indeed possible. The corresponding parameter region is inside of the parameter region where a single pendulum is stabilized.
Conjugate Film Flow Down a Heated Vertical Wall
Authors: Pop I. , Ingham D. B. , Lesnic D. 
Published: May 2007

AbstractThe conjugate flow of a film down a heated vertical wall of finite length is investigated theoretically. It is shown that the momentum boundary‐layer equation leads to an exact solution for the velocity field, but the energy equation is nonsimilar. Solutions of this nonsimilar equation, subject to appropriate boundary conditions, are obtained numerically using an efficient finite‐difference scheme. Series solutions which are valid near the leading edge of the wall and far downstream are also obtained and compared with the corresponding numerical solutions. The distribution of the surface wall temperature and in the film region are also determined for values of the Prandtl number of 0.6 (air) and 6.7 (water).
Rißausbreitungsvorgänge in thermomechanisch belasteten Zweikomponentenmedien: Analysis und Experiment
Authors: Herrmann K. P. 
Published: May 2007

AbstractIn dieser Arbeit wird eine Übersicht über bruchmechanische Untersuchungen zur Entstehung und Ausbreitung von Wärmespannungsrissen in einem Segment oder in der Materialgrenzfläche von zwei‐ und dreidimensionalen eingespannten Verbundstrukturen gegeben. Die resultierenden Randwertprobleme der stationären Thermoelastizitätstheorie für ungerissene und gerissene 2‐D‐ und 3‐D‐Zweikomponentenverbunde werden dabei mit Hilfe von Muskhelishvilis Methode der komplexen Potentiale sowie der FE‐Methode gelöst. Für die 2‐D‐Bimaterialien konnten dabei in den entsprechenden Querschnitten orthogonale Scharen von Hauptspannungstrajektorien erhalten werden, die einen Überblick über die thermisch induzierten Eigenspannungsfelder in den Verbundstrukturen vermitteln. Bei Anwendung eines geeigneten Rißausbreitungskriteriums, das auf der numerischen Berechnung der Gesamtenergiefreisetzungsrate einer Mixed‐Mode‐Rißausbreitung beruht, konnten schließlich die Rißwege von Wärmespannungsrissen in 2‐D‐ und 3‐D‐Bimaterialien vorhergesagt werden, die an der Schnittlinie von Materialgrenzfläche und spannungsfreier äußerer Oberfläche entstehen. Dabei zeigten im Fall der scheibenförmigen Zweikomponentenverbunde die theoretisch vorausgesagten Rißwege eine sehr gute Übereinstimmung mit aus zugehörigen Abkühlungsexperimenten erhaltenen Rißpfaden. Die bruchmechanischen Untersuchungen wurden für verschiedene Probengeometrien mit unterschiedlichen Materialkombinationen durchgeführt, die sowohl gleichförmigen als auch ungleichförmigen Temperaturverteilungen unterworfen waren. Als Ergebnis dieser Untersuchungen kann festgestellt werden, daß Wärmespannungsrisse, die sich vollständig in einem Segment eines Bimaterials ausbreiten, der Bedingung GII = 0 an der jeweiligen Rißspitze genügen, während im Falle der Grenzflächenrisse stets eine Mixed‐Mode‐Rißausbreitung vorliegt, bei der die GII‐Werte eine wichtige Rolle spielen. Weiterhin konnte bei Anwendung des vorgeschlagenen Rißausbreitungskriteriums auch der mögliche Rißablenkungswinkel ϑ* einer Grenzflächenrißspitze aus der Grenzfläche ermittelt werden, wobei auch die Dicke der Grenzschicht (interphase) berücksichtigt werden konnte.Schließlich wurden die Einflüsse dreidimensionaler Effekte auf die Wärmespannungsrißausbreitung in rotationssymmetrischen Bimaterialien unter Heranziehung der FE‐Methode sowie des bereits erwähnten Rißausbreitungskriteriums studiert. Dabei weisen die erzielten Ergebnisse für die ermittelten Rißwege sowie die zugehörigen bruchmechanischen Parameter auf einige bemerkenswerte Unterschiede zwischen den 2‐D‐ und 3‐D‐Bimaterialien hin.
State Space Approach to Viscoelastic Fluid Flow of Hydromagnetic Fluctuating Boundary‐Layer through a Porous Medium
Authors: Ezzat M. A. , Abd‐Elaal M. Z. 
Published: May 2007

AbstractThe method of the matrix exponential, which constitutes the basis of the state space approach of modern control theory, is applied to the non‐dimensional equations of a viscoelastic fluid flow of hydromagnetic fluctuating boundary‐layer through a porous medium bounded by an infinite non‐magnetic vertical plate. The formulation is valid for one‐dimensional problems. The resulting formulation together with the Laplace transform technique is applied to a variety of problems. The solution to a problem of an electrically conducting viscoelastic fluid in the presence of a transverse magnetic field and to a problem for the flow between two parallel fixed plates is obtained. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results for the velocity distribution and the induced magnetic field are given and illustrated graphically for each problem.
The Long‐Time Behavior of Solutions of a Nonlinear Fourth Order Wave Equation, Describing the Dynamics of Marine Risers
Authors: Kalantarov V. K. , Kurt A. 
Published: May 2007

AbstractThe fourth order nonlinear equation describing the dynamics of marine risers is considered. It is established that the zero solution of the boundary value problem for the considered equation is globally asymptotically stable. Moreover, an estimate of the rate of decay of the solutions is obtained.
Stochastic Reconstruction of Loading Histories from a Rainflow Matrix
Authors: Dressler K. , Hack M. , Krüger W. 
Published: May 2007

AbstractThis paper is devoted to the mathematical description of the solution of the so‐called rainflow reconstruction problem, i.e. the problem of constructing a time series with an a priori given rainflow matrix. The algorithm we present is mathematically exact in the sense that no approximations or heuristics are involved. Furthermore, it generates a uniform distribution of all possible reconstructions and thus an optimal randomization of the reconstructed series. The algorithm is a genuine on‐line scheme. It is easy adjustable to all variants of rainflow such as symmetric and asymmetric versions and different residue techniques.
Eigenfrequencies and Simplified Models of Semi‐Infinite Cascades with Variable Boundary Mass
Authors: Dieterman H. A. , Metrikine A. 
Published: May 2007

AbstractThe eigenfrequencies of a semi‐infinite cascade of mass‐spring systems with variable boundary mass are studied. The investigation shows that real eigenfrequencies only occur for a boundary mass equal to or smaller than half the mass of the bodies in the cascade. For values of the boundary mass between a half mass and a full mass the cascade shows to have no eigenfrequencies. For a boundary mass larger than the internal masses only imaginary eigenfrequencies are present. Frequency‐response functions for the different cases are derived. Some simplified models for the semi‐infinite system are given and a comparison is made with the dynamic behaviour of continuous systems.
Identification of Weakly Singular Memory Kernels in Heat Conduction
Authors: Janno J. , Von Wolfersdorf L. 
Published: May 2007

AbstractInverse problems of identification of memory kernels in linear heat conduction are dealt with in case of weakly singular kernels in the space Lp and of continuous kernels with power singularity. The problems are reduced to nonlinear Volterra integral equations of convolution type for which by the method of contraction with weighted norms global existence and stability of solutions are proved.
On the Unsteady Potential Plane Flow Past a Porous Circle
Authors: Keglević I. 
Published: May 2007

AbstractWe consider a nonstationary plane flow which is an ideal flow on the whole plane except on a circle. On the circle we assume inhomogeneous in time and position linear dependence between normal velocity and pressure difference. We reduce the problem to an operator differential equation with an initial condition and by use of partial differential equation theory from Lions and Magenes we prove the existence and uniqueness of a solution for t ϵ [0, ∞). For periodic in time input conditions we prove the existence and uniqueness of a periodic solution of the problem. We also consider the solution by time independent input conditions. In this case the solution has a limit in infinity and tends exponentially to this limit.
On Dynamic Multi‐Rigid‐Body Contact Problems with Coulomb Friction
Authors: Trinkle J. C. , Pang J.‐S. , Sudarsky S. , Lo G. 
Published: May 2007

AbstractThis paper is a summary of a comprehensive study of the problem of predicting the accelerations of a set of rigid, three‐dimensional bodies in contact in the presence of Coulomb friction. We begin with a brief introduction of this problem and its governing equations. This is followed by the introduction of complementarity formulations for the contact problem under two friction laws: Coulomb's Law of quadratic friction and an approximated pyramid law. Existence and uniqueness results for the complementary problems are presented. Algorithms for solving these problems are proposed and their convergence properties are discussed. Computational results are presented and conclusions are drawn.
Exact Piezothermoelastic Solution for Simply Supported Laminated Flat Panel in Cylindrical Bending
Authors: Kapuria S. , Dube G. P. , Dumir P. C. 
Published: May 2007

AbstractThe three‐dimensional exact solution is presented for infinite simply supported, cross‐ply laminated flat panel with piezoelectric layers in cylindrical bending. The variables are expanded in Fourier series to satisfy the boundary conditions at the simply supported ends. The governing equations reduce to ordinary differential equations with constant coefficients. For each layer, the general solutions of the thermal and the piezoelastic problems involve two and six arbitrary constants, respectively. These are determined from the boundary and interface conditions. The response of panels consisting of cross‐ply laminated substrate of graphite‐epoxy composite with a PVDF layer bonded to its one face has been determined for prescribed sinusoidal surface temperature distributions and electric potential difference applied to the piezoelectric layer. The effect of span to thickness ratio on the response has been investigated. The feasibility of reducing deflection and stresses by applying potential difference to the piezoelectric layer is reported.
The Application of Tensor Algebra on Manifolds to Nonlinear Continuum Mechanics — Invited Survey Article
Authors: Stumpf H. , Hoppe U. 
Published: May 2007

AbstractSome properties of the tensor algebra on manifolds are discussed with respect to the classical tensor algebra of continuum mechanics. Basic definitions and relations of linear maps are briefly recalled and applied to tensor spaces, where special attention is focused to the definition of dual and transposed maps. As application to nonlinear continuum mechanics, algebraic pull‐back and push‐forward maps, and Lie‐like time derivatives associated with linear maps are defined and used to build up commutative schemes for deformation measures, objective deformation rates, stresses, and frame‐invariant forms of the stress power. The transition to the classical formulation of tensor algebra by identifying vector spaces and their duals is examined. It is shown how this concept enables a straight‐forward derivation of the Doyle‐Ericksen formula and its possible variants.
A Rational Deduction of Plate Theories from the Three‐Dimensional Linear Elasticity
Authors: Bisegna P. , Sacco E. 
Published: May 2007

AbstractIn this paper a general procedure for a rational derivation of plate theories is proposed. The methodology is based on the conjecture that plate theories can be carried out from the three‐dimensional elasticity by imposing suitable constraints on the strain and stress fields. The powerful Lagrange multipliers theory is adopted to derive the variational principles, based on the Hu‐Washizu functional, governing the constrained elasticity problems. Both the first‐order shear deformation plate theory, and the higher‐order Lo‐Christensen‐Wu plate theory are derived. The governing equations are recovered, and the reactive fields, arising as a consequence of the imposed constraints, are carried out. When these reactive fields are taken into account, the equilibrium, congruence, and constitutive equations turn out to be exactly satisfied.
Numerical Algorithms for Dynamics of Thermopiezoceramic Bars
Authors: Altay G. Aşkar , Dökmeci M. C. 
Published: May 2007

AbstractThis paper is concerned with the numerical algorithms for the macromechanical analysis of a ceramic bar in which account is taken of mechanical, electrical, and thermal fields. In the first part of the paper, a hierarchic system of one‐dimensional equations of the thermopiezoceramic bar is deduced by a direct method of integration from the three‐dimensional equations of thermopiezoelectricity. Also, in a similar way, the method of moments is described for the macromechanical analysis. The second part is addressed to a direct method of solution which is essentially based on Kantorovich's method, as an alternative, for the macromechanical analysis. The resulting equations incorporate all the significant effects of ceramic bar under a general state of mechanical, electrical, and thermal loads. They accommodate the extensional, flexural, and torsional as well as coupled motions of thermopiezoceramic bar at both low and high frequencies. Lastly, in the third part, attention is confined to the cases involving special fields, motions, and material properties.
A Method for Determining the Lower Bound Dynamic Buckling Loads of Imperfection‐Sensitive Structures
Authors: Wu B. 
Published: May 2007

AbstractA perturbation method based on the static stability criterion associated with the vanishing of the total potential energy on a certain equilibrium point on the unstable postbuckling path is presented for the determination of lower bound dynamic buckling loads of imperfection‐sensitive structures under step load of infinite duration. Attention is focused on the effect of various possible sources of structural imperfections on the dynamic buckling strength of perfect structures. Under the assumption that the effect of structural imperfections is of the first order, the method can give any desired higher‐order approximation to the lower bound dynamic buckling loads and the corresponding displacements without solving the system of differential equations of motion numerically. Especially, the method applies to finite‐degree‐of‐freedom systems as well as continuous ones. The application of the method is illustrated on two examples. The results demonstrate the significant effect of other imperfection sources, besides the shape imperfections having the shape of the classical buckling mode.