bluuebunny/crossref_metadata_2025 huggingface dataset:
Model Order Reduction of a Drill‐String‐Model with Self‐Excited Stick‐Slip Vibrations
Authors: Kreuzer Edwin , Steidl Michael
Published: March 2010

The dynamical behavior of a drill‐string is defined by its small diameter‐to‐length ratio, which makes the string vulnerable to torsional vibrations. In combination with the nonlinear friction characteristic at the drill bit, this can lead to self‐excited stick‐slip vibrations which are detrimental to the drilling process. The string can be modeled by the Finite Element Method or as a Multi‐Body system to represent the distributed character of the system. The analysis of the resulting high‐dimensional model is, however, elaborate and time‐consuming. We show that through Galerkin Projection onto the first two Characteristic Functions gained from Karhunen‐Loève‐Transformation, a reduced system can be obtained which reproduces the essential dynamical properties of the original system, e.g. the stick‐slip motion. With the reduced system, the linear stability of the drill‐string can be analyzed. We show that by reducing the inertia of the rotary table the system can be stabilized. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Identification of chaos in a regenerative cutting process by the 0‐1 test
Authors: Litak Grzegorz , Radons Günter , Schubert Sven
Published: March 2010

We examine the regenerative cutting process by using a single degree of freedom non‐smooth model with a friction component and a time delay term. Instead of the standard Lyapunov exponent calculations, we propose a statistical 0‐1 test for chaos. This approach reveals the nature of the cutting process signaling regular or chaotic dynamics. We are able to show that regular or chaotic motion occur in the investigated model depending on the delay time. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Application of a revised cable theory to Rain‐Wind‐induced vibrations
Authors: Gilow T. , Heinen A.H.
Published: March 2010

Simultaneous occurrence of rain and wind can lead to vibrations with large amplitudes of inclined cables and hangers of arch bridges. These motion‐induced vibrations are usually described with models based on the strip theory, or on the cable theory which is the best developed model [1]. The own solution concept derives complete nonlinear cable equations being mechanical equal to those known in literature but with a significant more simple structure by using longitudinal Green's strains and non‐physical cable forces. The nonlinear effects of wind and rain forces are included.

As an example of application a cable of the Erasmus bridge in Rotterdam (NL) will be analyzed. The own results are compared with the vibration amplitudes in the literature and with observations. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Plane constrained uniaxial extension of a single crystal strip
Authors: Chau Le Khanh , Sembiring Pramio
Published: March 2010

Within continuum dislocation theory the plane constrained uniaxial extension of a single crystal strip deforming in single or double slip is analyzed. For the single and symmetric double slip, the closed‐form analytical solutions are found which exhibits the energetic and dissipative thresholds for dislocation nucleation, the Bauschinger translational work hardening, and the size effect. Numerical solutions for the non‐symmetric double slip are obtained by finite element procedures. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Micromechanically motivated finite element model for ferroelectric ceramics
Authors: K. Jayabal , Menzel A. , Arockiarajan A. , M.S. Srinivasan
Published: March 2010

Ferroelectric ceramics exhibit significant coupled electromechanical phenomena that have been widely employed in sensor and actuator applications. In regular finite element models dealing with electromechanical plane problems, each grain needs to be subdiscretized by many triangular or quadrilateral elements for required accuracy. This problem can be overcome by a polygonal finite element approach where each grain is modelled by a single finite element without compromising on the results. In this paper, a polygonal finite element approach has been employed to understand the anisotropic response of the ferroelectric ceramics in their piezoelectric region. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Formulation and application of models for anisotropic hardening in sheet metals subject to complex loading‐path changes
Authors: Clausmeyer Till , Noman Muhammad , Svendsen Bob
Published: March 2010

In this work material models for the simulation of forming processes involving non‐uniform loading path changes are investigated. Materials exhibiting an evolution of the yield surface due to the formation and interaction of dislocation structures on the micro structural level are modeled by employing evolving structural tensors. These account for the evolution of anisotropy and hardening behavior known from technical alloys on a phenomenological basis. In a first step material parameters are identified from experiments for non‐uniform loading conditions. In a second step, the evolution of structural tensors for varying loading conditions is investigated and related to the evolution of kinematic quantities. Finally applications relevant to the simulation of sheet metal forming processes are presented. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Analysis of deformation‐induced twinning at finite strains based on energy minimization
Authors: Homayonifar M. , Steglich D. , Mosler J.
Published: March 2010

In the present contribution, an energy‐based description of phase transformation suitable for the modeling of crystal reorientation during twinning is proposed. A homogenized relaxed stored energy (volume averaging) is utilized for the simulation of the pre‐ and post‐twinning hardening form of magnesium single crystal. The proposed energy‐driven model is applied to analyze the activity of deformation systems inside the twinning related phases. It is shown that the activity of the inter‐twin dislocation systems accommodates the plastic strain at larger deformation. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On a Sharp Interface Model for Phase Transitions in Steel
Authors: Petzold Thomas
Published: March 2010

Steel is one of the most widely used materials in the world with a broad spectrum of properties. The microstructure and the distribution of the different phases are of great importance, since they each possess different properties. A sharp interface model for the austenite‐ferrite phase transition is presented. Mechanical effects due to eigenstrains resulting from the different densities of the phases are taken into account. The governing PDEs in each phase are a diffusion equation for the carbon concentration and the balance of momentum. Across the free interface, separating the two phases, the physical quantities may have discontinuities, which are controlled by jump conditions. Consistency of the model with the 2nd law of thermodynamics is shown. Numerical simulations for these types of free boundary problems are quite complex and involve appropriate methods to determine the interface position. One possibility to circumvent the explicit determination of the free boundary is the use of regularization techniques in form of phase field methods, where the interface is tracked implicitly. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical simulation of shear band formation in hyperelastic material by energy relaxation
Authors: Trinh Bach Tuyet , Hackl Klaus
Published: March 2010

A theorical framework for the analysis of localized failure in hyperealstic material is presented based on the energy minimization principles associated with micro‐structure developments. The theory is predicated upon the assumptions that the thickness of shear band represented by its volume fraction tends to zero as well as that the energy inside shear band is a function of the norm of the deformation gradient. Shear bands are treated as laminates of first order. The existence of shear bands in the structure leads to an ill‐posed problem which can be solved by means of energy relaxation. An application of the proposed formulation to Neo‐Hookean material is presented. Numerical simulation is shown in order to evaluate the performance of the proposed energy relaxation. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical simulations of poly‐crystalline shape‐memory alloys based on a micromechanical model
Authors: Junker Philipp , Hackl Klaus
Published: March 2010

Based on a micormechanical model we describe the material behaviour of specimens made of shape memory alloys by a finite element implementation. These materials undergo solid to solid phase transformations during loading and unloading which determine the characteristic pseudo‐elastic or pseudo‐plastic material response. Phase transitions, orientation distribution (pole figures) and the influence of pre‐texture on the specimen, due to some previous treatment like rolling, are discussed. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Influence of the nonlinear matrix material behaviour on the effective properties of textile‐reinforced thermoplastics
Authors: Kästner Markus , Obst Martin , Brummund Jörg , Ulbricht Volker
Published: March 2010

For a consistent lightweight design the consideration of the nonlinear macroscopic material behaviour of composites, which is amongst others driven by damage and strain‐rate effects on the mesoscale, is required. Therefore, a modelling approach using numerical homogenization techniques is applied to predict the effective nonlinear material behaviour of the composite based on the finite element simulation of a representative volume element (RVE). In this RVE suitable constitutive relations account for the material behaviour of each constituents. While the reinforcing glass fibres are assumed to remain linear elastic, a viscoplastic constitutive law is applied to represent the strain‐rate dependent, inelastic deformation of the matrix material. In order to analyse the influence of the nonlinear matrix material behaviour on the global mechanical response of the composite, effective stress‐strain‐curves are computed for different load cases and compared to experimental observations. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Cellular rubber: Dependency between relaxation time and pretreatment
Authors: Koprowski Nadine , Diebels Stefan , Johlitz Michael
Published: March 2010

In this contribution we investigate experimentally a porous carbon‐filled rubber. The main focus is on the dependency of the mechanical behaviour using different pretreatments. Therfore, cyclic tests and relaxation tests with different pretreatment are performed. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Elastic shallow shells with functionally graded structure
Authors: Jędrysiak Jarosław , Woźniak Czesław
Published: March 2010

Main objects of considerations are linear‐elastic thin shallow shells with a tolerance‐periodic structure along one direction. Moreover, their properties along the perpendicular direction can be described by continuous, slowly‐varying functions. Hence, these objects can be treated as shells with a functionally graded structure. Here, the tolerance model of these shells is proposed. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Some problems of heat conduction in transversally graded composites
Authors: Radzikowska Alina , Jędrysiak Jarosław
Published: March 2010

The object of considerations is a two‐component layer made of conductors non‐periodically distributed in the form of laminas along the layer thickness. It is assumed that the distribution of the macroscopic properties of this laminate is approximated by continuous slowly‐varying functions across laminas. Media of this kind can be treated as made of a functionally graded material. The aim of the paper is to apply the tolerance model, [8], to analyse one‐directional, non‐stationary heat conduction along the axis perpendicular to laminas. Moreover, received results are compared to the solutions obtained in the framework of the higher‐order theory, [1]. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Higher‐order energy‐momentum consistent time‐stepping schemes for dynamic finite thermo‐viscoelasticity
Authors: Groß Michael , Betsch Peter
Published: March 2010

This paper is concerned with the energy consistent simulation of a finite thermo‐viscoelastic continuum body. The algorithm is based on a four‐field formulation in the Lagrangian description, in which the deformation field, the velocity field, the temperature field and a strain‐like viscous internal variable field are independent unknowns. The Lagrangian temperature field is determined by the entropy evolution equation associated with Fourier's law of isotropic heat conduction. The viscous evolution equation is derived from a nonlinear internal dissipation. The coupled nonlinear differential equations are discretised by a new space‐time finite element method, consisting of continuous as well as discontinuous finite element approximations in time. Owing to particular time approximations in the constitutive laws, the energy and momentum balances are exactly fulfilled in the fully discrete case. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Calculation of Flexibility of Vibrating Beam as the Subsystem of Mechatronic System by Means the Exact and Approximate Methods
Authors: Buchacz A.
Published: March 2010

The main aim of this paper is to investigate the transients of characteristics of vibrating beams obtained by the exact and approximate methods and to answer to the question – if the method can be used to nominate the characteristics of mechatronic systems. The approach was to nominate the relevance or irrelevance between the characteristics obtained by considered methods – especially concerning the relevance of the natural frequencies‐poles of characteristics of mechanical part of mechatronic system. The main subject of the research is the continuous vibrating beam. Findings of this approach is fact, that approximate solutions fulfill all conditions for vibrating beams and some conditions only, particularly for vibrating beams as the subsystems of mechatronic systems. Practical implications of this paper is the main point is the analysis and the examination of flexibly vibrating discrete‐continuous mechatronic systems which characteristics can be nominated with approximate methods only. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A Coupled Process‐Structure‐Model to Simulate Robot Based In‐cremental Sheet Metal Forming
Authors: Bertsch Christine , Laurischkat Roman , Reese Stefanie , Meier Horst
Published: March 2010

A coupled process‐structure model to predict path deviations in robot based sheet metal forming is presented. The model consists of a finite element (FE) approach to simulate the sheet forming and a multibody system (MBS) modelling the robot. By coupling both models a path prediction tool is provided. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A two‐phase Finite Element model for coupled heat flux and water flow in fully saturated soils
Authors: Zhou Mengmeng , Nagel Felix , Kruschwitz Jens , Meschke Günther
Published: March 2010

This paper is concerned with the implementation of a macroscopic model for coupled heat flux and water flow in fully saturated soils consisting of a rigid solid skeleton and a compressible fluid phase. In both phases, the same temperature is assumed and phase change of the water phase is neglected. Within the framework of the Theory of Porous Media (TPM), a two‐phase finite element model is developed for the description of fully saturated soils, based upon the governing balance equations (mass balance of the fluid phase and energy balance of the mixture) and constitutive relations (water density, Darcy velocity, free Helmholtz energy functions, heat flux vector and supply term of momentum). The applicability of the model is shown by selected results from the simulation of artificial ground freezing during tunnel construction. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modelling of multilayer transducer by means of the graph and structural numbers method
Authors: Buchacz A. , Wróbel A.
Published: March 2010

This paper presents the characteristics of piezoelectric plate vibration. Model of simple system were shown. The equations of piezoelectric plate have been derived in terms of longitudinal displacement and electric potential. Three ports system for investigated model was determined. Analysis was done by means the graph and structural numbers method. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Analytical inversion of the Jacobian for a class of generalized standard materials
Authors: Fritzen Felix , Böhlke Thomas
Published: March 2010

In this paper we derive an analytical expression for the inverse of the Jacobian occuring in the implicit time integration procedure for a large class of generalized standard materials. The resulting expression is easy to construct and implement into arbitrary programming languages. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Comparison of analytical and numerical methods for homogenization of nanotube‐reinforced polymers
Authors: Schmidt Ina
Published: March 2010

Carbon nanotubes are increasingly getting impact as reinforcing material for polymer based nanocomposites. Hence, new modeling strategies are necessary to calculate the behavior of these materials. In the last years some attempts have been made using and developing classical micromechanical models. On the other hand numerical homogenization methods are available to tackle this problem. Examples for both types of modeling strategies are presented with focus on the nanotube geometry. The nanotubes are modeled as hollow tubes as well as as isotropic and transversely isotropic cylinders. As expected the results of numerical and analytical methods are identical for isotropic cylinder inclusions. Small deviations occur for transversely isotropic cylinders in transverse direction. In the case of hollow tube inclusions, the analytical models lead to lower stiffness values in transverse direction and for shear. The largest deviations occur for longitudinal shear with magnitudes smaller than 10%. In contrast the effort to get numerical results is enormous, so that the analytical models are still useful. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Shakedown and limit analysis of periodic composites
Authors: Chen M. , Zhang LL. , Weichert D. , Tang WC.
Published: March 2010

The optimization of fiber distribution is analyzed in order to improve the strength performance of metal‐matrix composite material, which is submitted to two variable independent loads by coupling homogenization and shakedown theories. Numerical Direct Methods are applied to acquire the shakedown domain of three‐dimensional heterogeneous elastic‐perfectly plastic fiber‐reinforced composite for optimal design. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A Contact Homogenization Framework for Granular Interfaces
Authors: Temizer İlker , Wriggers Peter
Published: March 2010

A computational contact homogenization framework is developed for contact interfaces with dry granular third bodies. The micro‐to‐macro transition procedure that forms the basis of this framework consists of projecting the macroscale contact pressure and slip velocity to the observable test surface of a representative contact element. The solution of the local microscale problem reveals a macroscale friction coefficient where inelastic effects are taken into account in a finite deformation setting. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling and simulation of the microstructural behaviour in thermal sprayed coatings
Authors: Klusemann Benjamin , Hortig Christian , Svendsen Bob
Published: March 2010

The purpose of the current work is the investigation of the mechanical behavior of thermal sprayed coatings to predict the influence of the application of compaction on the coatings. Due to the porosity and the poor surface quality of thermal sprayed coatings, an additional process step is necessary to compact the coating and to increase the surface quality, though leading to a complex deformation behavior of the coating. In a first step the microstructural evolution is investigated. Due to the fact that the experimental determination of the mechanical properties of a coating is quite complicated and cost‐intensive, a general procedure is developed which generates the desired quantities for different coating composites from microstructural images which are compared to analytical mean‐field homogenization solutions for elastic material behavior. The discussed thermal sprayed coatings are multiphase systems consisting of a metal‐matrix composite with pores. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Mechanically homogenized material model for a pack of sheets
Authors: Vorhauer Larissa G. , Gerstmayr Johannes
Published: March 2010

In the present contribution we discuss the modeling of a large number of plane metal sheets under compressive forces. The direct approach to this contact problem is based on a finite element (FE) discretization of each sheet and a contact formulation between each adjacent sheet. The numerical problem is highly non‐linear and of very large dimension. Therefore it is difficult to be solved by conventional FE‐software. We propose to replace the contact model by a homogenized constitutive law, which behaves as a pack of infinitely thin sheets. A coarser discretization as for the contact model can be used. A pack of sheets under pressure normal to the sheet plane serves as a benchmark example. The model is verified and implemented for the 2D case and numerical results of the test case are shown. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Incremental self‐consistent approach for the estimation of nonlinear material behavior of metal matrix composites
Authors: Jöchen Katja , Böhlke Thomas
Published: March 2010

The application of homogenization methods to compute the macroscopic material response of metal matrix composites is a possibility to save memory and computation time in comparison to full field simulations. This paper deals with a method to extend the self‐consistent scheme from linear elasticity theory to nonlinear problems. The idea is to approximate the nonlinear problem by an incrementally linear one. Since time discretization of the deformation process implies a certain linearization, we use the algorithmic consistent tangent operator of the composite for defining the linear comparison material in each time step. This is in contrast to classical incremental self‐consistent approaches which use continuum tangent or secant operators. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On bridging domain methods to couple particle‐ and finite‐element‐based simulations
Authors: Pfaller Sebastian , Steinmann Paul
Published: March 2010

This contribution investigates schemes to couple domains of different resolutions in space, a problem frequently arising in multi‐scale modelling of materials. To couple a standard finite element domain with a high resolution atomistic or molecular, i.e. particle‐based domain, a so‐called bridging domain is considered, e.g. Xu and Belytschko [1], Zhang, Khare, Lu and Belytschko [2] and Bauman et al. [3]. The main goal is to separate the computation of finite element and atomistic domains as much as possible, amongst others, to calculate the different domains on several CPUs. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Multiphase Jet Flow in Abrasive Water Jet Cutting
Authors: Kubik Anna , Kleiser Leonhard
Published: March 2010

A numerical model for ultra‐high velocity abrasive water jets (AWJ) is developed and jet dynamic characteristics are calculated under steady‐state, turbulent, compressible, multi‐phase flow conditions. The model is tested by comparison with analytical solutions for related theoretical problems, generally with very good agreement. Simulations of more realistic flows produce the expected values and behavior. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Stability of a thin liquid layer, spreading on a quasi–rotating disk
Authors: Boettcher Konrad , Ehrhard Peter
Published: March 2010

In many industrial processes solids are coated to obtain specific surface properties, as e.g. corrosion resistance, mechanical (wear) resistance, optical, or electrical properties. Even today many coating processes are not fully understood and the choice of parameters is largely based on experience. Hence, a prediction of the complete hydrodynamic process and the appearance of instabilities in its dependency on the parameters appears highly desirable. This would serve to optimize the quality of the coating. A common coating technique is the so‐called spin coating. The coating agent is dissolved or suspended in a liquid, brought onto the solid, spread by rotation, and the carrier liquid is finally removed by evaporation or by chemical reactions. In this article an evolution equation is derived from lubrication theory, valid for thin liquid layers. The model involves a dynamic contact angle, centrifugal, capillary, and gravitational forces. The evolution equation can be solved analytically, provided the capillary number is small. Then a coupled linear stability analysis of the contact line and the free interface is performed. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical simulation of single gas bubbles under shear flow conditions
Authors: Lakshmanan Peter , Ehrhard Peter
Published: March 2010

Disperse gas bubbles play an important role in many industrial applications. Knowing the rising velocity, the interfacial area, or the critical size for break‐up or coalescence in different systems can be crucial for the process design. Usually the flow experienced by bubbles is not uniform but sheared. Under shear‐flow conditions bubbles develop a lift force perpendicular to the flow direction. In the present work direct numerical simulations are applied to examine the dependency of the lift force on the shear rate for bubbles in pure liquids. A level‐set based volume‐tracking method is implemented into the CFD‐code OpenFOAM, to follow the free interface of the gas bubble. Results show good agreement with available experimental results from single bubbles in a rotating chamber. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Computation of incompressible viscous flows in complex geometries by a velocity correction method.
Authors: Kosma Z. , Motyl P.
Published: March 2010

A method for simulation of viscous flows in complex geometries by resolving the Navier‐Stokes equations with the use of velocity correction procedure is developed. Its virtue lies in the simple description of the flows in terms of primitive variables, such as velocities and pressure, and in its algorithmic simplicity. Decoupling the pressure and velocity reduces the problem to the solution of a sequence of simpler problems. With this method some auxiliary velocity field is found and the projection into the divergence‐free space via the solution of a Poisson equation for some form of the pressure is performed. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Investigation of viscous flow phenomena in a rotating system
Authors: Zucht Andre , Böhme Gert , Müller Andre
Published: March 2010

In this work we have investigated viscous flow in a rotating system. The system consists of a horizontally oriented cylindrical drum rotating around the center and a fixed plate as a scraping internal tool. By this plate the inner volume is divided into two separate chambers. No mass transport between the chambers can take place. The drum is completely or partially filled with a highly viscous, optically transparent silicon oil. In the second case the remaining space is filled with air as a passive phase. Depending on the settings in the system, which are the rotational speed of the drum, material properties of the liquid and the volume ratio of the two phases, different flow phenomena can be observed [1, 2]. For the characterization of the flow dimensionless ratios given by the Reynolds number Re, the Froude number Fr, the Capillary number Ca and the volumetric filling degree F are used. The system is investigated applying the experimental method of Particle Image Velocimetry (PIV) as well as suitable models of Computational Fluid Dynamics (CFD). The goal of this investigation is to identify the velocity fields in the liquid phase for a better understanding of the observed phenomena. The results obtained by the different methods are presented and discussed. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Linear stability analysis of oscillating Ekman boundary layers
Authors: Withalm Martin , Röper Jasmin , Hoffmann Norbert P.
Published: March 2010

The analysed Ekman layer is generated in a fluid layer rotating around an axis normal to its two bounding rigid plates. One of the plates is stationary, the other moving at certain Reynolds numbers. An additional oscillation is added to the moving plate at different amplitudes and frequencies. The linear stability of this system is determined via a Floquet analysis and a Galerkin‐approximation of the corresponding Navier‐Stokes‐Equations. If the frequencies of the oscillations are small the critical Reynolds numbers of the Type I and Type II instabilities do not differ much from steady Ekman layers. Also for a purely oscillating system the critical values of the instabilities are almost consistent with those for a steady system. Interestingly, for higher frequencies the Type II instability does not appear any more. Instead the boundary layer becomes unstable only in terms of a Type I instability. In comparison with findings of other authors these results seem to be quite reasonable. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On solitary waves in one‐dimensional microstructured solids
Authors: Randrüüt Merle , Braun Manfred
Published: March 2010

In a microstructured solid with nonlinearities in macroscale and microscale, the propagation of 1D waves is governed by an extended KdV equation, which admits asymmetric solitary waves. An approximate solution is presented. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Aero‐Acoustic Optimisation of Airflow Components in Gas Turbines
Authors: Schroeder G. , Uffrecht W. , Odenbach S.
Published: March 2010

There is always a great interest in the improvement of the efficiency of gas turbines. This requires the reduction of energetic losses like pressure losses induced by vortices, turbulence and secondary flow. In the current investigation, effects caused by aero‐acoustic oscillation are of interest. The possibility to control these effects or to make them usable has several advantages, for example reducing pressure losses, reducing noise, and influencing the heat transfer and charging effects. This concerns potentially oscillatory flow systems in gas turbines like pipes, cavities and annuli. In particular annuli can not be considered theoretically using one‐dimensional pipe acoustic. The start of oscillation occurs due to turbulent shear stress, solid oscillating surfaces and time fluctuating pressure fields as well as thermal stimulation. This study focuses on the impact of aero‐acoustic oscillation caused by shear stress and rotating pressure fields on the through flow. A numerical study of axial, radial and circumferential acoustic eigen‐modes and a time harmonic analysis have been done with several boundary conditions. The achieved results have to be proved in a further experiment. An improvement in the aero‐acoustical design of gas turbine flow components will be possible thanks to the results gained from both the numerical study and planned experiment. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Experimental Feasibility Study for Guided Wave Propagation
Authors: Kern Dominik , Seemann Wolfgang
Published: March 2010

The paper presents the work on Structural Health Monitoring (SHM) which is now one of the most interesting subjects. Guided propagation of mechanical waves in elastic bodies can be applied in analogy to active phased radar antennas for electromagnetic waves. An array of bonded piezoelectric transducers can generate directed mechanical waves. In the current state of this work experiments on a beam are conducted in order to verify a mathematical model based on integral transform methods. Further experiments for plates and laminates have been designed and checked for feasibility of the mechanical and the electrical implementation. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Lamb wave propagation using Wave Finite Element Method
Authors: Ahmad Zair Asrar Bin , Perez Juan Miguel Vivar , Willberg Christian , Gabbert Ulrich
Published: March 2010

Some of the available techniques for Lamb wave propagation simulation are the Finite Element Method (FEM), the Boundary Element Method and the Finite Difference Method. The FEM is the best method when complex damage, geometry or boundary is involved. However, high Lamb wave frequency requires very small element size thus high computational cost in FEM analysis. By using the existence of periodicity in plates, an attempt to reduce this computational cost is done using Wave FEM. The applicability of this method to model Lamb wave propagation in plate is first assessed in this paper for the 1‐D wave propagation and compared with FEM explicit method. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Relaxation dynamics of the rheological properties of ferrofluids
Authors: Borin Dmitry , Odenbach Stefan
Published: March 2010

We studied experimentally the shear stress relaxation of two different ferrofluids under the action of an external magnetic field by stepwise changes of shear rate. It has been found that ferrofluids able to form significant structures under the influence of an applied magnetic field show a slow relaxation phenomenon. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Forced Alveolar Flows and Mixing in the Lung
Authors: Borer David , Rösgen Thomas
Published: March 2010

The air flows deep inside the lung are not only important in gas exchange processes but they also determine the efficiency of particle deposition and retention. The study aims at quantifying the relative influence of different flow components in the transport of small particles in alveolar geometries such as convective breathing patterns, wall movement, gravitational settling and Brownian motion. In addition, the possibility and efficiency of external forcing is studied, relying on the mechanism of internal acoustic streaming. A viscous oscillating boundary layer flow is converted into a steady, viscosity‐independent bulk motion which is very efficient at low Reynolds numbers. The streaming can be controlled by external parameters (excitation amplitude, frequency, beam shape) and may thus be of diagnostic and therapeutic relevance. Numerical simulations are performed to analyze the flow patterns in 3D model geometries and to measure deposition rates. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the existence for viscoelastodynamic problems with unilateral boundary conditions
Authors: Petrov Adrien , Schatzman Michelle
Published: March 2010

This note deals with a damped wave equation and the evolution of a Kelvin–Voigt viscoelastic material, both problems being subject to unilateral boundary conditions. The functional properties of all the traces are precisely identified through Fourier analysis, which implies the existence of a solution satisfying almost everywhere the unilateral boundary conditions. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Simulation of a siped tire tread block by an Euler‐Bernoulli beam
Authors: Ripka Stefan , Wangenheim Matthias
Published: March 2010

Winter tires earn more and more attention due to the increasing awareness of safety aspects also in emerging markets like Russia and China. Besides the rubber compound the siped geometry of the tread blocks is essential. The mechanical behaviour of sliding lamellas is modeled with the beam theory of Euler–Bernoulli. In this contribution the siped tread block model will be experimentally verified and first simulation results will be presented. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modelling and numerical analysis of the cutting process
Authors: Bohdal Lukasz , Kukielka Leon
Published: March 2010

The course of the cutting process with using wedge‐shaped tool is presented in the paper. To observe the kinematics of flowing of material, the states of displacement and deformations for any moment the model investigations were done. Some results of the analysis, which can be used in designing and optimization of the process, are presented. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Topology optimization based on the first optimization steps strain energy analysis.
Authors: Kutylowski Ryszard , Szwechlowicz Marek
Published: March 2010

The paper presents the algorithm for obtaining “the near optimal” topology very fast, based on the first optimization steps strain energy analysis. The objective function is the compliance of the structure. It is equal to the strain energy and it is minimized under the body mass constraints. Because the material density is proportional to the strain energy accumulated in discrete material point, the identification of more and less effort domains especially for the first optimization steps let analyse the structure from the topology point of view. This identification is the base of relative faster finding out material domains and void domains within the design domain which leads to the topology, which is very similar to the optimal topology even from the strain energy level point of view. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An approach for optimization of loading cycles of hydraulic mining excavators
Authors: Flores Geu , Xia Shuxian , Kecskeméthy Andrés , Pöttker Alois
Published: March 2010

The present paper describes an optimization multi‐stage approach for computing the optimal loading cycle of a heavy weight excavator along a predefined trajectory under dynamic constraints such as maximal ensuing forces, accelerations, and maximal allowed hydraulic power. The approach involves the use of splines of 3rd and 5th order for smooth interpolation of the spatial trajectory up to the level of linear and angular accelerations, as well as an SQP optimization routine to find the optimal end‐effector motion law along the trajectory, which finally leads to strokes and pressures at the hydraulic actuators as a function of time. The approach can also be extended to other multi‐body systems following a predetermined trajectory. The solution scheme can be included in a more general optimization routine aiming to optimize the trajectory itself. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Optimal PID control in case of random initial conditions
Authors: Schacher Michael
Published: March 2010

The aim of this presentation is to construct a robust optimal PID feedback controller, taking into account stochastic uncertainties in the initial conditions. Usually, a precomputed feedback control is based on exactly known model parameters. However, in practice, often exact information about model parameters and initial values is not given. Hence, having an inital point, which differs from the nominal values, a standard precomputed controller may produce bad results. Supposing now that the probability distribution of the random parameter variations is known, in the following stochastic optimisation methods will be applied in order to obtain robust optimal feedback controls. Taking into account stochastic parameter variations at the initial point, the method works with expected total costs arising from the primary control expenses and the tracking error. Furthermore, the free regulator parameters are selected then such that the expected total costs are minimized. After Taylor expansion to calculate expected cost functions and a few transformations an approximate deterministic substitute control problem follows. Here, retaining only linear terms, approximation of expectations and variances of the expected cost functions can be calculated explicitly. By means of splines, numerical approximations of the objective function and the differential equations are obtained then. Using stochastic optimization methods, random parameter variations are incorporated into the optimal control process. Hence, robust optimal feedback controls are obtained. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Sparse Data Representation of Random Fields
Authors: Litvinenko Alexander , Matthies Hermann G.
Published: March 2010

Mathematical models with uncertainties are often described by stochastic partial differential equations (SPDEs) with multiplicative noise. The coefficients, the right‐hand side, the boundary conditions are modelled by random fields. As a result the solution is also a random field. We offer to use the Karhunen‐Loève expansion (KLE) to compute a sparse data format for the fast generation and representation of these random fields. The KLE of a random field requires the solution of a large eigenvalue problem. Usually it is solved by a Krylov subspace method with a sparse matrix approximation. We demonstrate the use of both, the sparse hierarchical matrix format as well as the low‐rank Kronecker tensor format. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Iterative numerical method for integral models of a nonlinear dynamical system with unknown delay
Authors: Tynda Alexander N.
Published: March 2010

This paper is devoted to the construction of iterative numerical algorithm for the systems of nonlinear Volterra‐type equations of the special form related to the Vintage Capital Models (VCMs). One of the unknown functions of these equations is in the lower limit of integration. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Blending Dual Time Stepping and Newton‐Krylov Methods for Unsteady Flows
Authors: Birken Philipp , Jameson Antony
Published: March 2010

We explore the idea of using nonlinear schemes as preconditioners in Newton‐Krylov schemes for unsteady flow computations. Analysis shows that left preconditioning changes the Newton scheme in a non equivalent way, leading to a stall in Newton convergence, whereas right preconditioning leads to a sound method. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical determination of heat exchanger response
Authors: Milewska A.
Published: March 2010

In this paper there is presented approximative calculation of the temperature of fluid in fixed point of heat exchanger and in fixed time. In presented method are used Newton‐Cotes formulas. Moreover there is evaluated the error which is made during determination of heat exchanger response. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The sensitiveness of the speed of pile displacement to speed variations of hammer in beating down process
Authors: Milewska A. , Żukowska J.
Published: March 2010

In this paper there is presented dynamical system described speed of pile displacement during beating down process. Its response is determined by using Heaviside operator. There is introduced the convergence with regulator in partially ordered space. There is given an answer to the question, whether the researched dynamical system describing speed of pile displacement is sensitive to hammer's speed variations. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Projection‐Algebraic Scheme of Discrete Approximations for Linear and Nonlinear Differential Operator Equations in Banach Spaces
Authors: Luśtyk Mirosław , Prykarpatsky Anatoliy
Published: March 2010

The solution set, realizability and convergence of the projection‐algebraic method of discrete approximations for linear and nonlinear differential operator equations are studied. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Chatter Vibration Surveillance by the Optimal‐linear Control of Spindle Speed and Randomly Varying Spindle Speed
Authors: Kalinski Krzysztof , Galewski Marek
Published: March 2010

Tool‐workpiece relative vibration plays principal role during the process of milling with slender ball end mills. Due to certain conditions, a loss of stability and generation of self‐excited chatter vibration will appear. The paper is devoted to a new approach towards vibration surveillance of rotating tools in modern milling machines. Dynamic analysis of a slender ball end milling process has been performed and dynamics of controlled structure is described. In order to reduce vibration level, instantaneous change in the spindle speed appears as control command, and thus the method of vibration surveillance by the spindle speed optimal‐linear control has been developed. Due to quality of machined surface being worse while milling with high tilting angle of the tool, the other method of milling with randomly varying spindle speed is presented. It allows us to maintain a high efficiency of surveillance without worsening of the machining quality. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Control‐oriented Rotordynamics
Authors: Gosiewski Zdzisław
Published: March 2010

The rotor vibrations are coupled by many parameters: angular speed couples two radial directions, unbalance couples torsional and lateral vibrations, rotor support couples rigid body and flexible modes. Small changes of these parameters strongly influence the rotor dynamics. The full analysis of the rotor coupled vibrations is much simpler when we can divide the system into smaller subsystems. In this case the calculations are simplified and we have deep insight into mechanisms leading to good or bed behaviour of the rotor motion. It is particularly important in the case of the rotor working in the wide range of the angular speeds. For the vibration analysis the methods known from control theory can be applied.

The proposed approach was testified in the paper on the simple 3‐mode rotor model. The torsional vibrations were separated from the lateral vibrations and a feedback among the subsystems was established. The subsystems are coupled by rotor unbalance and root locus method allows to show the critical values of the unbalance which destabilize rotor motion for different angular speeds. The lateral vibrations are stabilized by angular speed and again it is possible to find how big value of the rotor speed is sufficient to stabilize the rotor motion. Such analysis of the rotor vibrations appeared very useful for the choice of the control strategy. It indicated such control laws which amplify the stabilizing mechanisms in the rotor dynamics. Such procedures can also lead to the energy saving control laws. In the case of the lateral vibrations there were considered four control strategies. And these strategies were compared to indicate optimal one. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Motion planning for planar bipeds using flatness: the single support phase
Authors: Krause Matthias , Rudolph Joachim , Woittennek Frank
Published: March 2010

Trajectory planning and control of planar motions of biped robots is considered. The robot is modeled as a hierarchical structure of rigid links with rotational joints, which may be seen as a pendulum tree. Motors are available at all rotational joints. However, by the absence of control torques at the contact points with the ground, the system is underactuated. It is shown how differential flatness and time scaling can be helpful for the design of walking motions. Emphasis is put on the single support phase, when the robot touches the floor at a single point. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Investigation of the mobile platform motion optimal control at energy performance index
Authors: Kalinski Krzysztof , Mazur Michal
Published: March 2010

The paper presents a method of optimal control of the mobile robot on example of the 2‐wheel mobile platform. The robot investigated has non‐holonomic constraints. Mathematical model of 2‐wheel mobile platform is characterized by finite number of nonlinear differential equations. The presented method of control is minimizing velocity and position errors. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)