Richter, Peter H.

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Richter, Peter H.
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Richter, Peter H.
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Richter, P. H.
Richter, Peter
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    Analyse und Modellierung der Keyhole-Dynamik beim Laserstrahlschweißen von Aluminiumlegierungen
    (2002-02-05)
    Pleteit, Hermann
    ;
    Jüptner, W.
    ;
    Richter, Peter H.
    ;
    Richter, Peter H.
    The subject of this thesis is the behaviour of the keyhole in the laser welding process. In deep penetration laser welding there exists a complex system of weld pool, keyhole, and solid material under the influence of the laser beam. The dynamics which are regarded are primarily the changes in the shape of the keyhole. The dynamics determine the intensity in radiation of the plasma plume which exists above the keyhole. The first part of this thesis focuses on the analysis of time series which contain the experimentally recorded radiation intensity. Since classical techniques like simple Fournier transformation don´t give crucial results, these time series are analysed with methods arising from the theory of nonlinear dynamics. The methods include singular value decomposition, the calculation of correlation sums, and the test of determinism in the origin of the time series by use of surrogate data. The results of this analysis shall give valuable information for the modelling of the keyhole dynamics. The content of the second part is the development of a model for keyhole dynamics from first principles. Several basic assumptions for the physical properties of the weld pool and the keyhole wall lead to a system of nonlinear differential equations. The numerical integration of the model system shows non-trivial behaviour in a wide range of the parameter space. The existence of an attractor, which consists of a complex periodic orbit, dominates the phase space. The model presented here can reproduce qualitatively some aspects of the real laser welding process such as the sensitive dependence of the weld process on the laser power.
    Dissertation
      450  215
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    Zwangskräfte bei einem Mehrkörpersystem mit drei Freiheitsgraden
    (2000-05-23)
    Tischenko, Oleg
    ;
    Kienzler, Reinhold
    ;
    Richter, Peter H.
    ;
    Richter, Peter H.
    A mechanical system with three degrees of freedom in a gravitational field is analyzed for chaotic versus regular behavior, and for moments of constraint that act on its axes. The system consists of three connected rigid bodies each of which rotating about one axes. The vertical axis of the first body is fixed to the immobile base; the second body rotates about a horizontal axis which moves with the first, and the third body rotates about an axis in the second. Its moments of inertia A, B, C are assumed to obey C=A B. The motion is regular if the body is symmetric, A=B, otherwise the asymmetry parameter µ=(B-A)/B determines the degree of chaoticity. The different types of motion were identified with the help of Poincaré sections while the study of forces of constraints as functions of time was carried out using methods of time-frequency analysis: Fourier analysis in the case of regular, and wavelet analysis in the case of chaotic motion. It was noticed that for large values of µ the motion of the system shows an effect that can be described as intermittency, that is, there exist of long phases of motion during which the system behaves regularly. The reason for the occurence of such an effect is explained. It is observed that the forces of constraints obtain their maximal values in connection with the transition from one regular phase to another. In spite of the presence of chaos in the Poincaré-sections, for large intervals of µ, the wavelet transformation diagrams reflect a relatively regular behavior of the forces of constraints. Using classical statistical methods it would be possible, on the basis of analysis, to evaluate the long-term effects of chaotic motion on the wearing of materials in the bearings of the system.
    Dissertation
      365  167
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    Renormalization Theory for Hamiltonian Systems
    (2002-12-16)
    Pronine, Mikhail
    ;
    Schwegler, Helmut
    ;
    Richter, Peter H.
    ;
    Richter, Peter H.
    We study the onset of widespread chaos in Hamiltonian systems with two degrees of freedom. Such systems and their stability properties are of interest in diverse fields (celestial mechanics, plasma physics, chemical physics to name just a few). Due to topological reasons, two-dimensional invariant tori of irrational winding numbers represent barriers to widespread chaos. The breakup of the "last" invariant torus can be viewed as the threshold to widespread chaos. We use the renormalization group approach in order to describe the breakup of invariant tori of irrational winding numbers. An approximate renormalization scheme is derived for this purpose.The scheme is implemented with the help of the "Maple" computer algebra system. The renormalization group approach is applied to a number of systems. We discuss the paradigm Hamiltonian of Escande and Doveil, the Walker and Fordmodel, a model of the ethane molecule, the double pendulum, the Baggott system, limacon billiards. The Poincare surface of section technique is used in order to study numerically the dynamic behavior of the systems and to check the results of the renormalization theory.
    Dissertation
      263  104