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Fakultät für Maschinenbau
Wissenschaftlicher Mitarbeiter

Dr.-Ing. Dominik Kern

2000-2007: Diplom Maschinenbau, TU Bergakademie Freiberg
2007-2013: Promotion in Dynamik/Mechatronik, Karlsruher Institut für Technologie (KIT)
2013-jetzt: Akademischer Rat, TU Chemnitz
  • Variationelle Zeitintegratoren für Steuerung und Regelung gekoppelter Systeme
  • Experimentelle Validierung numerischer Simulationen
  • Schwingungsbasierte Sensorik

Publikationen im Jahr 2020

  • Kern D., Gypstuhl R. and Groß M. (2020), Dynamic Stability of Viscoelastic Bars under Pulsating Axial Loads, Proc. Appl. Math. Mech., 20, submitted.

Publikationen im Jahr 2019

  • Kern D. and Römer U. J. (2019), A Brief Survey on Non-standard Constraints: Simulation and Optimal Control, 8th GACM Colloquium on Computational Mechanics, University of Kassel, Germany, August 28-30, 2019. ISBN 978-3-86219-5093-9 .
  • Kern D. and Groß M. (2019), Variational Integrators and Fluid-Structure-Interaction at Low Reynolds-Number, Proc. Appl. Math. Mech., 19 . doi:10.1002/pamm.201900365.
  • Kern D. and Groß M. (2018), A Variational Approach to Optimal Control of Underactuated Mechanical Systems with Collisions, INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2018, AIP Conference Proceedings 2116:340005, 2019,

Publikationen im Jahr 2018

  • Kern D. and Romero I. and Conde S.C. and Garcia-Orden J.C. (2018), Performance Assessment of Variational Integrators for Thermomechanical Problems, Journal of Theoretical and Applied Mechanics, 48(2):3-23, 2018. doi:10.2478/jtam-2018-0008 .
  • Kern D. and Groß M. (2018), Variational Integrators and Optimal Control for a Hybrid Pendulum-on-Cart-System, Proc. Appl. Math. Mech., 18: 1-2. doi: 10.1002/pamm.201800088.

Publikationen im Jahr 2017

  • Kern D., Wiegert B. and Groß M. (2017), Vibrations of rotors partially filled with liquids in hydrodynamically lubricated journal bearings, Proceedings of SIRM 2017 in Graz, Austria, 2017.
  • Kern D. and Gross M. (2017), Energy‐optimal swing‐up of an electromechanically actuated pendulum, Proc. Appl. Math. Mech., 17: 801-802. doi: 10.1002/pamm.201710368.

Publikationen im Jahr 2016

  • Kern D. and Romero I. and Conde S.C. and Garcia-Orden J.C. (2016), Performance Assessment of Variational Integrators for Thermomechanical Problems, arXiv preprint, 2016. arXiv:1610.08666.
  • Brack T., Kern D., Chen M. and Dual Jurg. (2016), Dynamics and Stability of Phase Controlled Oscillators, J. Dyn. Sys., Meas., Control 138(7), 071007 (May 13, 2016) (12 pages) Paper No: DS-15-1163; doi: 10.1115/1.4033176.
  • Kern D. and Jehle G. (2016), Dynamics of a rotor partially filled with a viscous incompressible fluid, Proc. Appl. Math. Mech., 16: 279-280. doi: 10.1002/pamm.201610128.

Publikationen im Jahr 2015

  • Kern, D., Romero, I. and Groß, M. (2015), Variational integrators for Thermo-Viscoelastic Discrete Systems. Proc. Appl. Math. Mech., 15: 55–56. doi: 10.1002/pamm.201510018
  • Tobias Brack, Dominik Kern und Jurg Dual. Damping measurement of oscillators using adaptive phase control. In: American Control Conference (ACC), 2015. IEEE. 2015, S. 1357-1362.

Publikationen im Jahr 2014

  • Kern, Dominik ; Bär, Sebastian and Groß, Michael: Variational Integrators for Thermomechanical Coupled Dynamic Systems with Heat Conduction. PAMM 14 (2014), Nr. 1, S. 47-48..
  • Sharma, Nikhil ; Kern, Dominik and Seemann, Wolfgang: Vibration analysis and robust control of highly deformable beams in a heavy pinched loop configuration, ZAMP 2014

Publikationen im Jahr 2013

  • Kern, Dominik ; Rösner, Malte ; Bauma, Elisabeth ; Seemann, Wolfgang ; Lammering, Rolf und Schuster, Thomas: Key features of flexure hinges used as rotational joints. In: Forschung im Ingenieurwesen (2013), S. 1–9.
  • Ayhan, Serdal ; Bauer, Jörg ; Gerdes, Arne ; Grimske, Silka ; Heinze, Tobias ; Kern, Dominik ; Müller, Christopher und Pollmann, Jan: Effektiv auf kleinstem Raum. In: maschine+werkzeug (2013), Nr. 2, S. 76–77.
  • Kern, Dominik: Neuartige Drehgelenke für reibungsarme Mechanismen-Auslegungskriterien und Berechnungsmethoden. Diss. Karlsruhe, Karlsruher Institut für Technologie (KIT), 2013.

Publikationen im Jahr 2012

  • Kern, Dominik ; Rösner, Malte and Seemann, Wolfgang: Failure analysis of highly predeformed beams used as flexure hinges. In: PAMM 12 (2012), Nr. 1, S. 209–210.
  • Kern, Dominik ; Brack, Tobias and Seemann, Wolfgang: Resonance Tracking of Continua Using Self-Sensing Actuators. In: Journal of Dynamic Systems Measurement and Control 134 (2012), Nr. 5.
  • Kern, D ; Bauer, J und Seemann, W: Control of Compliant Mechanisms with Large Deflections. In: Advances in Mechanisms Design. Springer Netherlands, 2012, S. 193–199.
  • Fleischer, J. ; Seemann, W. ; Zwick, T. ; Ayhan, S. ; Bauer, J. ; Kern, D. und Scherr, S.: Antriebsmodul für die Mikrobearbeitung. In: wt-online (2012), Nr. 11/12-2012, S. 724–729.

Publikationen im Jahr 2011

  • Seemann, Wolfgang ; Kern, Dominik and Brack, Tobias: Tracking of Eigenfrequencies of Vibrating Beams by Phase-Locked Loops. In: International Symposium on Vibrations of Continuous Systems. Proceedings. 2011, S. 46–47.
  • Kern, Dominik and Seemann, Wolfgang: Analysis of a Compliant Mechanism for Positioning in the cm-Range. In: PAMM 11 (2011), Nr. 1, S. 235–236.

Publikationen im Jahr 2010

  • Munzinger, Christian ; Weis, Martin ; Seemann, Wolgang ; Rudolf, Christian und Kern, Dominik: Dynamiksteigerung adaptronische Strebe zur Kompensation geometrischer Maschinenfehler. In: Adaptronik für Werkzeugmaschinen. Bd. 1. Shaker Verlag, 2010, S. 19–45.
  • Kern, Dominik and Seemann, Wolfgang: Tracking of Mechanical System Parameters by Phase-Locked Loops. In: PAMM 10 (2010), Nr. 1, S. 613–614.
  • Jehle, Georg ; Kern, Dominik und Seemann, Wolfgang: Wavebased Micromotor for Plane Motions (3-DoF). In: COMSOL User Conference. 2010.
  • Glushkov, Evgeny ; Glushkova, Natalia ; Kvasha, Oleg ; Kern, Dominik und Seemann, Wolfgang: Guided Wave Generation and Sensing in an Elastic Beam Using MFC Piezoelectric Elements: Theory and Experiment. In: Journal of Intelligent Material Systems and Structures 21 (2010), Nr. 16, S. 1617.

Publikationen im Jahr 2009

  • Kern, Dominik and Seemann, Wolfgang: Experimental Feasibility Study for Guided Wave Propagation. In: PAMM 9 (2009), Nr. 1, S. 501–502.

Publikationen im Jahr 2008

  • Liedke, Thomas ; Kern, Dominik ; Kuna, Meinhard ; Ams, Alfons und Scherzer, Mathias: Mikromechanische Simulation des Drahtsägeprozesses unter Verwendung der Diskreten Elemente Methode und Kriterien der Indenter-Bruchmechanik. In: Zuverlässigkeit von Bauteilen durch bruchmechanische Bewertung: Regelwerke, Anwendungen und Trends, Berichtsband der 40. Tagung des DVM-Arbeitskreises Bruchvorgänge. DVM. 2008, S. 289–298.

GAMM 2014

Variational integrators are modern time-integration schemes based on a discretization of the underlying variational principle. They thus skip the direct formulation and time discretization of partial differential equations. In terms of mechanics, Hamilton’s Principle is approximated by an action sum whose variation should be equal to zero, resulting in discrete Euler-Lagrange equations in analogue to their discrete Position-Momentum-Equations. Variational integrators are by design structure preserving (symplecticity) and show excellent longtime behavior. They lead to one-step maps that may be directly utilized as discrete state space model for controller design. In order to consider the coupling between mechanical and thermal quantities Hamilton’s prin- ciple is extended following the formulation proposed by Maugin et al by using the notion of thermacy as analogue to mechanical displacements in classical mechanics. From this varia- tional formulation higher order accurate methods, such as multi-point variational integrators, are constructed. In this presentation, as example problem serves a thermoelastic double pen- dulum with heat conduction. Reference solutions for this system, which were obtained by al- ternative methods, namely energy-entropy consistent methods (TC-integrator), are taken from the literature.

GAMM 2015

Variational integrators are modern time-integration schemes based on a discretization of the underlying variational principle. They thus skip the direct formulation and time discretization of differential equations. In this paper, Hamilton's principle is approximated by an action sum, whose vanishing variation results in discrete Euler-Lagrange equations or, equivalently, in discrete evolution equations for the position and momentum. Variational integrators are, by design, structure preserving (symplecticity and momentum) and show excellent long-time behavior in total energy. In this work, heat transfer is accounted for after the dissipationless type II model of Green and Naghdi. We will show that, in this way, thermal effects enter the variational principle both via the free energy, and Fourier's law of heat conduction accounting for thermal dissipation. This formulation requires the notion of thermacy, a quantity also called ``thermal displacement'' whose time derivative corresponds to the temperature. It results in a natural definition of the entropy as ``thermal momentum'' and entropy flux as ``thermal force''. The viscoelastic effects are also introduced via the free energy by an internal variable formulation. In order to include the corresponding viscous and thermal virtual work (mechanical and thermal virtual dissipation), Hamilton's principle is extended by D'Alembert terms, which account for the time evolution equation of the internal variable and Fourier's law. From this variational formulation, variational integrators using different orders of approximation of the state variables as well as of the quadrature of the action integral are constructed and compared. A thermo-viscoelastic double pendulum comprised of two discrete masses connected by thermoelastic springs and dash pots (Poynting-elements), and subject to heat conduction both between the two springs and between each of the springs and the environment, serves as a discrete model problem.

GAMM 2016

A rotor partially filled with a viscous incompressible fluid is modeled as planar system. Its structural part, i.e. the rotor, is assumed to be rigid, circular, elastically supported and running with a prescribed time-dependent angular velocity. Both parts, structure and fluid, interact via the no-slip condition and the pressure. The point of departure for the mathematical formulation of the fluid filling is the Navier-Stokes equation, which is complemented by an additional equation for the evolution of its free inner boundary. Further, rotor and fluid are subjected to volume forces, namely gravitation. Trial functions are chosen for the fluid velocity field, the pressure field and the moving boundary, which fulfill the incompressibility constraint as well as the boundary conditions. Inserting these trial functions into the partial differential equations of the fluid motion, and applying the method of weighted residuals yields equations with time derivatives only. Finally, in combination with the rotor equations, a nonlinear system of 12 differential-algebraic equations results, which sufficiently describes solutions near the circular symmetric state and which may indicate the loss of its stability.

SAMM 2016

The topic of the GAMM Juniors' School on Applied Mathematics and Mechanics (SAMM) are Geometric Methods in Multi-Body and Structural Dynamics Modelling, Simulation and Control. This summerschool introduces variational integrators and Lie-group integrators from the basics, emphasizing their geometrical properties. Then, optimal control is combined with these structure preserving integrators, in order to exploit the natural coupling between mathematical modeling, numerical integration and control. These methods are exemplarily applied to mechanical multi-body systems. The extensions to structural dynamics, non-smooth systems (e.g. elastic collisions) and electrical systems are outlined.

SIRM 2017

Rotors, partially filled with liquid, form an important subclass of rotating machinery. The liquid may either be part of the main functionality, e.g. in centrifuges and washing machines, or fulfill an auxiliary function such as cooling in motors and turbines. Many of these rotors run in hydrodynamically lubricated journal bearings. Both, the fluid filling as well as the fluid film in the journal bearings, may cause self-excited oscillations. The latter is known as oil whirl and oil whip instabilities, which have been experimentally observed by Newkirk & Taylor and later on exhaustively studied by many authors. Whereas the former may not only lead to instabilities but also to synchronization and balancing effects, experimentally observed by Kollmann and also theoretically investigated by many authors. This paper unites both branches of development and tries to answer the questions: how do these effects influence each other, and how can stabilizing effects be reached, if they exist. Therefore the classical planar model of a Laval rotor, with circular cross section, symmetry to the middle plane (axial direction), imbalance and running with a prescribed rotational speed is modified. It is combined with reduced models for the bearings and the filling. The bearing forces are calculated by the Reynolds' equation under the simplifying assumption for short bearings, as was done by Moser. The fluid filling is modeled under certain assumptions by a reduction to an equivalent rigid body, as proposed by Derendyaev et al. The fluid-filled rotor-bearing-system is characterized by transient run-up simulation and a bifurcation analysis with respect to the rotational speed.

GAMM 2017

A control strategy for swinging up a planar pendulum, from its hanging to its upright position, is presented. The pendulum hinge is electro-mechanically actuated. This is a simple example for a nonlinear control problem. In contrast to the frequently used model of torque control, the DC-motor is included as RLC circuits of stator and armature in this paper. The armature voltage is used as input signal, while the stator voltage is fixed. In order to compute the optimal feed-forward control Hamilton’s principle is applied and discretized by a variational integrator (VI). Thus, the resulting optimal control problem is transferred into a finite-dimensional optimization problem, and solved by SQP methods. The cost function to be minimized is the consumed electrical energy needed to swing up the pendulum in a prescribed time. In addition to the feed-forward control (offline), a feed-back controller (online) is added in order to stabilize the swing-up and the upright position. This feedback-controller is designed as linear-quadratic regulator (LQR) around the linearization of the nominal trajectory.

GAMM 2018

Hybrid systems combine time continuous and time discrete dynamics. They emerge in mechanical systems, when collisions are modelled by an impulse-like contact force. During such a collision of two or more bodies, their positions go on continuously, but their velocities jump. On the one hand this non-smoothness complicates the optimal control problem significantly, on the other hand it opens up new horizons. This contribution uses a nested optimization in order to swing up a hybrid pendulum-on-cart-system. Both, pendulum and cart, move in finite ranges which are bounded by limiters. While the inner loop optimizes the continuous motions from start to collision, from collision to collision and finally to the final state, the outer loop optimizes time and state of the collisions. The time discretization and the optimal control during continuous motions are based on the Discrete-Mechanics-and-Optimal-Control (DMOC) approach.


In real machines and mechanisms, almost all joints are limited. A common hard limiter in mechanical systems is a collision between bodies, or between bodies and system boundaries. Often these collisions are modelled by impulse-like contact forces. During such a collision of two or more bodies, their positions go on continuously, but their velocities jump. We consider this non-smoothness and its consequences for simulation and control in a variational setting, from which a discretization follows in a systematic way. The resulting variational integrator (VI) for collisions is known from the literature, but the incorporation of the collision equations into the Discrete Mechanics and Optimal Control (DMOC) approach follows a new idea. As many technical systems are underactuated, we take this into account, too. The feed-forward control for the swing-up of a pendulum-on-cart-system, a.k.a. inverted pendulum, proves the concept. The sequence of collisions is not optimized yet, but for a given sequence, we find the cart force to optimally steer the pendulum into its final state.

GAMM 2019

Variational formulations are a good point of departure for numerical methods, however there exists no variational principle for the Navier-Stokes Equations in general. Only certain approximations, either for very high or very low Reynolds Number, can be formulated as stationarity condition of some functional. In viscous flow the viscous terms dominate the inertia terms (Re<<1). Further assuming an incompressible fluid leads to the Stokes Equations. Velocity and pressure field in the fluid are spatially discretized by global approximations, which comply to the continuity equation and certain requirements for solutions of Stokes Equations. The corresponding free coefficients are chosen by a best fit on the boundary in the sense of Trefftz. As long as the modelling assumptions for Stokes Equations are valid, the precision depends on the set of spatial approximation functions. As example serves the planar problem of Stokes Drag on rigid bodies.

GACM 2019

In terms of simulation and control holonomic constraints are well documented and thus termed standard. As non-standard constraints, we understand non-holonomic and unilateral constraints. We limit this survey to mechanical systems with a finite number of degrees of freedom. The long-term behavior of nonholonomic integrators as compared to structure-preserving integrators for holonomically constrained systems is briefly discussed. Some recent research regarding the treatment of unilaterally constrained systems by event-driven or time-stepping schemes for time integration and in the context of optimal control problems is outlined.

GAMM 2020

Recent applications require the extension of stability theory for axially loaded bars to viscoelasticity. For the elastic bar it is known that a pulsating load leads to a Mathieu equation, meaning there are some instable regions before the static buckling load and some stable regions beyond, depending on the excitation (amplitude, frequency, offset). This work follows the same lines as Weidenhammer and adopts the classical Euler-Bernoulli-beam kinematics for coupled longitudinal and bending vibrations. Modeling viscoelasticity by the Standard Linear Solid model, a.k.a. Zener model, introduces an internal variable. Hence, there are auxiliary transversal and longitudinal displacements corresponding to the internal variable in addition to the physical transversal and longitudinal displacements of the bar centerline. The modeling further assumes only longitudinal vibrations in the stable regime. In the absence of transversal vibrations a linear partial differential equation system for the longitudinal vibrations results, which is solved analytically for a pulsating load. Further, a one-sided coupling is assumed for the stability analysis, i.e. the longitudinal vibrations are prescribed and induce transversal vibrations. Still, the time-variant coefficients of the transversal dynamics make it difficult to find an analytical solution, consequently an approximation is obtained by Ritz' method from Hamilton's principle. Applying the eigenforms of elastic buckling as trial functions finally leads to a rheolinear ordinary differential equation. The stability chart with respect to static and harmonic load is calculated numerically by Floquet theory.