Abstract. Underactuated multibody systems have fewer control inputs than degrees of freedom. In trajectory tracking control of such systems an accurate and efficient feedforward control is often necessary. For multibody systems feedforward control by model inversion can be designed using servo-constraints. So far servo-constraints have been mostly applied to differentially flat underactuated mechanical systems. Differentially flat systems can be inverted purely by algebraic manipulations and using a finite number of differentiations of the desired output trajectory. However, such algebraic solutions are often hard to find and therefore the servo-constraint approach provides an efficient and practical solution method. Recently first results on servo-constraint problems of non-flat underactuated multibody systems have been reported. Hereby additional dynamics arise, so-called internal dynamics, yielding a dynamical system as inverse model. In this paper the servo-constraint problem is analyzed for both, differentially flat and non-flat systems. Different arising important phenomena are demonstrated using two illustrative examples. Also strategies for the numerical solution of servo-constraint problems are discussed.
This review article presents methods for treatment of impact problems in multibody dynamics with a special focus on the coefficient of restitution. The impact modelling in multi-body systems is presented, including the impact kinematics, different definitions of the coefficient of restitution, the instantaneous impact modelling, and the continuous impact modelling. A main topic is the multi-scale simulation approach for the numerical evaluation of the coefficient of restitution using additional simulations on a fast time scale. Different models on the fast time scale are proposed and techniques for experimental validation of the models are given. Many numerical and experimental results for impacts of two and more bodies are presented. Thereby the efficiency and accuracy of the multi-scale simulation approach are verified; the influence of physical parameters on the impact process as well as the agreement of the instantaneous and continuous impact modelling are demonstrated. Finally, the extension of the presented methods to particle systems consisting of thousands of impacting bodies is briefly reviewed.
Particle dampers show a huge potential to reduce undesired vibrations in technical applications even under harsh environmental conditions. However, their energy dissipation depends on many effects on the micro- and macroscopic scale, which are not fully understood yet. This paper aims toward the development of design rules for particle dampers by looking at both scales. This shall shorten the design process for future applications. The energy dissipation and loss factor of different configurations are analyzed via the complex power for a large excitation range. Comparisons to discrete element simulations show a good qualitative agreement. These simulations give an insight into the process in the damper. For monodisperse systems, a direct correlation of the loss factor to the motion modes of the rheology behavior is shown. For well-known excitation conditions, simple design rules are derived. First investigations into polydisperse settings are made, showing a potential for a more robust damping behavior.
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