131 research outputs found
Het gebruik van reductiemethoden bij het bepalen van het transient gedrag van niet-lineaire dynamische systemen met veel vrijheidsgraden:literatuurstudie
Full text linkExperimental modeling of hysteresis in stage systems: A Maxwell–Iwan approach
No full textDynamic links of high-precision stage systems consist of wires and hoses that are used for example to transport electrical current to the actuators and sensors or cooling liquids to the stages. During stage motion, these dynamic links typically express complex hysteretic behavior due to internal friction and viscoelastic properties. As such, dynamic links give rise to unwanted disturbances acting on the high-precision stage systems. This paper presents a simple but accurate physics-based and experimental modeling procedure. The generalized Maxwell model and a modification of the Iwan model are combined in parallel to capture both frequency dependencies by viscoelastic effects and amplitude dependencies by friction-based effects. The modified and physically meaningful Iwan model is shown to be equivalent to the well-known Bouc–Wen model. A so-called normalized dissipation factor is introduced to quickly recognize frequency and/or amplitude dependent behavior using measured data. Using this information, a well-founded choice for an (initial) model structure to be identified can be made. Subsequently, an identification procedure is proposed to estimate values of the model parameters again using the measured data. A simulated experiment is used to show the use of the normalized dissipation factor and validate the identification procedure. Finally, the validity and usefulness of the Maxwell–Iwan modeling approach is demonstrated by experimental results obtained from an industrial wafer stage system
Dynamic Stability of a Base-Excited Thin Beam with Top Mass
No full textThis paper deals with a base-excited clamped-clamped vertical thin beam carrying a top mass. The thin beam is considered to be inextensible and initially not perfectly straight. Based on Taylor series expansions of the inextensibility constraint and the exact curvature, and by using one or more basis functions, a semi-analytical model is derived. This model is numerically validated through a comparison with quasi-static and modal analysis results obtained using finite element modelling. The steadystate nonlinear dynamics of the base-excited beam are investigated using numerical continuation of periodic solutions and bifurcations. Using these numerical tools, the dynamic stability of the beam is investigated for various parameter settings, including the effect of nonlinear damping. The continuation of bifurcations appears to be very suitable to determine whether or not parametric resonance occurs for certain parameter settings
An experimental study on synchronization of nonlinear oscillators with Huygens' coupling
Full text link"In this experimental study, phase synchronization is studied in pairs of nonlinear oscillators coupled through a movable support. In particular, the dynamics of two discontinuous mass-spring-damper oscillators and the dynamics of the classical Huygens' pendulum clocks are considered. In both systems the individual oscillators are self-sustained. It is shown that in both cases, the oscillators exhibit in-phase and anti-phase synchronization. All experiments are executed on a new experimental setup consisting of two controllable mass-spring-damper oscillators coupled through an elastically supported rigid bar. The results suggest, that the synchronized motion observed by Christiaan Huygens around 1650 in a pair of pendulum clocks mounted on a flexible support, in many cases can also be observed when the pendulum clocks are replaced by other self-sustained nonlinear oscillators.
Controlling nonlinear resonances in thin-walled structures: modeling, simulations, and experiments
No full textSteady-state behaviour of a solar array system with elastic stops
No full textIn recent years a method was developed by the authors for efficient analysis of the long term behaviour of mechanical systems with local nonlinearities under periodic excita-tien. In this method the linear parts of the system are modelled using the finite element method. In order to keep the cpu-time for the nonlinear analyses acceptable, the number of degrees of freedom (dof) of the linear part of the system is reduced using a compo-nent mode synthesis (cms) technique. The cms technique used is based on free-interface eigenmodes and residual flexibility modes. Eigenmodes are kept up to a user-defined cut-off frequency. Subsequently, the reduced linear model is coupled to local nonline-arities, such as nonlinear springs and dampers, dry fiction elements, backlash etc. The model obtained in this way is analysed using a nonlinear dynamics toolbox, which among others contains solvers for the calculation of periodic solutions and their stability and a path following method. The approach outlined above is described in Fey (1992) and Fey et al. (1996) and was integrated in the finite element package DIANA (1997). Until now, this approach was applied to rather academie, archetypal problems in order to verify its value. The approach turned out to be very successful: numerical resuits were compared with experimental resuits and a Bood correspondence was achieved (van de Vorst, 1996, van de Vorst et al., 1996a, van de Vorst et al., 1996b)
Sine sweep and steady-state response of simplified solar array models with nonlinear elements
No full textIn this paper the nonlinear dynamic behaviour of two simplified solar array systems is investigated experimentally and numerically. A simplified beam model supported by one snubber (a bilinear spring which can only take compressive forces) is used to investigate the dynamics of the extension arm on the onset of gapping. A dual plate model is used to investigate the dynamics of two folded solar array panels, which are separated by two snubbers. The number of degrees of freedom of the linear part of the numerical models is reduced using a component mode synthesis technique. The systems show rich nonlinear dynamic behaviour: hysteresis loops, cyclic fold and secondary Hopf bifurcations, quasi-periodic, subharmonic and chaotic solutions, superharmonic resonances, etcetera. Good correspondence between numerical and experimental results is obtained. The insight in the nonlinear dynamic behaviour of solar array panels has been increased considerably thanks to the studies presented in this paper
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