854 resultados para dynamic modeling and simulation
Resumo:
The applications of the Finite Element Method (FEM) for three-dimensional domains are already well documented in the framework of Computational Electromagnetics. However, despite the power and reliability of this technique for solving partial differential equations, there are only a few examples of open source codes available and dedicated to the solid modeling and automatic constrained tetrahedralization, which are the most time consuming steps in a typical three-dimensional FEM simulation. Besides, these open source codes are usually developed separately by distinct software teams, and even under conflicting specifications. In this paper, we describe an experiment of open source code integration for solid modeling and automatic mesh generation. The integration strategy and techniques are discussed, and examples and performance results are given, specially for complicated and irregular volumes which are not simply connected. © 2011 IEEE.
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This paper describes strategies and techniques to perform modeling and automatic mesh generation of the aorta artery and its tunics (adventitia, media and intima walls), using open source codes. The models were constructed in the Blender package and Python scripts were used to export the data necessary for the mesh generation in TetGen. The strategies proposed are able to provide meshes of complicated and irregular volumes, with a large number of mesh elements involved (12,000,000 tetrahedrons approximately). These meshes can be used to perform computational simulations by Finite Element Method (FEM). © Published under licence by IOP Publishing Ltd.
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This paper proposes a straightforward compromising method to determine the output power of all committed units during the scheduling time horizon. Unlike the conventional methods that work based on a constant pollution control cost (CPCC), this method works based on the system topology such as demand, minimum cost and minimum output emission of the system. In order to have a meaningful compromise between costs and emission in economic and emission dispatch (EED) problem, a flexible pollution control cost (FPCC) is proposed. Also a dynamic economic emission dispatch (DEED) approach is considered where the ramping constraints couple the scheduling hours; the inclusion of valve-point effect makes the DEED modeling more practical. The validity and effectiveness of the unproblematic FPCC approach is verified through an IEEE 30-bus test system with 6 unit for the 6-hour scheduling horizon. © 2013 IEEE.
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Blast traumatic brain injury (BTBI) has become an important topic of study because of the increase of such incidents, especially due to the recent growth of improvised explosive devices (IEDs). This thesis discusses a project in which laboratory testing of BTBI was made possible by performing blast loading on experimental models simulating the human head. Three versions of experimental models were prepared – one having a simple geometry and the other two having geometry similar to a human head. For developing the head models, three important parts of the head were considered for material modeling and analysis – the skin, skull and brain. The materials simulating skin, skull and brain went through many testing procedures including dynamic mechanical analysis (DMA). For finding a suitable brain simulant, several materials were tested under low and high frequencies. Step response analysis, rheometry and DMA tests were performed on materials such as water based gels, oil based mixtures and silicone gels cured at different temperatures. The gelatins and silicone gels showed promising results toward their use as brain surrogate materials. Temperature degradation tests were performed on gelatins, indicating the fast degradation of gelatins at room temperature. Silicone gels were much more stable compared to the water based gels. Silicone gels were further processed using a thinner-type additive gel to bring the dynamic modulus values closer to those of human brain matter. The obtained values from DMA were compared to the values for human brain as found in literature. Then a silicone rubber brain mold was prepared to give the brain model accurate geometry. All the components were put together to make the entire head model. A steel mount was prepared to attach the head for testing at the end of the shock tube. Instrumentation was implemented in the head model to obtain effective results for understanding more about the possible mechanisms of BTBI. The final head model was named the Realistic Explosive Dummy Head or the “RED Head.” The RED Head offered potential for realistic experimental testing in blast loading conditions by virtue of its material properties and geometrical accuracy.
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A semi-autonomous unmanned underwater vehicle (UUV), named LAURS, is being developed at the Laboratory of Sensors and Actuators at the University of Sao Paulo. The vehicle has been designed to provide inspection and intervention capabilities in specific missions of deep water oil fields. In this work, a method of modeling and identification of yaw motion dynamic system model of an open-frame underwater vehicle is presented. Using an on-board low cost magnetic compass sensor the method is based on the utilization of an uncoupled 1-DOF (degree of freedom) dynamic system equation and the application of the integral method which is the classical least squares algorithm applied to the integral form of the dynamic system equations. Experimental trials with the actual vehicle have been performed in a test tank and diving pool. During these experiments, thrusters responsible for yaw motion are driven by sinusoidal voltage signal profiles. An assessment of the feasibility of the method reveals that estimated dynamic system models are more reliable when considering slow and small sinusoidal voltage signal profiles, i.e. with larger periods and with relatively small amplitude and offset.
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A systematic approach to model nonlinear systems using norm-bounded linear differential inclusions (NLDIs) is proposed in this paper. The resulting NLDI model is suitable for the application of linear control design techniques and, therefore, it is possible to fulfill certain specifications for the underlying nonlinear system, within an operating region of interest in the state-space, using a linear controller designed for this NLDI model. Hence, a procedure to design a dynamic output feedback controller for the NLDI model is also proposed in this paper. One of the main contributions of the proposed modeling and control approach is the use of the mean-value theorem to represent the nonlinear system by a linear parameter-varying model, which is then mapped into a polytopic linear differential inclusion (PLDI) within the region of interest. To avoid the combinatorial problem that is inherent of polytopic models for medium- and large-sized systems, the PLDI is transformed into an NLDI, and the whole process is carried out ensuring that all trajectories of the underlying nonlinear system are also trajectories of the resulting NLDI within the operating region of interest. Furthermore, it is also possible to choose a particular structure for the NLDI parameters to reduce the conservatism in the representation of the nonlinear system by the NLDI model, and this feature is also one important contribution of this paper. Once the NLDI representation of the nonlinear system is obtained, the paper proposes the application of a linear control design method to this representation. The design is based on quadratic Lyapunov functions and formulated as search problem over a set of bilinear matrix inequalities (BMIs), which is solved using a two-step separation procedure that maps the BMIs into a set of corresponding linear matrix inequalities. Two numerical examples are given to demonstrate the effectiveness of the proposed approach.
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Abstract. This thesis presents a discussion on a few specific topics regarding the low velocity impact behaviour of laminated composites. These topics were chosen because of their significance as well as the relatively limited attention received so far by the scientific community. The first issue considered is the comparison between the effects induced by a low velocity impact and by a quasi-static indentation experimental test. An analysis of both test conditions is presented, based on the results of experiments carried out on carbon fibre laminates and on numerical computations by a finite element model. It is shown that both quasi-static and dynamic tests led to qualitatively similar failure patterns; three characteristic contact force thresholds, corresponding to the main steps of damage progression, were identified and found to be equal for impact and indentation. On the other hand, an equal energy absorption resulted in a larger delaminated area in quasi-static than in dynamic tests, while the maximum displacement of the impactor (or indentor) was higher in the case of impact, suggesting a probably more severe fibre damage than in indentation. Secondly, the effect of different specimen dimensions and boundary conditions on its impact response was examined. Experimental testing showed that the relationships of delaminated area with two significant impact parameters, the absorbed energy and the maximum contact force, did not depend on the in-plane dimensions and on the support condition of the coupons. The possibility of predicting, by means of a simplified numerical computation, the occurrence of delaminations during a specific impact event is also discussed. A study about the compressive behaviour of impact damaged laminates is also presented. Unlike most of the contributions available about this subject, the results of compression after impact tests on thin laminates are described in which the global specimen buckling was not prevented. Two different quasi-isotropic stacking sequences, as well as two specimen geometries, were considered. It is shown that in the case of rectangular coupons the lay-up can significantly affect the damage induced by impact. Different buckling shapes were observed in laminates with different stacking sequences, in agreement with the results of numerical analysis. In addition, the experiments showed that impact damage can alter the buckling mode of the laminates in certain situations, whereas it did not affect the compressive strength in every case, depending on the buckling shape. Some considerations about the significance of the test method employed are also proposed. Finally, a comprehensive study is presented regarding the influence of pre-existing in-plane loads on the impact response of laminates. Impact events in several conditions, including both tensile and compressive preloads, both uniaxial and biaxial, were analysed by means of numerical finite element simulations; the case of laminates impacted in postbuckling conditions was also considered. The study focused on how the effect of preload varies with the span-to-thickness ratio of the specimen, which was found to be a key parameter. It is shown that a tensile preload has the strongest effect on the peak stresses at low span-to-thickness ratios, leading to a reduction of the minimum impact energy required to initiate damage, whereas this effect tends to disappear as the span-to-thickness ratio increases. On the other hand, a compression preload exhibits the most detrimental effects at medium span-to-thickness ratios, at which the laminate compressive strength and the critical instability load are close to each other, while the influence of preload can be negligible for thin plates or even beneficial for very thick plates. The possibility to obtain a better explanation of the experimental results described in the literature, in view of the present findings, is highlighted. Throughout the thesis the capabilities and limitations of the finite element model, which was implemented in an in-house program, are discussed. The program did not include any damage model of the material. It is shown that, although this kind of analysis can yield accurate results as long as damage has little effect on the overall mechanical properties of a laminate, it can be helpful in explaining some phenomena and also in distinguishing between what can be modelled without taking into account the material degradation and what requires an appropriate simulation of damage. Sommario. Questa tesi presenta una discussione su alcune tematiche specifiche riguardanti il comportamento dei compositi laminati soggetti ad impatto a bassa velocità. Tali tematiche sono state scelte per la loro importanza, oltre che per l’attenzione relativamente limitata ricevuta finora dalla comunità scientifica. La prima delle problematiche considerate è il confronto fra gli effetti prodotti da una prova sperimentale di impatto a bassa velocità e da una prova di indentazione quasi statica. Viene presentata un’analisi di entrambe le condizioni di prova, basata sui risultati di esperimenti condotti su laminati in fibra di carbonio e su calcoli numerici svolti con un modello ad elementi finiti. È mostrato che sia le prove quasi statiche sia quelle dinamiche portano a un danneggiamento con caratteristiche qualitativamente simili; tre valori di soglia caratteristici della forza di contatto, corrispondenti alle fasi principali di progressione del danno, sono stati individuati e stimati uguali per impatto e indentazione. D’altro canto lo stesso assorbimento di energia ha portato ad un’area delaminata maggiore nelle prove statiche rispetto a quelle dinamiche, mentre il massimo spostamento dell’impattatore (o indentatore) è risultato maggiore nel caso dell’impatto, indicando la probabilità di un danneggiamento delle fibre più severo rispetto al caso dell’indentazione. In secondo luogo è stato esaminato l’effetto di diverse dimensioni del provino e diverse condizioni al contorno sulla sua risposta all’impatto. Le prove sperimentali hanno mostrato che le relazioni fra l’area delaminata e due parametri di impatto significativi, l’energia assorbita e la massima forza di contatto, non dipendono dalle dimensioni nel piano dei provini e dalle loro condizioni di supporto. Viene anche discussa la possibilità di prevedere, per mezzo di un calcolo numerico semplificato, il verificarsi di delaminazioni durante un determinato caso di impatto. È presentato anche uno studio sul comportamento a compressione di laminati danneggiati da impatto. Diversamente della maggior parte della letteratura disponibile su questo argomento, vengono qui descritti i risultati di prove di compressione dopo impatto su laminati sottili durante le quali l’instabilità elastica globale dei provini non è stata impedita. Sono state considerate due differenti sequenze di laminazione quasi isotrope, oltre a due geometrie per i provini. Viene mostrato come nel caso di provini rettangolari la sequenza di laminazione possa influenzare sensibilmente il danno prodotto dall’impatto. Due diversi tipi di deformate in condizioni di instabilità sono stati osservati per laminati con diversa laminazione, in accordo con i risultati dell’analisi numerica. Gli esperimenti hanno mostrato inoltre che in certe situazioni il danno da impatto può alterare la deformata che il laminato assume in seguito ad instabilità; d’altra parte tale danno non ha sempre influenzato la resistenza a compressione, a seconda della deformata. Vengono proposte anche alcune considerazioni sulla significatività del metodo di prova utilizzato. Infine viene presentato uno studio esaustivo riguardo all’influenza di carichi membranali preesistenti sulla risposta all’impatto dei laminati. Sono stati analizzati con simulazioni numeriche ad elementi finiti casi di impatto in diverse condizioni di precarico, sia di trazione sia di compressione, sia monoassiali sia biassiali; è stato preso in considerazione anche il caso di laminati impattati in condizioni di postbuckling. Lo studio si è concentrato in particolare sulla dipendenza degli effetti del precarico dal rapporto larghezza-spessore del provino, che si è rivelato un parametro fondamentale. Viene illustrato che un precarico di trazione ha l’effetto più marcato sulle massime tensioni per bassi rapporti larghezza-spessore, portando ad una riduzione della minima energia di impatto necessaria per innescare il danneggiamento, mentre questo effetto tende a scomparire all’aumentare di tale rapporto. Il precarico di compressione evidenzia invece gli effetti più deleteri a rapporti larghezza-spessore intermedi, ai quali la resistenza a compressione del laminato e il suo carico critico di instabilità sono paragonabili, mentre l’influenza del precarico può essere trascurabile per piastre sottili o addirittura benefica per piastre molto spesse. Viene evidenziata la possibilità di trovare una spiegazione più soddisfacente dei risultati sperimentali riportati in letteratura, alla luce del presente contributo. Nel corso della tesi vengono anche discussi le potenzialità ed i limiti del modello ad elementi finiti utilizzato, che è stato implementato in un programma scritto in proprio. Il programma non comprende alcuna modellazione del danneggiamento del materiale. Viene però spiegato come, nonostante questo tipo di analisi possa portare a risultati accurati soltanto finché il danno ha scarsi effetti sulle proprietà meccaniche d’insieme del laminato, esso possa essere utile per spiegare alcuni fenomeni, oltre che per distinguere fra ciò che si può riprodurre senza tenere conto del degrado del materiale e ciò che invece richiede una simulazione adeguata del danneggiamento.
Resumo:
The research activity described in this thesis is focused mainly on the study of finite-element techniques applied to thermo-fluid dynamic problems of plant components and on the study of dynamic simulation techniques applied to integrated building design in order to enhance the energy performance of the building. The first part of this doctorate thesis is a broad dissertation on second law analysis of thermodynamic processes with the purpose of including the issue of the energy efficiency of buildings within a wider cultural context which is usually not considered by professionals in the energy sector. In particular, the first chapter includes, a rigorous scheme for the deduction of the expressions for molar exergy and molar flow exergy of pure chemical fuels. The study shows that molar exergy and molar flow exergy coincide when the temperature and pressure of the fuel are equal to those of the environment in which the combustion reaction takes place. A simple method to determine the Gibbs free energy for non-standard values of the temperature and pressure of the environment is then clarified. For hydrogen, carbon dioxide, and several hydrocarbons, the dependence of the molar exergy on the temperature and relative humidity of the environment is reported, together with an evaluation of molar exergy and molar flow exergy when the temperature and pressure of the fuel are different from those of the environment. As an application of second law analysis, a comparison of the thermodynamic efficiency of a condensing boiler and of a heat pump is also reported. The second chapter presents a study of borehole heat exchangers, that is, a polyethylene piping network buried in the soil which allows a ground-coupled heat pump to exchange heat with the ground. After a brief overview of low-enthalpy geothermal plants, an apparatus designed and assembled by the author to carry out thermal response tests is presented. Data obtained by means of in situ thermal response tests are reported and evaluated by means of a finite-element simulation method, implemented through the software package COMSOL Multyphysics. The simulation method allows the determination of the precise value of the effective thermal properties of the ground and of the grout, which are essential for the design of borehole heat exchangers. In addition to the study of a single plant component, namely the borehole heat exchanger, in the third chapter is presented a thorough process for the plant design of a zero carbon building complex. The plant is composed of: 1) a ground-coupled heat pump system for space heating and cooling, with electricity supplied by photovoltaic solar collectors; 2) air dehumidifiers; 3) thermal solar collectors to match 70% of domestic hot water energy use, and a wood pellet boiler for the remaining domestic hot water energy use and for exceptional winter peaks. This chapter includes the design methodology adopted: 1) dynamic simulation of the building complex with the software package TRNSYS for evaluating the energy requirements of the building complex; 2) ground-coupled heat pumps modelled by means of TRNSYS; and 3) evaluation of the total length of the borehole heat exchanger by an iterative method developed by the author. An economic feasibility and an exergy analysis of the proposed plant, compared with two other plants, are reported. The exergy analysis was performed by considering the embodied energy of the components of each plant and the exergy loss during the functioning of the plants.
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The research is aimed at contributing to the identification of reliable fully predictive Computational Fluid Dynamics (CFD) methods for the numerical simulation of equipment typically adopted in the chemical and process industries. The apparatuses selected for the investigation, specifically membrane modules, stirred vessels and fluidized beds, were characterized by a different and often complex fluid dynamic behaviour and in some cases the momentum transfer phenomena were coupled with mass transfer or multiphase interactions. Firs of all, a novel modelling approach based on CFD for the prediction of the gas separation process in membrane modules for hydrogen purification is developed. The reliability of the gas velocity field calculated numerically is assessed by comparison of the predictions with experimental velocity data collected by Particle Image Velocimetry, while the applicability of the model to properly predict the separation process under a wide range of operating conditions is assessed through a strict comparison with permeation experimental data. Then, the effect of numerical issues on the RANS-based predictions of single phase stirred tanks is analysed. The homogenisation process of a scalar tracer is also investigated and simulation results are compared to original passive tracer homogenisation curves determined with Planar Laser Induced Fluorescence. The capability of a CFD approach based on the solution of RANS equations is also investigated for describing the fluid dynamic characteristics of the dispersion of organics in water. Finally, an Eulerian-Eulerian fluid-dynamic model is used to simulate mono-disperse suspensions of Geldart A Group particles fluidized by a Newtonian incompressible fluid as well as binary segregating fluidized beds of particles differing in size and density. The results obtained under a number of different operating conditions are compared with literature experimental data and the effect of numerical uncertainties on axial segregation is also discussed.
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The present work is devoted to the assessment of the energy fluxes physics in the space of scales and physical space of wall-turbulent flows. The generalized Kolmogorov equation will be applied to DNS data of a turbulent channel flow in order to describe the energy fluxes paths from production to dissipation in the augmented space of wall-turbulent flows. This multidimensional description will be shown to be crucial to understand the formation and sustainment of the turbulent fluctuations fed by the energy fluxes coming from the near-wall production region. An unexpected behavior of the energy fluxes comes out from this analysis consisting of spiral-like paths in the combined physical/scale space where the controversial reverse energy cascade plays a central role. The observed behavior conflicts with the classical notion of the Richardson/Kolmogorov energy cascade and may have strong repercussions on both theoretical and modeling approaches to wall-turbulence. To this aim a new relation stating the leading physical processes governing the energy transfer in wall-turbulence is suggested and shown able to capture most of the rich dynamics of the shear dominated region of the flow. Two dynamical processes are identified as driving mechanisms for the fluxes, one in the near wall region and a second one further away from the wall. The former, stronger one is related to the dynamics involved in the near-wall turbulence regeneration cycle. The second suggests an outer self-sustaining mechanism which is asymptotically expected to take place in the log-layer and could explain the debated mixed inner/outer scaling of the near-wall statistics. The same approach is applied for the first time to a filtered velocity field. A generalized Kolmogorov equation specialized for filtered velocity field is derived and discussed. The results will show what effects the subgrid scales have on the resolved motion in both physical and scale space, singling out the prominent role of the filter length compared to the cross-over scale between production dominated scales and inertial range, lc, and the reverse energy cascade region lb. The systematic characterization of the resolved and subgrid physics as function of the filter scale and of the wall-distance will be shown instrumental for a correct use of LES models in the simulation of wall turbulent flows. Taking inspiration from the new relation for the energy transfer in wall turbulence, a new class of LES models will be also proposed. Finally, the generalized Kolmogorov equation specialized for filtered velocity fields will be shown to be an helpful statistical tool for the assessment of LES models and for the development of new ones. As example, some classical purely dissipative eddy viscosity models are analyzed via an a priori procedure.
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This dissertation consists of three self-contained papers that are related to two main topics. In particular, the first and third studies focus on labor market modeling, whereas the second essay presents a dynamic international trade setup.rnrnIn Chapter "Expenses on Labor Market Reforms during Transitional Dynamics", we investigate the arising costs of a potential labor market reform from a government point of view. To analyze various effects of unemployment benefits system changes, this chapter develops a dynamic model with heterogeneous employed and unemployed workers.rn rnIn Chapter "Endogenous Markup Distributions", we study how markup distributions adjust when a closed economy opens up. In order to perform this analysis, we first present a closed-economy general-equilibrium industry dynamics model, where firms enter and exit markets, and then extend our analysis to the open-economy case.rn rnIn Chapter "Unemployment in the OECD - Pure Chance or Institutions?", we examine effects of aggregate shocks on the distribution of the unemployment rates in OECD member countries.rn rnIn all three chapters we model systems that behave randomly and operate on stochastic processes. We therefore exploit stochastic calculus that establishes clear methodological links between the chapters.
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Riparian zones are dynamic, transitional ecosystems between aquatic and terrestrial ecosystems with well defined vegetation and soil characteristics. Development of an all-encompassing definition for riparian ecotones, because of their high variability, is challenging. However, there are two primary factors that all riparian ecotones are dependent on: the watercourse and its associated floodplain. Previous approaches to riparian boundary delineation have utilized fixed width buffers, but this methodology has proven to be inadequate as it only takes the watercourse into consideration and ignores critical geomorphology, associated vegetation and soil characteristics. Our approach offers advantages over other previously used methods by utilizing: the geospatial modeling capabilities of ArcMap GIS; a better sampling technique along the water course that can distinguish the 50-year flood plain, which is the optimal hydrologic descriptor of riparian ecotones; the Soil Survey Database (SSURGO) and National Wetland Inventory (NWI) databases to distinguish contiguous areas beyond the 50-year plain; and land use/cover characteristics associated with the delineated riparian zones. The model utilizes spatial data readily available from Federal and State agencies and geospatial clearinghouses. An accuracy assessment was performed to assess the impact of varying the 50-year flood height, changing the DEM spatial resolution (1, 3, 5 and 10m), and positional inaccuracies with the National Hydrography Dataset (NHD) streams layer on the boundary placement of the delineated variable width riparian ecotones area. The result of this study is a robust and automated GIS based model attached to ESRI ArcMap software to delineate and classify variable-width riparian ecotones.
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This thesis develops an effective modeling and simulation procedure for a specific thermal energy storage system commonly used and recommended for various applications (such as an auxiliary energy storage system for solar heating based Rankine cycle power plant). This thermal energy storage system transfers heat from a hot fluid (termed as heat transfer fluid - HTF) flowing in a tube to the surrounding phase change material (PCM). Through unsteady melting or freezing process, the PCM absorbs or releases thermal energy in the form of latent heat. Both scientific and engineering information is obtained by the proposed first-principle based modeling and simulation procedure. On the scientific side, the approach accurately tracks the moving melt-front (modeled as a sharp liquid-solid interface) and provides all necessary information about the time-varying heat-flow rates, temperature profiles, stored thermal energy, etc. On the engineering side, the proposed approach is unique in its ability to accurately solve – both individually and collectively – all the conjugate unsteady heat transfer problems for each of the components of the thermal storage system. This yields critical system level information on the various time-varying effectiveness and efficiency parameters for the thermal storage system.
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This report presents the research results of battery modeling and control for hybrid electric vehicles (HEV). The simulation study is conducted using plug-and-play powertrain and vehicle development software, Autonomie. The base vehicle model used for testing the performance of battery model and battery control strategy is the Prius MY04, a power-split hybrid electric vehicle model in Autonomie. To evaluate the battery performance for HEV applications, the Prius MY04 model and its powertrain energy flow in various vehicle operating modes are analyzed. The power outputs of the major powertrain components under different driving cycles are discussed with a focus on battery performance. The simulation results show that the vehicle fuel economy calculated by the Autonomie Prius MY04 model does not match very well with the official data provided by the department of energy (DOE). It is also found that the original battery model does not consider the impact of environmental temperature on battery cell capacities. To improve battery model, this study includes battery current loss on coulomb coefficient and the impact of environmental temperature on battery cell capacity in the model. In addition, voltage losses on both double layer effect and diffusion effect are included in the new battery model. The simulation results with new battery model show the reduced fuel economy error to the DOE data comparing with the original Autonomie Prius MY04 model.
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Telescopic systems of structural members with clearance are found in many applications, e.g., mobile cranes, rack feeders, fork lifters, stacker cranes (see Figure 1). Operating these machines, undesirable vibrations may reduce the performance and increase safety problems. Therefore, this contribution has the aim to reduce these harmful vibrations. For a better understanding, the dynamic behaviour of these constructions is analysed. The main interest is the overlapping area of each two sections of the above described systems (see markings in Figure 1) which is investigated by measurements and by computations. A test rig is constructed to determine the dynamic behaviour by measuring fundamental vibrations and higher frequent oscillations, damping coefficients, special appearances and more. For an appropriate physical model, the governing boundary value problem is derived by applying Hamilton’s principle and a classical discretisation procedure is used to generate a coupled system of nonlinear ordinary differential equations as the corresponding truncated mathematical model. On the basis of this model, a controller concept for preventing harmful vibrations is developed.