GAMM Mitteilungen最新文献

{"title":"Preface to the topical issue on applied and nonlinear dynamics: Part II","authors":"Jörg Fehr,&nbsp;Kristin de Payrebrune,&nbsp;Robert Seifried","doi":"10.1002/gamm.202300011","DOIUrl":"https://doi.org/10.1002/gamm.202300011","url":null,"abstract":"<p>The current special issue of the GAMM Mitteilungen, which is the second of a two-part series, contains several contributions on the topic of Applied and Nonlinear Dynamics. We are very happy that several teams of authors have accepted our invitation to report on recent developments, research highlights and emerging application areas in Applied and Nonlinear Dynamics.</p><p>This second part of the topical issue on Applied and Nonlinear Dynamics includes five interesting papers. These are devoted to numerical and experimental methods in applied and nonlinear dynamics as well as advanced applications of multibody systems and optimal control methods to dynamical systems.</p><p>Contribution <span>3</span> deals with stationary solutions in applied dynamics. Thereby a unified framework for the numerical calculation and stability assessment of periodic and quasi-periodic solutions based on invariant manifolds is presented. Paper <span>2</span> gives an overview of dynamic human body models in vehicle safety, a unique application of multibody dynamics. In paper <span>1</span>, a family of total Lagrangian Petrov-Galerkin Cosserat rod finite element formulations is presented. Paper <span>5</span> discusses continuation methods for lab experiments of nonlinear vibrations. Finally paper <span>4</span> deals with the optimal operation of dielectric elastomer wave energy converters under harmonic and stochastic excitation.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"46 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202300011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50147062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Continuation methods for lab experiments of nonlinear vibrations","authors":"Sebastian Tatzko,&nbsp;Gleb Kleyman,&nbsp;Jörg Wallaschek","doi":"10.1002/gamm.202300009","DOIUrl":"https://doi.org/10.1002/gamm.202300009","url":null,"abstract":"<p>In this work, we will give an overview of our recent progress in experimental continuation. First, three different approaches are explained and compared which can be found in scientific papers on the topic. We then show S-Curve measurements of a Duffing oscillator experiment for which we derived optimal controller gains analytically. The derived formula for stabilizing PD-controller gains makes trial and error search for suitable values unnecessary. Since feedback control introduces higher harmonics in the driving signal, we consider a harmonization of the forcing signal. This harmonization is important to reduce shaker-structure interaction in the treatment of nonlinear frequency responses. Finally, the controlled nonlinear testing and harmonization is enhanced by a continuation algorithm adapted from numerical analysis and applied to a geometrically nonlinear beam test rig for which we measure the nonlinear forced response directly in the displacement-frequency plane.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"46 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202300009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50128293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A family of total Lagrangian Petrov–Galerkin Cosserat rod finite element formulations","authors":"Simon R. Eugster,&nbsp;Jonas Harsch","doi":"10.1002/gamm.202300008","DOIUrl":"https://doi.org/10.1002/gamm.202300008","url":null,"abstract":"<p>The standard in rod finite element formulations is the Bubnov–Galerkin projection method, where the test functions arise from a consistent variation of the ansatz functions. This approach becomes increasingly complex when highly nonlinear ansatz functions are chosen to approximate the rod's centerline and cross-section orientations. Using a Petrov–Galerkin projection method, we propose a whole family of rod finite element formulations where the nodal generalized virtual displacements and generalized velocities are interpolated instead of using the consistent variations and time derivatives of the ansatz functions. This approach leads to a significant simplification of the expressions in the discrete virtual work functionals. In addition, independent strategies can be chosen for interpolating the nodal centerline points and cross-section orientations. We discuss three objective interpolation strategies and give an in-depth analysis concerning locking and convergence behavior for the whole family of rod finite element formulations.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"46 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202300008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50125423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stationary solutions in applied dynamics: A unified framework for the numerical calculation and stability assessment of periodic and quasi-periodic solutions based on invariant manifolds","authors":"Hartmut Hetzler,&nbsp;Simon Bäuerle","doi":"10.1002/gamm.202300006","DOIUrl":"https://doi.org/10.1002/gamm.202300006","url":null,"abstract":"<p>The determination of stationary solutions of dynamical systems as well as analyzing their stability is of high relevance in science and engineering. For static and periodic solutions a lot of methods are available to find stationary motions and analyze their stability. In contrast, there are only few approaches to find stationary solutions to the important class of quasi-periodic motions–which represent solutions of generalized periodicity–available so far. Furthermore, no generally applicable approach to determine their stability is readily available. This contribution presents a unified framework for the analysis of equilibria, periodic as well as quasi-periodic motions alike. To this end, the dynamical problem is changed from a formulation in terms of the trajectory to an alternative formulation based on the invariant manifold as geometrical object in the state space. Using a so-called hypertime parametrization offers a direct relation between the frequency base of the solution and the parametrization of the invariant manifold. Over the domain of hypertimes, the invariant manifold is given as solution to a PDE, which can be solved using standard methods as Finite Differences (FD), <span>Fourier-Galerkin</span>-methods (FGM) or quasi-periodic shooting (QPS). As a particular advantage, the invariant manifold represents the entire stationary dynamics on a finite domain even for quasi-periodic motions – whereas obtaining the same information from trajectories would require knowing them over an infinite time interval. Based on the invariant manifold, a method for stability assessment of quasi-periodic solutions by means of efficient calculation of <span>Lyapunov</span>-exponents is devised. Here, the basic idea is to introduce a Generalized Monodromy Mapping, which may be determined in a pre-processing step: using this mapping, the <span>Lyapunov</span>-exponents may efficiently be calculated by iterating this mapping.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"46 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202300006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50144433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamic human body models in vehicle safety: An overview","authors":"N. Fahse,&nbsp;M. Millard,&nbsp;F. Kempter,&nbsp;S. Maier,&nbsp;M. Roller,&nbsp;J. Fehr","doi":"10.1002/gamm.202300007","DOIUrl":"https://doi.org/10.1002/gamm.202300007","url":null,"abstract":"<p>Significant trends in the vehicle industry are autonomous driving, micromobility, electrification and the increased use of shared mobility solutions. These new vehicle automation and mobility classes lead to a larger number of occupant positions, interiors and load directions. As safety systems interact with and protect occupants, it is essential to place the human, with its variability and vulnerability, at the center of the design and operation of these systems. Digital human body models (HBMs) can help meet these requirements and are therefore increasingly being integrated into the development of new vehicle models. This contribution provides an overview of current HBMs and their applications in vehicle safety in different driving modes. The authors briefly introduce the underlying mathematical methods and present a selection of HBMs to the reader. An overview table with guideline values for simulation times, common applications and available variants of the models is provided. To provide insight into the broad application of HBMs, the authors present three case studies in the field of vehicle safety: (i) in-crash finite element simulations and injuries of riders on a motorcycle; (ii) scenario-based assessment of the active pre-crash behavior of occupants with the Madymo multibody HBM; (iii) prediction of human behavior in a take-over scenario using the EMMA model.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"46 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202300007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50144387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Preface to the topical issue on applied and nonlinear dynamics: Part I","authors":"Jörg Fehr,&nbsp;Kristin de Payrebrune,&nbsp;Robert Seifried","doi":"10.1002/gamm.202300005","DOIUrl":"https://doi.org/10.1002/gamm.202300005","url":null,"abstract":"The current special issue of the GAMM Mitteilungen, which is the first of a two-part series, contains several contributions on the topic of applied and nonlinear dynamics. Dynamical problems occur in a wide range of engineering systems, such as all kinds of vehicles, wind power plants, turbines, engines, machine tools or in robotics, ranging from industrial robotics to service and medical robots. Dynamical questions are also essential in the modeling of biomechanical systems, for example in the description of the (human) musculoskeletal system or in the development of human dummies for crash tests. Nowadays a wide range of analytical, numerical, data-based and experimental tools and methods exists to foster the investigation of all kinds of dynamical systems. Hereby also the issue of model reduction plays an increasingly important role. Modern dynamical systems are often active systems, thus methods from system dynamics and control theory have to be included. This important connection between these communities is also reflected in the GAMM activity group (Fachausschuss) “Dynamics and Control Theory.” Many researchers contributing to this topical issue on applied and nonlinear dynamics are members of this GAMM activity group. We are very happy that several teams of authors have accepted our invitation to report on recent developments, research highlights and emerging application areas in applied and nonlinear dynamics. The four papers in this first part of the topical issue on applied and nonlinear dynamics are devoted to the above mentioned topics. The first paper [1] presents a minimal model for investigation of the influence of equilibrium positions on brake squeal. Paper [2] deals with an interpolation-based parametric model order reduction of automotive brake systems for frequency-domain analyses. In the contribution [3] nonlinear vibration phenomena in hydrodynamically supported rotor systems are discussed. Finally the last paper [4] presents the application of stable inversion methods to flexible manipulators modeled by the absolute nodal coordinate formulation for feedforward control design.","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50137407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonlinear vibration phenomena in hydrodynamically supported rotor systems","authors":"Steffen Nitzschke,&nbsp;Elmar Woschke,&nbsp;Cornelius Strackeljan","doi":"10.1002/gamm.202300003","DOIUrl":"https://doi.org/10.1002/gamm.202300003","url":null,"abstract":"<p>It is a well-known fact, that hydrodynamically supported systems are prone to nonlinear vibrations. Their exact simulative prediction with respect to frequency and amplitude is complicated by the fact that different system properties interact. The paper at hand outlines an approach that takes all relevant influences like rigid body motions, elastic deformations, nonlinear relation between fluid film pressure and bearing kinematics as well as temperature increase due to power loss or adjacent heat sources into account as detailed as necessary. Both journal and thrust bearings are considered as they contribute to the system's stiffness and damping capabilities. The approach is applied to self-excited pad vibrations of tilting pad thrust bearings as well as the run-up simulation of a turbocharger rotor under different axial loads. Both models are validated against measurements.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202300003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50137406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A minimal model for the influence of equilibrium positions on brake squeal","authors":"Sebastian Koch,&nbsp;Nils Gräbner,&nbsp;Utz von Wagner","doi":"10.1002/gamm.202300001","DOIUrl":"https://doi.org/10.1002/gamm.202300001","url":null,"abstract":"<p>The phenomenon brake squeal has been an ongoing topic for decades, both in the automotive industry and in science. Although there is agreement on the excitation mechanism of brake squeal, namely self-excitation due to frictional forces between the disk and the pad, in the subject of squeal it is very complex to discover all relevant effects and to take them into account. Several of these problems are related to nonlinearities, for example, in the contact between pad and disk or drum or in the behavior of the brake pad material. One of these nonlinear effects, which has been almost completely neglected so far, is that the brake can engage, mainly due to the bushing and joint elements within the brake, different equilibrium positions. This in fact has serious influence on the noise behavior as shown in experimental studies. For example, it is observed in experiments that, despite identical operating parameters, squeal sometimes occurs and sometimes not. In initial experimental studies, this could be related to the engaged equilibrium position. Following these experimental studies, the present paper introduces a minimal model by extending the well-known minimal model by Hoffmann et al. by corresponding elements and nonlinearities allowing the system to engage different equilibrium positions. As will be presented, the stability behavior strongly depends on the engaged equilibrium position. Therefore, the minimal model represents the key experimentally observed issues. Additionally, a limit cycle behavior can also be observed.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202300001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50116537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Application of stable inversion to flexible manipulators modeled by the absolute nodal coordinate formulation","authors":"Svenja Drücker,&nbsp;Robert Seifried","doi":"10.1002/gamm.202300004","DOIUrl":"https://doi.org/10.1002/gamm.202300004","url":null,"abstract":"<p>Compared to conventional robots, flexible manipulators offer many advantages, such as faster end-effector velocities and less energy consumption. However, their flexible structure can lead to undesired oscillations. Therefore, the applied control strategy should account for these elasticities. A feedforward controller based on an inverse model of the system is an efficient way to improve the performance. However, unstable internal dynamics arise for many common flexible robots and stable inversion must be applied. In this contribution, an approximation of the original stable inversion approach is proposed. The approximation simplifies the problem setup, since the internal dynamics do not need to be derived explicitly for the definition of the boundary conditions. From a practical point of view, this makes the method applicable to more complex systems with many unactuated degrees of freedom. Flexible manipulators modeled by the absolute nodal coordinate formulation (ANCF) are considered as an application example.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202300004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50116534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Interpolation-based parametric model order reduction of automotive brake systems for frequency-domain analyses","authors":"Fabian Matter,&nbsp;Igor Iroz,&nbsp;Peter Eberhard","doi":"10.1002/gamm.202300002","DOIUrl":"https://doi.org/10.1002/gamm.202300002","url":null,"abstract":"<p>Brake squeal describes noise with different frequencies that can be emitted during the braking process. Typically, the frequencies are in the range of 1 to 16 kHz. Although the noise has virtually no effect on braking performance, strong attempts are made to identify and eliminate the noise as it can be very unpleasant and annoying. In the field of numerical simulation, the brake is typically modeled using the Finite Element method, and this results in a high-dimensional equation of motion. For the analysis of brake squeal, gyroscopic and circulatory effects, as well as damping and friction, must be considered correctly. For the subsequent analysis, the high-dimensional damped nonlinear equation system is linearized. This results in terms that are non-symmetric and dependent on the rotational frequency of the brake rotor. Many parameter points to be evaluated implies many evaluations to determine the relevant parameters of the unstable system. In order to increase the efficiency of the process, the system is typically reduced with a truncated modal transformation. However, with this method the damping and the velocity-dependent terms, which have a significant influence on the system, are neglected for the calculation of the eigenmodes, and this can lead to inaccurate reduced models. In this paper, we present results of other methods of model order reduction applied on an industrial high-dimensional brake model. Using moment matching methods combined with parametric model order reduction, both the damping and the various parameter-dependent terms of the brake model can be taken into account in the reduction step. Thus, better results in the frequency domain can be obtained. On the one hand, as usual in brake analysis, the complex eigenvalues are evaluated, but on the other hand also the transfer behavior in terms of the frequency response. In each case, the classical and the new reduction method are compared with each other.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202300002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50146353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}