Universität Stuttgart

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Institute: search.filters.UBSInstitut.Institut für Nichtlineare MechanikPublication Type: search.filters.UBSTyp.Zeitschriftenartikel

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    Easy scalable, low-cost open-source magnetic field detection system for evaluating low-field MRI magnets using a motion-tracked robot
    (2025) Povolni, Pavel; Bendfeld, Robin; Maltsev, Sergej; Samlow, Judith; Glang, Felix; Valsala, Praveen Iyyappan; Goerner, Dominique; Bosch, Dario; Mueller, Sebastian; Birk, Florian; Buckenmaier, Kai; Scheffler, Klaus
    Objective. Low-field magnetic resonance imaging is currently developing into a valuable diagnostic tool due to its simplicity of magnet array designs. Particularly, this allows the development of scanners as part of educational workshops, thus ensuring knowledge transfer and empowering local scientists to design tailored solutions for specific local problems. To obtain the maximum performance, the magnet needs to be shimmed requiring an automated system measuring the spatial magnetic field distribution. Methods. A self-designed measuring probe based on commercial integrated Hall sensor chips is used and optimized by calibrating it in an easy-to-build calibration system. For positioning of the sensor, a low-cost five-degree-of-freedom robot arm is used and improved by camera-based motion tracking for precise localization of the sensor. Results. The system is able to map the field of a 45mT-Halbach desktop MR magnet, as well as a self-designed x-gradient (used inside the magnet) with an efficiency of 2mT/m/A. The built-up Hall sensor demonstrates a level of precision that is competitive with commercial sensors. The entire positioning system can be freely scaled to accommodate larger designs by adjusting the kinematics. Conclusion. The presented system is demonstrated to be comparable to already established measurement systems, while the costs, setup times, and mapping duration are greatly reduced.
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    A nonsmooth generalized‐alpha method for mechanical systems with frictional contact
    (2021) Capobianco, Giuseppe; Harsch, Jonas; Eugster, Simon R.; Leine, Remco I.
    In this article, the existing nonsmooth generalized‐α method for the simulation of mechanical systems with frictionless contacts, modeled as unilateral constraints, is extended to systems with frictional contacts. On that account, we complement the unilateral constraints with set‐valued Coulomb‐type friction laws. Moreover, we devise a set of benchmark systems, which can be used to validate numerical schemes for mechanical systems with frictional contacts. Finally, this set of benchmarks is used to numerically assert the properties striven for during the derivation of the presented scheme. Specifically, we show that the presented scheme can reproduce the dynamics of the frictional contact adequately and no numerical penetration of the contacting bodies arises - a big issue for most popular time‐stepping schemes such as the one of Moreau. Moreover, we demonstrate that the presented scheme performs well for multibody systems containing flexible parts and that it allows general parametrizations such as the use of unit quaternions for the rotation of rigid bodies.
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    Hill-type stability analysis of periodic solutions of fractional-order differential equations
    (2026) Haacker, Paul-Erik; Leine, Remco I.; Chaudhary, Renu; Diethelm, Kai; Schmidt, André; Hashemishahraki, Safoura
    This paper explores stability properties of periodic solutions of (nonlinear) fractional-order differential equations (FODEs). As classical Caputo-type FODEs do not admit exactly periodic solutions, we propose a framework of Liouville-Weyl-type FODEs, which do admit exactly periodic solutions and are an extension of Caputo-type FODEs. Local linearization around a periodic solution results in perturbation dynamics governed by a linear time-periodic differential equation. In the classical integer-order case, the perturbation dynamics is therefore described by Floquet theory, i.e. the exponential growth or decay of perturbations is expressed by Floquet exponents which can be assessed using the Hill matrix approach. For fractional-order systems, however, a rigorous Floquet theory is lacking. Here, we explore the limitations when trying to extend Floquet theory and the Hill matrix method to linear time-periodic fractional-order differential equations (LTP-FODEs) as local linearization of nonlinear fractional-order systems. A key result of the paper is that such an extended Floquet theory can only assess exponentially growing solutions of LTP-FODEs. Moreover, we provide an analysis of linear time-invariant fractional-order systems (LTI-FODEs) with algebraically decaying solutions and show that the inaccessibility of decaying solutions through Floquet theory is already present in the time-invariant case.
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    A family of total Lagrangian Petrov-Galerkin Cosserat rod finite element formulations
    (2023) Eugster, Simon R.; Harsch, Jonas
    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.
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    Asymmetric vibro-impact nonlinear energy sink with dry friction : an impact map approach
    (2025) Youssef, Balkis; Karoui, A. Yassine; Leine, Remco I.
    This paper examines the dynamics of a vibro-impact nonlinear energy sink (VI-NES) using a generalized impact map approach. The study incorporates asymmetry and dry friction, reflecting realistic conditions. The proposed method identifies all periodic solutions and determines their stability, and is applicable to various VI-NES configurations, including horizontal and vertical orientations. Numerical results validate prior findings for symmetric frictionless cases and extend them to include frictional and asymmetric dynamics, providing a powerful tool for optimizing the performance of VI-NES in vibration mitigation.
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    The “Fluid Jacobian” : modeling force-motion relationships in fluid-driven soft robots
    (2024) Remy, C. David; Brei, Zachary; Bruder, Daniel; Remy, Jan; Buffinton, Keith; Gillespie, R. Brent
    In this paper, we introduce the concept of the Fluid Jacobian, which provides a description of the power transmission that operates between the fluid and mechanical domains in soft robotic systems. It can be understood as a generalization of the traditional kinematic Jacobian that relates the joint space torques and velocities to the task space forces and velocities of a robot. In a similar way, the Fluid Jacobian relates fluid pressure to task space forces and fluid flow to task space velocities. In addition, the Fluid Jacobian can also be regarded as a generalization of the piston cross-sectional area in a fluid-driven cylinder that extends to complex geometries and multiple dimensions. In the following, we present a theoretical derivation of this framework, focus on important special cases, and illustrate the meaning and practical applicability of the Fluid Jacobian in four brief examples.
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    Model reduction of a periodically forced slow-fast continuous piecewise linear system
    (2023) Karoui, A. Yassine; Leine, Remco I.
    In this paper, singular perturbation theory is exploited to obtain a reduced-order model of a slow-fast piecewise linear 2-DOF oscillator subjected to harmonic excitation. The nonsmooth nonlinearity of piecewise linear nature is studied in the case of bilinear damping as well as with bilinear stiffness characteristics. We propose a continuous matching of the locally invariant slow manifolds obtained in each subregion of the state space, which yields a reduced-order model of the same nature as the full dynamics. The frequency-response curves obtained from the full system and the reduced-order models suggest that the proposed reduction method can capture nonlinear behaviors such as super- and subharmonic resonances.
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    Nonunit quaternion parametrization of a Petrov-Galerkin Cosserat rod finite element
    (2023) Harsch, Jonas; Eugster, Simon R.
    The application of the Petrov-Galerkin projection method in Cosserat rod finite element formulations offers significant advantages in simplifying the expressions within the discrete virtual work functionals. Moreover, it enables a straight‐forward and systematic exchange of the ansatz functions, specifically for centerline positions and cross‐section orientations. In this concise communication, we present a total Lagrangian finite element formulation for Cosserat rods that attempts to minimize the number of required theoretical concepts. The chosen discretization preserves objectivity and allows for large displacements/rotations and for large strains. The orientation parametrization with nonunit quaternions results in a singularity‐free formulation.
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    State observers for the time discretization of a class of impulsive mechanical systems
    (2022) Preiswerk, Pascal V.; Leine, Remco I.
    In this work, we investigate the state observer problem for linear mechanical systems with a single unilateral constraint, for which neither the impact time instants nor the contact distance is explicitly measured. We propose to attack the observer problem by transforming and approximating the original continuous‐time system by a discrete linear complementarity system (LCS) through the use of the Schatzman-Paoli scheme. From there, we derive a deadbeat observer in the form of a linear complementarity problem. Sufficient conditions guaranteeing the uniqueness of its solution then serve as observability conditions. In addition, the discrete adaptation of an existing passivity‐based observer design for LCSs can be applied. A key point in using a time discretization is that the discretization acts as a regularization, that is, the impacts take place over multiple time steps (here two time steps). This makes it possible to render the estimation error dynamics asymptotically stable. Furthermore, the so‐called peaking phenomenon appears as singularity within the time discretization approach, posing a challenge for robust observer design.
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    Stability of rigid body motion through an extended intermediate axis theorem : application to rockfall simulation
    (2021) Leine, Remco I.; Capobianco, Giuseppe; Bartelt, Perry; Christen, Marc; Caviezel, Andrin
    The stability properties of a freely rotating rigid body are governed by the intermediate axis theorem, i.e., rotation around the major and minor principal axes is stable whereas rotation around the intermediate axis is unstable. The stability of the principal axes is of importance for the prediction of rockfall. Current numerical schemes for 3D rockfall simulation, however, are not able to correctly represent these stability properties. In this paper an extended intermediate axis theorem is presented, which not only involves the angular momentum equations but also the orientation of the body, and we prove the theorem using Lyapunov’s direct method. Based on the stability proof, we present a novel scheme which respects the stability properties of a freely rotating body and which can be incorporated in numerical schemes for the simulation of rigid bodies with frictional unilateral constraints. In particular, we show how this scheme is incorporated in an existing 3D rockfall simulation code. Simulations results reveal that the stability properties of rotating rocks play an essential role in the run-out length and lateral spreading of rocks.