Eigenpath analysis of rotating mechanical systems based on ALE formulation - Weidauer, Tim; Willner, Kai (PAMM, Volume 16, Issue 1, 2016)
When bodies rotate they are subjected to velocity-dependent gyroscopic and inertia effects, which alter the dynamic behaviour of the structure. Analysing its eigenpairs consisting of eigenvalues and eigenvectors, these parameter-dependent changes can be tracked as eigenpaths by means of a continuation algorithm as in [1]. For rotationally symmetric structures an ALE approach (ALE = Arbitrary LAGRANGIAN-EULERIAN) for the finite element method as described in [2] can be employed. It allows simulating rotational influences on the body without actually having to rotate the mesh of the structure itself. This still-standing mesh facilitates further steps like coupling of other, static components with the rotating body. The combination of ALE with eigenpath analysis including an example is described in the following. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
Keywords: eigenpath; continuation; rotation; ALE

Model reduction of gyroscopic systems in ALE formulation with and without non-linearities - Weidauer, Tim; Willner, Kai (PAMM, Volume 18, 2018)
Rotating systems are subject to gyroscopic inﬂuences which alter their dynamic behaviour. The Arbitrary Lagrangian Eulerian (ALE) formulation is a popular approach for related models, e.g. for the simulation of tire rolling contact. It allows for decoupling the rotational guiding motion from the relative deformation of the rotating structure. At the same time it complicates contact computations as the relative displacement between two material particles is not tracked naturally by the ALE observer. Model reduction techniques for (non-linear) systems face additional challenges in this context, of which a variety is discussed here for common approaches such as the Second order modal truncation, the Krylov subspace method or the Craig-Bampton method.<br
Keywords: ALE; Model reduction; gyroscopic system; contact

Numerical and experimental modal analysis of structures under gyroscopic inﬂuence in ALE formulation - Weidauer, Tim; Willner, Kai (ISMA2018, 2018)
A test set-up for the modal analysis of gyroscopic, rotationally symmetric systems is presented. It employs laser Doppler vibrometry along with automatic impulse excitation installed on a rotary table and is applied to a glass structure rotating about its ﬁgure axis. The effects of gyroscopic inﬂuences on the modal behaviour such as the split of eigenfrequencies and the treatment of complex eigenmodes as travelling waves are deduced analytically and shown experimentally. Finally numerical computations using the Arbitrary-Lagrangian-Eulerian (ALE) ﬁnite element formulation separating the rigid body rotation from the mesh deformation are conducted. With the combination of analytical, experimental and numerical analysis a broad overview of modal characteristics of gyroscopic systems is given.<br

Numerical treatment of frictional contact in ALE formulation for disc brake assemblies - Weidauer, Tim; Willner, Kai (Mechanical Systems and Signal Processing, 2020)
The Arbitrary-LAGRANGIAN-EULERIAN (ALE) formulation is a popular approach for finite element (FE) models governed by large rigid body movement. It facilitates the decomposition of guiding motions and relative deformation inside the model by considering the main motion of the system in the form of a material flow inside the FE mesh. This way, similar to fluid dynamics, an observer focused on spatial positions rather than individual material particles is introduced. Among others, this approach serves as an established tool in the simulation of tire rolling contact and its dynamics. However, while allowing for specific mesh refinement and simplifying issues such as finite displacements due to rigid body motions, it complicates contact computations. The history of contacting particles is not inherently tracked, demanding a special treatment of their relative displacement for evaluating their frictional contact state. The handling of stationary problems in this context is well-studied for the examples of elastic-rigid rolling contact, including inelastic material properties and thermo-mechanical coupling. This work attends to the remaining area of frictional contact in transient ALE problems and extends the methods towards elastic-elastic contact coupling in a three dimensional framework. To this end, classic Zero-Thickness contact elements, whose application in these surroundings is enabled by the relative kinematic ALE framework in the first place, are extended towards ALE compatibility. The proposed approach involves a slip-based contact formulation including inelastic slip variables and is applied in the field of disc brake assemblies. In here, several stationary and transient studies of emerging contact patterns and limit cycles are accomplished, outlining the capabilities of the proposed implementation.
CRIS-Team Scopus Importer:2020-06-09
Keywords: Arbitrary-LAGRANGIAN-EULERIAN (ALE); Disc brake; Friction oscillator; Limit cycle; Transient frictional contact; Zero-Thickness element

Reduced Order Modelling for Non-Linear Rotating Systems in ALE Formulation with Contact - Weidauer, Tim; Willner, Kai (Nonlinear Dynamics, Volume 1; Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics 2018, 2018)
One approach for the simulation of rotating systems is the Arbitrary-Lagrangian-Eulerian (ALE) finite element formulation, which is well-established in the field of rolling contact mechanics for tires. With this formulation the rotational motion is handled from an Eulerian viewpoint and thus can be separated from the occurring Lagrangian deformation of the finite element mesh. In this context of (non-linear) systems undergoing gyroscopic and/or contact forces, e.g. for tires or disc brakes, model reduction techniques such as the Second order modal truncation, the Krylov subspace technique and the Craig-Bampton method are employed and analysed in their applicability.
Keywords: Gyroscopic system; ALE; non-linear dynamics; model order reduction; contact