Daniel J. Rixen's research while affiliated with Technische Universität München and other places

In experimental dynamic substructuring, coupling of substructures sharing a line-or surface-like interface proves to be a challenge due to the difficulties in interface modelling. Modelling a high number of degrees of freedom at the common interface can be too stringent when imposing compatibility and equilibrium conditions , thereby causing redundancy and ill-conditioning. To mitigate the effects of overdetermination and experimental errors, that can lead to a high error amplification, several techniques have been developed, proposing different reduction spaces to weaken the interface conditions. This work investigates reduction space definitions in dynamic substructuring for coupling continuous interfaces. In particular, a comparative investigation of three established techniques, namely the frequency-based modal constraints for fixture and subsystem, singular vector transformation, and virtual point transformation, is conducted within the frequency domain. The feasibility of all approaches is supported by an experimental case study, which can guide practitioners in selecting a suitable approach for their specific needs.

Artificial neural networks (NNs) are a type of machine learning (ML) algorithm that mimics the functioning of the human brain to learn and generalize patterns from large amounts of data without the need for explicit knowledge of the system's physics. Employing NNs to predict time responses in the field of mechanical system dynamics is still in its infancy. The aim of this contribution is to give an overview of design considerations for NN-based time stepping schemes for non-linear mechanical systems. To this end numerous design parameters and choices available when creating a NN are presented and their effects on the accuracy of predicting the dynamics of non-linear mechanical systems are discussed. The findings are presented with the support of three test cases: a double pendulum, a duffing oscillator, and a gyroscope. Factors such as initial conditions, external forcing as well as system parameters were varied to demonstrate the robustness of the proposed approaches. Furthermore, practical design considerations such as noise- sensitivity as well as the ability to extrapolate are examined. Ultimately, we are able to show that NNs are capable of functioning as a time-stepping schemes for non-linear mechanical system dynamics applications.

Dynamic substructuring, especially the frequency-based variant (FBS) using frequency response functions (FRF), is gaining in popularity and importance, with countless successful applications, both numerically and experimentally. One drawback, however, is found when the responses to shocks are determined. Numerically, this might be especially expensive when a huge number of high-frequency modes have to be accounted for to correctly predict response amplitudes to shocks. In all cases, the initial response predicted using frequency-based substructuring might be erroneous, due to the forced periodization of the Fourier transform. This drawback can be eliminated by completely avoiding the frequency domain and remaining in the time domain, using the impulse-based substruc-turing method (IBS), which utilizes impulse response functions (IRF). While this method has already been utilized successfully for numerical test cases, none of the attempted experimental applications were successful. In this paper, an experimental application of IBS to rods considered as one-dimensional is tested in the context of shock analysis, with the goal of correctly predicting the maximum driving point response peak. The challenges related to experimental IBS applications are discussed and an improvement attempt is made by limiting the frequency content considered through low-pass filtering and downsampling. The combination of a purely time domain based estimation procedure for the IRFs and the application of low-pass filtering with downsampling to the measured responses enabled a correct prediction of the initial shock responses of the rods with IBS experimentally, using displacements, velocities and accelerations.

A successful application of experimental substructuring in the frequency domain relies heavily on an adequate choice/number of measured degrees of freedom as well as high-quality acquisitions. The construction of the FRF dataset is commonly performed via impact testing using a modal hammer and accelerometers. In this scenario, the use of intrusive sensors could lead to undesired dynamic effects and represents a serious hindrance to a spatially-rich design of experiments. This paper investigates the use of full-field non-intrusive measurements for Frequency Based Substructuring applications. The use of a high-speed camera enables remote sensing and significantly enhance the measured space. The high level of noise arising from the camera data is treated using both a modal and a singular value-based filtering approach. A sensitivity study of image acquisition and processing parameters is also provided. Benefits, limitations, and potential of the presented strategy are shown in the context of a substructuring coupling example.

Dynamic substructuring enables to analyze the dynamics of complex systems on a substructure level. In experimental context , a successful substructuring prediction relies on reliable and accurate measurement acquisitions as well as proper design of experiments and description of the interface dynamics. Depending on the quality and quantity of information stored, system dynamics , frequency range of interest and interface connection, several strategies based on directly estimated transfer functions or identified modal properties may be adopted. In this paper, a frequency-based substructuring and a modal-based substructuring approach are compared on a coupling prediction of a continuous/flexible-like connection on the SEM Dynamic Substructuring round robin testbed. Focus is on measurement setup (e.g. design of experiments.. .), experimental modeling of the interface (e.g. discretization, reduction basis, additional fixtures.. .) and data processing (e.g. filtering, selection, reconstruction.. .) to ensure a robust substructuring prediction given the assembly configuration and dynamics. Benefits and drawbacks of the applied strategies are highlighted, as well as key assumptions and methodological differences. Both a numerical and experimental application are presented.

As industries strive for enhanced reliability and efficiency in product optimization, virtual prototyping has gained prominence over its physical counterpart. Advanced engineering simulation tools have thus become essential for addressing the complexities of today's technology-driven world. The field of rotordynamics plays a critical role in the design and analysis of rotating machinery as they are widely found in various engineering devices for, e.g., energy transmission. Over the years, numerous techniques have been developed to capture the dynamic behavior of rotors. Among these, continuum finite element formulations have emerged as powerful and generic tools. Nevertheless, rotordynamics analysts often rely on simple models based on beam and rigid elements. Moreover, a variety of different formulations and implementations in commercial software exist but their relationship to one another is oftentimes not clear. This work, therefore, presents an overview of rotordynamics finite element formulations based on continuum elements for generic geometries from a structural and multibody dynamics perspective. A derivation of the equations of motion for rotordynamic analyses according to a nodal-based floating frame of reference formulation is provided. Throughout the contribution, emphasis is placed on the comparison and evaluation of different modeling techniques and solution strategies, especially with respect to standard FE commercial softwares approaches. The discussion includes modal and steady-state analyses.

Raw time series of impact measurements for materials and manual impact hammer tips as labeled. Displacements and velocities are stored as ’H11’ (drivingpoint responses) and ’H21’ (opposing side), where responses have the shape [time points, quantity, impact number] and first quantity = displacements, second quantity = velocities. Accelerations are stored in ’acc’, with the shape [time points, dof, impact number], where dof = [S1_X, S1_Y, S1_Z, S2_X, S2_Y, S2_Z] with S1 on driving point side and S2 opposite, x and y responses unused and not included. Download of measurement data available through mediaTUM: https://dataserv.ub.tum.de/index.php/s/m1729648

Hubs, bearings and other rotor components can be connected to rotor shafts with connections that are mechanically locked, friction-based, bonded or a combination of these. In order to create accurate, predictive models of rotor systems, the stiffness and damping or the dynamics of these connections must be known in advance. Substructuring techniques provide methods for the identification of linear joints. Linear joint identification techniques have been presented for some engineering connections like bolted joints or rubbers. This contribution presents a workflow to identify shaft-to-hub connection dynamics on the example of a friction-based connection via cone-clamping elements. A system with two parts connected by the clamping element is designed and frequency-response functions (FRFs) are measured on the assembly and on the individual parts. Using a virtual point transformation the dynamics are projected in a collocated connection point in 6 degrees of freedom and quasi-static and dynamic substructuring is used to isolate the connection element. Stiffness is identified from the isolated joint. The methodology is validated by comparing re-synthesized FRFs on the test structure, giving good agreement for some directions.

The FETI-method is well known for its scalability and applicability to nonlinear structural dynamics [3, 4].