Browsing by Author "Monjaraz Tec, Carlo Daniel"

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Numerical prediction of frictional vibro-impacts : combining massless boundaries and component mode synthesis
(2025) Monjaraz Tec, Carlo Daniel; Krack, Malte (Prof. Dr.-Ing.)
Vibro-impact processes are a subset of nonlinear vibrations. They involve the essential interaction of instant contacts and vibrations. Their correct prediction and experimental characterization, using dedicated simulation and testing methods, enlarge the design space and robustness of technologies such as Impact Energy Scatterers. Numerical predictions of vibro-impact have contradicting requirements. A fine spatial and time discretization is needed; however, this yields large model problem sizes which impede long-term simulation. Frequency domain solutions are not applicable for non-periodic states, which are likely to be present in these vibrations. Furthermore, the existing time-domain methods rely on empirical parameters for contact modeling which reduces the predictive nature of the simulation. This thesis aims to develop and validate a time-domain simulation method for frictional vibro-impact, which is useful for industrial applications. The novel core concept of the method is to unite the concept of massless boundary (originating from computational mechanics) and the idea of component mode synthesis (standard in structural dynamics) by exploiting the key advantages of each. The massless boundaries allow a quasi-static solution of the contact forces, leading to stable contact enforcement, and are numerically more robust than conventional approaches. Until now, massless boundaries have been implemented in finite element models, but such models are still too large, and thus unsuitable to simulate long steady-states. Therefore, model-order reduction with component mode synthesis is quintessential. The developed method is based on four key components: an underlying finite element model, a time integration scheme compatible with massless boundaries, a solution for dynamic normal and frictional contact enforcement, and a component mode synthesis method compatible with massless boundaries. The semi-explicit time integration scheme is developed to work with singular mass matrices, resulting in a scheme that solves contacts quasi-statically and prioritizes energy conservation. Normal and frictional contacts are modeled as set-valued laws and imposed locally within the spatially resolved contact domain. The finite element model is reduced using the MacNeal method and a mass-boundary compatible variant of the Craig-Bampton method derived in this work. This framework limits the method to linear elasticity and kinematics, while addressing nonsmooth (and therefore nonlinear) contact behavior. Numerical benchmarks are used to evaluate the method. The kinematics, energy conservation, and computational cost of the conventional mass-carrying models and the proposed method are compared. A variant of the Moreau time integration scheme and the harmonic balance method in conjunction with a dynamic Lagrangian formulation are considered. The results show that the massless boundary models have better energy conservation and convergence properties while reducing the computational time by at least one order of magnitude. As a first validation step, experimental measurements are used to evaluate the predicted post-impact velocity response and its modal energy distribution. A metal sphere impacts a steel beam, where the velocity response of the beam is measured for a single collision. The measurements are compared with predictions obtained using two different approaches: state-of-the-art finite element analysis and the proposed method. The proposed method reduces the numerical effort by 3-4 orders of magnitude compared to the finite element model without compromising the excellent agreement with the measurements. Finally, for a second validation step, two cantilever beams subjected to frictional impacts at the free end are measured experimentally. The beams have similar geometries and close but unequal natural frequencies. The underlying linear model is updated based on the natural frequencies and damping ratios identified in the non-impact regime. The nonlinear simulation of the steady-state response to forward and backward stepped-sine excitation is compared with measurements. The results are in excellent agreement with respect to amplitude response, frequency content, and contact activity, especially considering the uncertainty associated with the observed material loss in the contact region and the nonlinear behavior of the clamping.