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Motivated by the current demands in high-performance structural analysis, and by a need to better model systems with localized nonlinearities, analysts have developed a number of different approaches for modeling and simulating the dynamics of a bolted-joint structure. However, it is still unclear which approach might be most effective for a given system or set of conditions. To better grasp their similarities and differences, this paper presents a numerical benchmark that assesses how well two diametrically differing joint modeling approaches -a time-domain wholejoint approach and a frequency-domain node-to-node approach -predict and simulate a mechanical joint. These approaches were applied to model the Brake-Reuß beam, a prismatic structure comprised of two beams with a bolted joint interface. The two approaches were validated first by updating the models to reproduce the nonlinear response for the first bending mode of an experimental Brake-Reuß beam. Afterwards, the tuned models were evaluated on their ability to predict the nonlinearity in the dynamic response for the second and third bending modes. The results show that the two joint modeling approaches perform about equally as well in simulating the Brake-Reuß beam. In addition, the exposition highlights improvements that were made in each method during the course of this work and reveal further challenges in advancing the state-of-the-art.

In this paper, a validation approach for a turbine blade component test with frictional contacts is presented. The investigated system is derived from a high cycle fatigue test setup, where a turbine blade is base-excited in the clamped blade foot. The setup has been extended by laser scanning vibrometry, a force measurement platform, and feedback-controllers for both force level and phase. At first, a conventional validation of a linearized model of the system is performed at low amplitudes to ensure the correct modal basis for model reduction. After that, the nonlinear behavior around the fundamental mode is analyzed in detail. Frequency responses for different excitation levels and backbone curves are measured and assessed regarding repeatability and robustness of the measurement chain. Among other effects, overhanging branches of the frequency response were encountered. Nonlinear, amplitude-dependent modal frequencies and damping ratios are identified from the backbone curves. These data form the validation basis for a reduced-order model of the system considering nonlinear friction in the blade foot. The correlation of measurement and simulation is investigated and advantages and shortcomings of the different validation metrics are discussed.

It is well-known that nonlinear dry friction damping has the potential to bound the otherwise unboundedly growing vibrations of self-excited structures. An important technical example are the flutter-induced friction-damped limit cycle oscillations of turbomachinery blade rows. Due to symmetries, natural frequencies are inevitably closely spaced and they can generally be multiples of each other. Not much is known on the nonlinear dynamics of self-excited friction-damped systems in the presence of such internal resonances. In this work, we analyze this situation numerically by regarding a two-degree-of-freedom system. We demonstrate that in the case of closely-spaced natural frequencies, the self-excitation of the lower-frequency mode gives rise to non-periodic oscillations, and the occurrence of unbounded behavior well before reaching the maximum friction damping value. If the system is close to a 1:3 internal resonance, limit cycles associated with much higher frictional damping appear, however, most of these are unstable. If more than one mode is subjected to self-excitation, the maximum resistance against self-excitation is at least given by the damping capacity of the most weakly friction-damped mode. These results are of high technical relevance, as the prevailing practice is to analyze only periodic limit states and argue the stability solely by the slope of the damping-amplitude curve. Our results demonstrate that this practice leads to considerable mis- and overestimation of the resistance against self-excitation, and a more rigorous stability analysis is required.

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