Experimental analysis of the TRC benchmark system

The Tribomechadynamics Research Challenge (TRC) was a blind prediction of the vibration behavior of a thin plate clamped on two sides using bolted joints. The first bending mode's natural frequency and damping ratio were requested as function of the amplitude, starting from the linear regime until high levels, where both frictional contact and nonlinear bending-stretching coupling become relevant. The predictions were confronted with experimental results in a companion paper; the present article addresses the experimental analysis of this benchmark system. Amplitude-dependent modal data was obtained from phase resonance and response controlled tests. An original variant of response controlled testing is proposed: Instead of a fixed frequency interval, a fixed phase interval is analyzed. This way, the high excitation levels required outside resonance, which could activate unwanted exciter nonlinearity, are avoided. Consistency of testing methods is carefully analyzed. Overall, these measures have permitted to gain high confidence in the acquired modal data. The different sources of the remaining uncertainty were further analyzed. A low reassembly-variability but a moderate time-variability were identified, where the latter is attributed to some thermal sensitivity of the system. Two nominally identical plates were analyzed, which both have an appreciable initial curvature, and a significant effect on the vibration behavior was found depending on whether the plate is aligned/misaligned with the support structure. Further, a 1:2 nonlinear modal interaction with the first torsion mode was observed, which only occurs in the aligned configurations.

Nonlinear damping quantification from phase-resonant tests under base excitation

The present work addresses the experimental identification of amplitude-dependent modal parameters (modal frequency, damping ratio, Fourier coefficients of periodic modal oscillation). Phase-resonant testing has emerged as an important method for this task, as it substantially reduces the amount of data required for the identification compared to conventional frequency-response testing at different excitation/response levels. In the case of shaker-stinger excitation, the applied excitation force is commonly measured in order to quantify the amplitude-dependent modal damping ratio from the phase-resonant test data. In the case of base excitation, however, the applied excitation force is challenging or impossible to measure. In this work we develop an original method for damping quantification from phase-resonant tests. It relies solely on response measurement; it avoids the need to resort to force measurement. The key idea is to estimate the power provided by the distributed inertia force imposed by the base motion. We develop both a model-free and a model-based variant of the method. We validate the developed method first in virtual experiments of a friction-damped and a geometrically nonlinear system, and then in a physical experiment involving a thin beam clamped at both ends via bolted joints. We conclude that the method is highly robust and provides high accuracy already for a reasonable number of sensors.