PSI - Issue 73

Marek Kawulok et al. / Procedia Structural Integrity 73 (2025) 51–57 Marek Kawulok et al. / Structural Integrity Procedia 00 (20 2 5) 000 – 000

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1. Introduction Mechanical vibrations are one of the important external factors to which building structures are exposed. Their effects may cause discomfort to people who use the structure, limit the operation of sensitive equipment, or, in extreme cases, damage or collapse the structure. The increasing size of structures, the greater emphasis on human comfort, and stricter standards require effective solutions to the problem of vibrations. Unfortunately, vibration cannot be completely avoided, but its effects can be significantly reduced by using appropriate damping mechanisms. Damping mechanisms can generally be categorised as passive, active, semi-active, and hybrid systems (Elias and Matsagar, 2017). Among these, passive absorbers remain the most widely used type. A representative example is the tuned mass damper, which includes the ball vibration absorber. This device consists of two main components, namely a supporting bowl that serves as the surface for the rolling motion of a ball. The absorber has been gaining popularity mainly due to its robustness, low maintenance requirements, and relatively compact design. Additional advantages include its tunability over a wide frequency range and the possibility of various configurations. However, this type of absorber also has difficulties such as motion instability, bifurcation, and auto-parametric oscillations. (Náprstek et al., 2013; Náprstek and Fischer, 2020). Numerical simulations of the absorber response under harmonic excitation further reveal the growing influence of nonlinear effects and the emergence of unstable solution regions. The results of the simulations also reveal a softening effect in the resonance curves (Kawulok et al., 2024). These findings underscore the need for further analysis of the absorber behaviour, both through numerical modelling and experimental investigations. Numerical simulations represent an effective tool for obtaining information about the behaviour of dynamic systems defined by equations of motion. However, their formulation often involves some simplifications that simplify the work during analytical derivation but may cause inaccuracies when it comes to describing the behaviour of the physical system. Therefore, it is essential to validate the simulation results using experimental measurements. These measurements provide data on the actual response of physical models and can also reveal dynamic characteristics not fully captured by the mathematical model. Based on such experimental insights, the numerical models can be further refined, improving their accuracy and predictive capabilities. One of the key parameters affecting the response of a dynamic system is damping, which primarily affects the rate and magnitude of the amplitude decay. Among the most used damping models in engineering applications are viscous damping and Coulomb (friction) damping (Chopra, 1995). To accurately describe and predict the complex behaviour of vibration absorbers, it is essential to precisely identify the damping characteristics involved. This identification is critical for developing mathematical models that reflect the true physics of the system, moving beyond oversimplified assumptions. Viscous damping models, although widely used for their mathematical simplicity, constitute an extreme simplification and may fail to accurately represent the complex energy dissipation mechanisms occurring in real absorbers. Therefore, a more precise understanding and modelling of damping can significantly improve the reliability of analytical and numerical predictions. The aim of this contribution is to identify the damping model that most accurately captures the amplitude decay observed in free oscillation experiments. The experiment was recorded on video, and the position of the ball centre was obtained through post-processing of the footage. The motion was restricted to a planar trajectory and two types of surfaces, a smooth wooden track and a modified track with attached rubber tubing, were examined. In the first stage of the analysis, the logarithmic decrement and damping ratio were calculated based on the full response from the initial to the final amplitude. The analysis was further extended by fitting the sequence of peak amplitudes using both viscous and Coulomb damping models. The quality of each fit was evaluated using the coefficient of determination and the root mean square error, allowing a comparison of the models in terms of their ability to describe the damping

behaviour of the system. 2. Experimental setup

The experimental setup designed for this study comprises three primary components. The first is a steel frame fitted with linear rails and a movable trolley, which has two wheels on one side and one wheel on the other side. This carriage can be connected to a harmonic exciter during forced vibration experiments. However, for the purposes of this contribution, which focusses on free vibration, mechanical stoppers were installed to prevent the trolley from