PSI - Issue 77

Job S. Silva et al. / Procedia Structural Integrity 77 (2026) 550–558 Author name / Structural Integrity Procedia 00 (2026) 000–000

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( a )

( b )

Fig. 2. Y25 bogie with parabolic springs: (a) Running gear model; (b) Diagram of the friction damper with Lenoir link (Melnik et al., 2024).

However, friction-based damping systems present significant drawbacks. Their effectiveness varies with the surface condition, contamination, wear, and lubrication, leading to inconsistent damping performance during operation (Crosbee and Wang, 2023). Moreover, frictional damping is inherently nonlinear, depending on the normal load and the dynamic contact state (stick–slip behaviour). This nonlinearity introduces several disadvantages, such as difficulties in accurately modelling and predicting system behaviour, sensitivity to excitation amplitude and frequency, and potential for unstable or unpredictable responses under varying operating conditions. 2.2. Alternative Damping Concepts To overcome the limitations of dry friction damping, viscous and viscoelastic systems have been investigated as potential alternatives for freight wagons (Iwnicki et al., 2015). Viscous dampers dissipate vibrational energy through fluid shear, whereas viscoelastic materials absorb energy via internal deformation and molecular friction. While these systems provide more stable damping performance across a wide range of operating conditions, their application in railway freight vehicles remains limited by integration challenges and durability considerations (Iwnicki et al., 2015). 2.3. Modal Identification Methods The accurate identification of modal parameters is fundamental to evaluate the effectiveness of damping strategies. A rigorous estimation of natural frequencies, damping ratios, and mode shapes is essential to characterize the structure’s dynamic behavior. In the present study, the excitation applied to the experimental model was not directly measured, as no dedicated equipment was available to record the input force or the initial displacement imposed on the structure. Consequently, output-only modal identification techniques were employed, relying exclusively on vibration responses measured by accelerometers. Two complementary methods were selected for extracting modal information: the Power Spectral Density (PSD) and the Stochastic Subspace Identification (SSI) techniques (Ewins, 2009) . The PSD method analyses the frequency content of acceleration responses and in equation (1): ( ) = 1 �∫ ( ) − 2 0 � 2 (1) Peaks in the PSD correspond to dominant vibration modes of the structure. The method provides a straightforward and computationally efficient means to identify resonance frequencies and to obtain an initial overview of global dynamic behavior. However, PSD does not directly yield damping ratios or mode shapes and is sensitive to measurement noise and the presence of closely spaced modes (Ewins, 2009) . In contrast, the SSI method operates in the time domain. It constructs a block Hankel matrix from the measured responses to estimate the state-space representation of the system. By analyzing the evolution of identified poles as the model order increases, stable modes—those with nearly constant frequency and damping—can be distinguished from numerical artefacts (Peeters and De Roeck, 2001). SSI is thus capable of estimating the complete set of modal

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