Numerous theoretical and experimental studies have explored the effect of external excitation in modulating friction forces. To align with experimental findings, various friction models have been employed, with dynamic constitutive laws of friction often showing better correlations, though parameter tuning is always required for each different case. In this work, the focus is on enhancing the overall system dynamics rather than increasing the complexity of the friction law, with the aim of providing a better understanding of how system dynamics influence friction modulation under vibration. Specifically, two cases are investigated. A first one-degree-of-freedom case explores a resonant (and nearby resonance) case with a weak and strong friction force, for which an enhanced implicit expression for the velocity response (needed to compute the modulated friction quantity) is provided. The second case investigates the influence of transverse stiffness on friction modulation in a two-degree-of-freedom system subjected to combined longitudinal and transverse loading. On a qualitative basis, this study indicates that the results obtained using dynamic friction laws can also be obtained by employing Amonton-Coulomb’s law, provided the system’s dynamics is captured at a more detailed level.

Accurate prediction of train-induced settlement in railway transition zones is of paramount importance for ensuring the safety and serviceability of high-speed railway (HSR) infrastructure. The inherent complexity of mechanical properties and settlement distribution in these zones stems from the significant stiffness variation between different track structures. This study presents a novel iterative framework for long-term settlement prediction specifically tailored to ballastless track transition zones of HSR systems. The framework couples a dynamic Train-Track-Transition Zone (TTTZ) model with a plastic strain prediction model for soil, enhanced by a jump-step iterative algorithm that improves computational efficiency while maintaining accuracy. The model's validity has been verified through comprehensive comparisons with in-situ measurements and existing analytical solutions. Numerical results demonstrate that the iterative updating of track irregularities is crucial for accurate settlement prediction, as it accounts for the time-dependent dynamic characteristics of the TTTZ system. Furthermore, a wavelet transform-short energy method is developed to identify high-density vibration energy distributions in the spatial domain, establishing a robust correlation between dynamic responses and settlement evolution. This study underscores the importance of iterative modeling and advanced time-frequency analysis in settlement prediction and track quality assessment, offering valuable insights for the design, maintenance, and evaluation of HSR transition zones.

Transition zones, characterized by significant variation in track properties (e.g., foundation stiffness) near rigid structures like bridges and tunnels, necessitate more frequent maintenance compared to standard track sections due to higher levels of differential settlements observed at transition zones. Field measurements on one-way tracks reveal asymmetric settlement patterns (i.e., different settlement in the soft-to-stiff vs. stiff-to-soft transitions), yet existing literature often investigate either one or the other transition type without investigating the potential limited validity of results. This study investigates the similar aspects as well as the dissimilar ones regarding the behaviour of soft-to-stiff and stiff-to-soft transitions. Modelling results show that the behaviour of the two transitions can be considerably different. These results strongly suggest that for a mitigation measure to be efficient, it may be necessary to have different designs for the two types of transition wherever possible (i.e., in one-way tracks). This study can help researchers and engineers understand the different degradation patterns obtained using more complex models or from field measurements.

In this paper, we investigate the response of a cavity embedded in an elastic half-plane (2D) subjected to a harmonic SH wave. In previous work, the method of conformal mapping and the indirect boundary element method (indirect BEM) were employed to solve the 3D wave scattering from a cylindrical tunnel embedded in a half-space. Inaccurate results were obtained particularly at high frequencies (method of conformal mapping). Therefore, in this study we focus on a comparison of the two methods with the method of images, which serves as a benchmark solution. Through a systematic evaluation, we confirm that the two methods accurately work within the complete considered ranges of the dimensionless frequency and the embedded cavity depth. This suggests that representing the waves scattered from the free surface by cylindrical waves in the method of conformal mapping is the cause of the inaccuracies at high frequency in the 3D problem; the cylindrical waves are probably not able to fully capture all wave conversions taking place at the free surface. The presented results reveal significant effects of the system parameters on the responses. The system's response curves display nearly equally spaced resonances, which is in line with those of the 1D shear layer subject to bedrock motion, while similar response curves for the 3D case do not have this feature.

Several studies have been dedicated to altering friction forces, with external excitation being one of the approaches explored. When the latter is considered, its influence has primarily been studied within the context of discrete systems. Therefore, in this study, a moving oscillator in frictional contact with an elastic rod of finite length subjected to distributed damping is considered, to study the influence of external excitation in the presence of support flexibility on friction modulation. The modal expansion method is used to derive the modal equations of motion, which are then solved numerically. Two cases are investigated, one with the load acting on the mass and the other with the load acting on the rod. It is found that, for both cases, friction modulation varies along the rod's length, and it differs from that obtained assuming a rigid rod. Moreover, for the load-on-mass scenario, a critical velocity is defined, providing direct insight into the friction modulation differences between flexible and rigid rod cases. For the load-on-rod scenario, large deformations are observed close to and above resonance, and geometric nonlinearity is accounted for to describe the system dynamics accurately. To link theoretical results to applications, the findings are used to qualitatively interpret slip-joint vibration-assisted decommissioning tests, and are compared with experimental results in which friction force reduction is explained through the use of elasto-plastic friction models that account for surface deformability, showing good qualitative agreements between the theoretical and experimental outcomes.

Maglev and the newer Hyperloop technologies are advanced transportation systems that eliminate wheel–rail friction using electromagnetic suspension/levitation. The electromagnetic suspension is inherently unstable and requires a control strategy for safe operation, which has been previously studied in the context of Maglev. However, the interaction between electromagnetic instability and another instability mechanism, known as wave-induced instability, occurring at high vehicle velocities, has not been explored. This interaction between two distinct instability mechanisms is the focus of this study. From a practical perspective, this study examines the stability of magnetically suspended vehicles (e.g., Maglev or Hyperloop) in relation to vehicle velocity and control gains. To account for this, this study properly includes the infinite guideway, thus allowing vehicle velocity to influence system stability. The results show that at sub-critical velocities, the guideway's reaction force helps suppress perturbations and stabilize the system, with instability driven solely by improper electromagnetic control. However, at super-critical velocities, wave-induced instability drastically reduces the stable parameter space. This study further proposes a methodology to distinguish the contribution of each instability mechanism to the overall system stability, which is important for efficient mitigation measures. The findings reveal that beyond a certain super-critical velocity, wave-induced instability dominates much of the control-gain plane, with the control strategy effective in only limited regions. In conclusion, the study recommends revising control design strategies, as solely focusing on maximizing energy dissipation through control can trigger wave-induced instability. A more effective approach balances energy dissipation with avoiding the activation of wave-induced instability by steering clear of problematic vibration frequencies. These insights provide guidance for improving control strategies.

A novel nonlinear 1-D gradient model has been previously proposed by the authors, combining (i) the higher-order gradient terms that capture the influence of material micro-structure and (ii) a nonlinear softening material behavior through the use of a hyperbolic constitutive model. While the previous study focused on the existence and properties of solitary-type waves, the current study focuses on the characteristics of the transient wave propagation in the proposed model. Findings show that as nonlinearity increases, the bulk of the wave slows down, and its shape becomes more distorted in comparison to the response of the linear system. The energy analysis reveals that, unlike the linear system, the nonlinear one continuously exchanges energy, in which the kinetic energy decreases over time while the potential one increases. Furthermore, the spectral (wavenumber) energy density of the nonlinear-elastic system presents peaks at large wavenumbers. However, these are eliminated when a small amount of linear viscous damping is added indicating that they are not physically relevant. A notable feature that persists despite the presence of damping is the formation of small-amplitude waves traveling in the opposite direction to the main wave. Generalized continua, like gradient elasticity models, miss the small energy scatter by the micro-structure. This study shows that adding material nonlinearity to a homogeneous generalized continuum can capture reverse energy propagation, though at much smaller magnitudes than the main wave. These findings shed light on the characteristics of the transient wave propagation predicted by the proposed nonlinear 1-D gradient model and its applicability in, for example, predicting the seismic site response.