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.

This study addresses the dynamic stability of a moving mass suspended electromagnetically from a flexible beam that is supported periodically by discrete elastic springs. The stability is generally determined by the interaction of the wave-induced and electromagnetic instability mechanisms. Both are related to a potentially destabilizing force: the controlled electromagnetic force and the reaction force of the guideway (beam-foundation system). The former is destabilizing if the control is inappropriate, and the latter when sufficiently energetic anomalous Doppler waves are excited in the guideway that feedback energy into the vehicle vibration. Using a generalization of Hill’s method, the stability boundary is determined in the plane of electromagnetic-control parameters. The obtained boundary is roughly triangular, like for the equivalent non-periodic system. The left, straight boundary marks the emergence of a divergence instability. The right boundary generally marks the emergence of an oscillatory (flutter-type) instability, but specific, elliptical indentations are related to parametric resonances. The divergence instability is always electromagnetics induced, but the oscillatory instability and parametric resonances can be either wave or electromagnetics induced, although the latter are often electromagnetics induced. Wave-induced instability takes place mostly for large speeds and only for small values of the control parameters. The stability boundary locally bends back there, reducing the size of the stable zone considerably. Next to the T and 2T parametric-resonance indentations, the right boundary has a significant amorphous indentation compared to that of the non-periodic system. Furthermore, the 2T parametric resonance ellipse is very significant in size when the inhomogeneity of the periodic guideway is relatively strong. Interestingly, the amorphous indentation is related to the occurrence of an evanescent wave in the periodic guideway, but parametric resonance appears to be not uniquely related to a single wave type. Although the current study is fundamental in nature, the findings do pave the way towards the design of safe and cost-effective Maglev and Hyperloop infrastructure as well as of electromagnetic-suspension controllers. We emphasize that the wave-induced instability mechanism, and more generally speaking the influence of the periodic guideway, is also relevant in the context of other (than the simple PD) control strategies as well as for different Maglev and Hyperloop suspension/levitation systems such as the electrodynamic, the hybrid and the superconducting magnet suspensions.

A novel boundary formulation is presented by applying the Boundary Element Method (BEM) to a dynamically loaded medium modelled as a discrete system. The two-dimensional medium is divided into a nonlinear discrete lattice in the near field, and a corresponding linear viscoelastic far field. The resulting boundary formulation is derived from the dynamic reciprocal work theorem and describes the far-field response through a Laplace domain force–displacement relation. The involved dynamic compliance matrix is composed of newly derived expressions for the Green’s functions of a viscoelastic half-plane of particles. It is demonstrated that the presented method yields a perfectly non-reflective boundary in the Laplace domain, without the need for artificial absorbing boundaries. Additionally, this contribution shows the successful time-domain application of the boundary method to a medium that exhibits non-smooth behaviour in the vicinity of a load source. In the time domain, the boundary equations are obtained by numerical application of the inverse Laplace transform, and the non-reflectiveness of the boundary is sensitive to the size of the time step. The presented method provides a consistent boundary approach for discrete lattices, and provides an alternative to continuum-based boundary methods for the dynamic response of solid media.

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.

In this paper, we study the stability of a simple model of a hyperloop vehicle resulting from the interaction between electromagnetic and aeroelastic forces for both constant and periodically varying coefficients (i.e., parametric excitation). For the constant coefficients, through linear stability analysis, we analytically identify three distinct regions for the physically significant equilibrium point. Further inspection reveals that the system exhibits limit-cycle vibrations in one of these regions. Using the harmonic balance method, we determine the properties of the limit cycle, thereby unraveling the frequency and amplitude that characterize the periodic oscillations of the system's variables. For the varying coefficients case, the stability is studied using Floquet analysis and Hill's determinant method. The part of the stability boundary related to parametric resonance has an elliptical shape, while the remaining part remains unchanged. One of the major findings is that a linear parametric force can suppress or amplify the parametric resonance induced by another parametric force depending on the amplitude of the former. In the context of the hyperloop system, this means that parametric resonance caused by base excitation—in other words by the linearized parametric electromagnetic force—can be suppressed by modulating the coefficient of the aeroelastic force in the same frequency. The effectiveness is also highly dependent on the phase difference between the modulation and the base excitation. The origin of the suppression is attributed to the stabilizing character of the parametric aeroelastic force as revealed through energy analysis. We provide analytical expressions for the stability boundaries and for the stability's dependence on the phase shift of the modulation. Finally, we emphasize that suppressing parametric resonance through an added, linear state-dependent force with the coefficient having the same period as the original force can be achieved in other physical systems too.

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.

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 two degree of freedom mass on a moving belt system has been considered to study the effect of friction-induced oscillations, due to nonlinear contact properties and external excitation, on friction modulation. Both tangential and normal excitation are present and the Hertz-Damp model governs the normal contact. The combined presence of the normal-tangential coupling through friction and of the external excitation, results in a parametric excitation and triggers friction-induced oscillations. Using a numerical analysis, the occurrence of such oscillations is explained through the inspection of the friction force versus relative velocity plots, which indicate the presence of a negative damping effect in the tangential direction, despite considering Amontons-Coulomb law. Hence, a linearized stability analysis of the steady sliding state, by taking advantage of the Method of Direct Separation of Motion, is employed to predict the bifurcation point as function of system parameters. It is shown that the linearized stability analysis provides a good qualitative agreement for the occurrence of the friction-induced oscillations for the investigated system, while the quantitative match varies depending on the system parameters and their values. Lastly, the effect of the observed friction-induced oscillations on the friction modulation is studied. Through a numerical analysis, a significant degree of scatteredness in friction force modulation is observed. Such scatteredness is significantly linked to the emergence of friction-induced oscillations, and it also depends on the averaging procedure used to quantify the effective friction reduction.

Railway transition zones (RTZs), where rail tracks undergo abrupt changes in foundation types, represent critical challenges in railway infrastructure due to their higher degradation rates compared to open tracks. This study synthesizes insights from multiple research efforts to propose a robust design solution and an energy-based design criterion for RTZ management. We present a two-step approach to establish the design criterion based on a systematic analysis of each RTZ component, focusing on variations in kinematic responses, stresses, and energies. Based on this analysis, the energy-based design criterion is proposed, asserting that minimizing the total strain energy within the trackbed layers and uniformly distributing it in the longitudinal direction can significantly mitigate uneven track geometry and reduce degradation. A novel safe hull-inspired energy limiting design (SHIELD) is introduced and evaluated against traditional transition structures like approach slabs and transition wedges. SHIELD’s effectiveness in managing energy flow at RTZs is demonstrated, highlighting its potential as a transformative solution in RTZ design. Further, we explore the impact of stiffness variations in both vertical and longitudinal track directions and the temporal changes in material properties on RTZ dynamics, suggesting permissible stiffness ratios to control strain energy amplification. A detailed investigation is thus performed to understand the role of geometry in energy management. The influence of different geometric profiles of SHIELD and standard embankment-bridge transitions on strain energy distributions is studied using 3D finite element models. The findings emphasize the strategic use of geometry to channel and scatter energy, and thus mitigate energy concentrations, enhancing the performance and lifespan of RTZs. In conclusion, this comprehensive research not only highlights the importance of an energy-based design criterion and the innovative SHIELD structure in RTZ management but also underscores the need for further research into the geometric profiles and their interplay with energy flow and mechanical properties. This study lays a foundation for future explorations aimed at optimizing RTZ design, ensuring robustness, and extending the operational life of these crucial railway sections.

Railway transition zones (RTZs) are subjected to amplified degradation leading to high maintenance costs and reduced availability of tracks for operation. Over the years, several mitigation measures have been investigated to deal with the amplified degradation of these zones. However, to ensure the robustness of a design solution, it must be evaluated for critical conditions arising due to certain loading and track conditions. In this paper, the critical load conditions arising due to different velocities (sub-critical, critical and super-critical), the direction of the moving load, the combination of inertial effects and track imperfections (non-straight rail and hanging sleepers) and passage of multiple axles (using a comprehensive vehicle model) are investigated for an embankment-bridge transition. The results are then compared against the recently proposed design of a transition structure called SHIELD (Safe Hull Inspired Energy Limiting Design) to evaluate its performance under these critical conditions using various vehicle models and finite element models of the RTZs. It was found that the novel design of the transition structure effectively mitigates dynamic amplifications and results in smooth strain energy distribution across sub-critical, critical, and super-critical velocity regimes in both directions of movement implying that the expected operation-induced degradation will be as uniform as possible in longitudinal direction. Furthermore, even though this transition structure is designed to deal with initial track conditions (perfectly straight track), its superior performance is not confined to tracks in perfect condition; it also efficiently addresses adverse effects from track imperfections such as hanging sleepers and non-straight rail. In the end, this work demonstrates the robustness of the design solution for all the critical conditions under study.

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.

Railway tracks are subjected to constant degradation over the operational period leading to high maintenance and operation costs. To add to this railway transition zones experience 4–8 times more degradation and need more frequent maintenance compared to normal tracks. Railway transition zones are areas where the railway tracks cross a different transportation modality (road, waterway, etc.) or where the rail experiences major changes in the type of track support structure. Several studies have pointed out that the transition zones show amplified dynamic responses due to abrupt changes in stiffness and differential settlement in these zones. Consequently, an increased deterioration of geometry and material is observed in these zones. Numerous attempts have been made to address the abovementioned factors at the superstructure and substructure level. However, an effective intervention to mitigate the amplified degradation in these zones is missing. In this chapter, an overview of the problem and existing solutions is presented. Moreover, a novel design methodology to design railway transition zones is proposed and discussed in detail. The design methodology includes the formulation of a design criterion, identification of design parameters, investigation of key phenomena governing design and proposing an optimized design solution.

The railway transition zone where the track transitions from a ballasted track to a slab track, is a crucial area that can experience amplified dynamic responses. This work aims to develop a deeper insight into the mechanisms leading to the amplified dynamic response in railway transition zones. The study employs a finite element model to investigate the amplification of total strain energy due to the phenomena of reflection and redistribution of energy close to the transition interface. The results of the study are obtained for three case studies involving non-reflecting boundary (representing an energy sink) and homogeneous material along the vertical direction of the track, and the responses are studied for individual and combined effects in comparison to a benchmark case. The findings of the study show that eliminating the phenomena results in no dynamic amplification in total strain energy in railway transition zones. The conclusion highlights the importance of understanding these phenomena in order to design an efficient railway transition structure.

In recent times, railway transportation has received increasing attention, particularly for its ability to operate entirely on electricity sourced from renewable sources. However, the growing demand for railway services has transformed previously acceptable issues into significant challenges, disrupting normal traffic operations. One such issue is ground-borne vibration especially in urban and inter-urban locations. This study explores the efficacy of a novel mitigation technique, termed a "metawedge," in reducing ground-borne vibration at the receiving end. The metawedge consists of a series of periodically arranged barriers that act as resonators. Unlike traditional metamaterials, each resonator within the metawedge possesses slightly different natural frequencies compared to its neighbours. With an appropriate choice of this variation, incoming Rayleigh (surface) waves are converted into body waves, redirecting energy deeper into the ground. Simulation results demonstrate that the metawedge can significantly diminish vibration levels with just a few resonators. Additionally, unlike conventional single trenches, which effectively mitigate vibrations only at specific angles of incoming waves (outside the critical cone), the metawedge remains efficient within this cone. While a theoretical proof-of-concept has been previously presented by the authors, this study makes a step forward by proposing a realizable design. Consequently, this work showcases the potential and feasibility of metamaterials to address present and future challenges in railway transportation.

While most recent models of railway tracks include the nonlocal nature of the foundation reaction force, few studies have investigated the influence of its nonlocal nature on the response. Accounting for the nonlocal nature of the foundation force is computationally expensive and increases the complexity of the model, thus, knowing when and when not to account for it is important. This paper aims to shed light on the influence of the nonlocal, both in time and space, reaction force provided by the foundation on the transient response at railway transition zones. To this end, a 2-D system in which the soil layer is modelled as a viscoelastic continuum is compared to an equivalent 1-D system with a local foundation reaction force (i.e., Winkler foundation). Results show that, in general, the response of the 2-D system with shallow and/or stiff soil layers can be well captured by the equivalent 1-D model. However, for medium-to-deep and/or soft soil layers, the nonlocality of the foundation reaction force is influential and the transient response at transition zones cannot be satisfactorily captured by 1-D models. Finally, the ballast settlement is also poorly captured for medium-to-deep and/or soft soil layers, with the main cause being the inability of the 1-D model to separate between ballast and soil stresses, and not the locality of the reaction force.

The current study is concerned with ground-borne vibrations induced by railways and their impact on nearby structures and inhabitants. More specifically, it explores the efficacy of the so-called metawedge, a novel mitigation measure, in reducing ground-borne vibrations along the propagation path. A metawedge comprises a series of periodically arranged resonators along the propagation direction positioned either on the ground surface or embedded into the soil at varying depths. The difference between the metawedge and a classical locally-resonant metamaterial is that the metawedge resonators have a smooth variation of the resonance frequency with longitudinal direction. This arrangement enables the conversion of incoming Rayleigh waves into body waves, effectively channeling the energy deeper into the ground. While a theoretical proof-of-concept has been previously presented by the authors, this study makes a step forward by proposing a realizable design. Simulations indicate that a metawedge with realistic properties can significantly diminish vibration levels. Unlike conventional single trenches, which are effective only against incoming waves beyond a specific angle (outside a critical cone), the metawedge proves efficient also within this cone. This work aims to showcase the potential and feasibility of metamaterials to address present and future challenges in railway transportation.

The reliable design of high-rise buildings subject to wind-induced vibrations is important for ensuring comfort and safety. However, the Eurocode recommendations and common design practices used to estimate natural frequency and damping parameters in the design stage have been found to be inaccurate, leading to unreliable predictions of building accelerations. Previous studies have shown that soil-structure interaction (SSI) can have a significant influence on these parameters, especially for high-rise buildings on soft soils. This study presents a formulation of a simple model to include soil-structure interaction effects in the natural frequency and damping parameters. It also demonstrates the compatibility of this model with the current Eurocode procedures. The study compares the results of the simple SSI model with those of a continuous model of the New Orleans tower under design wind loading. In previous work, this continuous model was validated against in-situ measurements on the New Orleans tower. The results demonstrate that the simple SSI model significantly improves the accuracy of the predicted building accelerations under wind loading for the New Orleans tower, compared to accelerations determined in the original design and accelerations computed with the Eurocode guidelines.

Railway transition zones are the most critical part of the railway infrastructures that experience 4-8 times more degradation compared to open tracks. Despite several attempts to reduce the maintenance and operation costs in these critical zones, a robust and comprehensive solution remains unknown. In recent studies, a robust safe hull inspired energy limiting design of a transition structure was proposed for an embankment-bridge transition (without ballast layer over the bridge) to deal with operation-induced degradation. However, this solution was investigated in detail for only this particular type of transition. In this work, the scope of this mitigation measure is extended for an embankment-bridge transition with ballast running over the bridge and its performance is evaluated using a strain-energy criterion. It was concluded in the end that the safe hull inspired energy limiting design can effectively mitigate the operation-induced dynamic amplification for more than one type of railway transition zones.

Railway transition zones (RTZs) are regions where abrupt track stiffness changes occur that may lead to dynamic amplifications and subsequent track deterioration. The design challenges for these zones arise due to variations in material properties in both the depth (trackbed layers composed of different materials) and longitudinal directions of the track, as well as temporal variations in mechanical properties of materials due to several external factors over the operational period. This research aims to investigate the effects of these variations in material properties (i.e., of the resulting stiffness distributions in vertical and longitudinal directions) on the behaviour of RTZs, assess from this perspective the performance of a novel transition structure called the SHIELD, and establish a methodology for designing a robust solution to mitigate the dynamic amplifications in these zones. Results indicate that stiffness variations in both vertical and longitudinal directions significantly influence the dynamic behaviour of the RTZs. The study also suggests a permissible range of stiffness ratios to control the amplification of strain energy in the most critical components of RTZs, both in the initial state as well as during the operational phase (where material properties may vary over time). Moreover, the proposed methodology offers a valuable tool for the design and evaluation of RTZs and is applicable to various transition types and a broad spectrum of material properties.