The Perfectly Matched Layer (PML) has become a powerful tool in computational underwater acoustics and elastodynamics. By employing complex coordinate stretching in the wavenumber–frequency domain, PMLs effectively attenuate outgoing waves from the physical domain and thereby provide an efficient means to truncate the computational domain. Although PMLs have been widely adopted in the finite element and finite difference communities, their use in semi-analytical solutions remains limited. A major challenge is that, when modal analysis is applied to the acousto-elastic domain with PML in a semi-analytical framework, the found modes are not orthogonal. This challenge formulates the main motivation of this research. On the other hand, the modes obtained from the discrete solution of the elastic layer with PML, based on the thin-layer method, do preserve orthogonality. Therefore, this thesis aims to understand the differences between the modal solutions of the semi-analytical and thin-layer methods in the elastic domains with PMLs, which may provide insights into the reasons why modes in the semi-analytical solution are not orthogonal to each other.

The main storyline of this thesis is developed through four cases with increasing system complexity. In the first case, the modes of the elastic domain are computed using both the semi-analytical approach and the thin-layer method (TLM), and the comparison demonstrates the equivalence of the two methods in the absence of PMLs. In the second case, the acoustic domain with PML is investigated using the semi-analytical approach, with emphasis on the polynomial order of the complex-stretching function. Mathematical derivations show that a zero-order polynomial induces discontinuities at the interface, leading to uneliminated boundary terms and perturbing modal orthogonality, while numerical results confirm that higher-order polynomials preserve the cross-orthogonality of modes, as well as the continuous slopes of the potential functions at the interface. In the third case, a quadratic complex-stretching function is employed, and the elastic domain with PML is analyzed using both approaches. The comparison reveals differences in eigenvalues and eigenvectors; finer TLM discretization yields increased matches between the two methods, but excessive discretization results in orthogonality violations. Finally, in the fourth case, the semi-analytical modes of the acousto-elastic domain with PML are studied. Propagating, evanescent, and Bérenger modes are identified, with cross-orthogonality preserved given sufficient integration points. Bérenger modes consistently arise in PML formulations and exhibit anomalous dispersion characteristics.

The main contribution of this thesis lies in revealing the influence of the polynomial order of the complex stretching function on the modes of the acoustic domain with PML. When a quadratic complex-stretching functions are employed, the numerical results suggest that the semi-analytical modes of the elastic or acousto-elastic domains with PML are orthogonal. Therefore, it is suggested that a positive value of polynomial order is recommended when computing normal modes of the acousto-elastic domain with PML. However, in the future, a systematic study on the influence of the polynomial order should be conducted for the elastic layer or acousto-elastic domain with PML.
Furthermore, the comparative study of modal solutions highlights the differences between the semi-analytical approach and the thin-layer method. The nature of modal solutions comes from the different formulations of the eigenvalue problem, leading to different eigenvalues and eigenmodes. For TLM, the over-discretization of the PML domain is not suggested due to the violated orthogonality, although the reasons behind that require further investigations.

Overall, this thesis advances the fundamental understanding of the modal basis of acoustic, elastic, and acousto-elastic layers with PML formulations, providing a foundation for future research in two main directions: (i) the study on modes of the acoustic layers coupled with multiple elastic layers with PML, which better represent realistic ocean environments with geological strata; and (ii) the computation of forced responses of structures in acousto-elastic layers with PMLs to model the pile-water-soil interactions using modal matching techniques. ... Read more

Hyperloop is a novel high-speed transportation system that combines electromagnetic suspension with a low-pressure environment within a tubular shell to enable travel velocities well above those of existing high-speed rail. While this concept promises high efficiency and reduced resistance, it also introduces dynamic effects and potential instabilities that become increasingly significant at such speeds. This thesis investigates these phenomena with particular focus on the influence of periodic supports and shell behaviour on the structural response, aiming to provide a more realistic guideway model than those previously adopted in the literature.

The guideway is modelled as a thin-walled cylindrical shell with discrete supports, while the vehicle is represented as a moving mass suspended through a non-contact electromagnetic force governed by a proportional–derivative control system. This setup enables more physically representative modelling by incorporating discrete support spacing and allowing for the inclusion of circumferential pre-stress from the vacuum environment, a feature intrinsic to Hyperloop systems.

Two themes are central to the study. The first concerns the steady-state response of the shell under a constant moving load, which isolates the structural behaviour of the guideway. Using a semi-analytical approach, the governing equations are projected onto circumferential modes, transformed into the frequency–wavenumber domain, and solved with a periodicity condition to reconstruct the steady-state response. This analysis shows that periodic supports strongly modify wave propagation, leading to multiple resonance peaks, including in ranges where operational velocities may lie. As a result, simplified continuous models risk overestimating safe operating speeds and overlooking significant amplifications. The results also demonstrate how geometric and damping parameters affect the critical velocity, offering practical strategies for vibration reduction. Furthermore, the inclusion of circumferential pre-stress is shown to be essential, since vacuum-induced compression reduces the effective stiffness of the shell and shifts the system closer to resonance conditions.

The second theme addresses the stability of the coupled vehicle–structure system, where two distinct instability mechanisms are considered: wave-induced instability from anomalous Doppler waves, and electromagnetic instability from the suspension control system. The periodicity of the support structure enables the potential manifestation of wave-induced instability in the form of parametric instability, which is absent in continuously supported models. The analysis is carried out using a semi-analytical approach that combines Floquet theory, Fourier expansion, and harmonic balance to reformulate the problem as an eigenvalue analysis, from which stability boundaries are identified. The findings highlight the need for careful controller design at operational speeds, with periodicity shown to play a role in shaping instability zones.

Overall, this research demonstrates the importance of accounting for both shell behaviour and support periodicity when assessing the dynamic performance and stability of Hyperloop systems. In doing so, it advances the understanding of Hyperloop dynamics and provides a foundation for future research and the further development of this emerging mode of transportation. ... Read more

As urbanization intensifies and rail and road traffic increase, infrastructure and buildings face growing challenges from ground-borne vibrations, particularly at low frequencies. Traditional mitigation methods, such as heavy masses or stiff trenches, are often ineffective due to the large wavelengths involved. This research investigates metamaterials—mass–spring systems with viscous damping—as a novel solution capable of attenuating low-frequency vibrations through local resonance. Three metawedge configurations—uniform, wave conversion, and rainbow trapping—were evaluated at a target frequency of 10 Hz, typical of soil vibrations induced by trains and traffic. The wave conversion metawedge proved most effective at mitigating surface vibrations, while the rainbow trapping metawedge minimized impact on the surrounding environment by dissipating rather than redirecting energy. Based on these findings, design criteria were developed, including the relative resonator bandwidth (RRBN), optimal mass range, and resonator spacing considerations. Additionally, the potential of impact-based resonators to enhance energy dissipation by exciting higher frequencies was explored. While promising results were observed in a simplified two-degree-of-freedom system, numerical simulations on a soil domain revealed unexpected amplification, highlighting the need for further investigation. This work establishes a foundation for the practical design of metawedges and identifies directions for future research into nonlinear and impact-based vibration mitigation strategies.

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Understanding the dynamic behaviour of soil is crucial for the design of geotechnical structures, particularly for offshore wind turbine foundations. This study evaluates the performance of a nonlinear numerical model in accurately capturing soil response under dynamic shear loading, comparing its simulated response to experimental data obtained from Resonant Column Tests (RCT). The research systematically investigates the role of higher-order odd harmonics in the numerical solution, assesses the differences between linear and nonlinear models, and validates the nonlinear model against experimental results.

The findings reveal that higher-order harmonics contribute negligibly to the numerical response, simplifying the model's implementation. Furthermore, the nonlinear model effectively captures the resonance shift observed in experimental data, outperforming the linear model, particularly at higher strain levels where soil softening effects become significant. While the model demonstrates a strong correlation with experimental results, discrepancies arise in high-strain scenarios, primarily due to limitations in damping representation. To address this, corrective approaches such as a damping correction factor and strain radius adjustments were explored, improving model accuracy but failing to eliminate errors entirely. The study highlights the necessity of incorporating a strain-dependent damping formulation to enhance predictive capabilities for high-strain soil behaviour.

The results confirm that nonlinear numerical modelling is a valuable tool for capturing essential soil dynamics, but further refinements in damping representation are required to improve alignment with experimental data. Future research should focus on advanced damping models to ensure greater accuracy in high-strain dynamic soil simulations.
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Advancements in structural engineering increasingly lead to more slender and architecturally challenging footbridge designs, characterized by reduced height-to-span ratios and lower self-weight. These designs, often serving as landmarks with aesthetic and functional purposes, are becoming more susceptible to human-induced vibrations. The increased live-to-dead load ratio and reduced eigenfrequencies increase the risk of resonance when pedestrian step frequencies align with the structure’s natural frequencies. This resonance amplifies deck accelerations, compromising pedestrian comfort and freedom of movement. Synchronization effects are at risk of further intensifying amplification and obstructing movement. No studies have demonstrated that human-induced vibrations cause structural failure in the ultimate limit state (ULS); rather, they primarily affect user comfort in the serviceability limit state (SLS).

Over the past three decades, substantial research has focused on understanding and mitigating humaninduced vibrations in footbridges. The temporary closures of iconic structures such as the Passerelle Solférino in Paris (1999) and the London Millennium Bridge (2000) have potentially accelerated findings and highlighted the significant challenges posed by pedestrian-structure interaction. In particular, a focus is drawn to the lateral lock-in phenomenon, which resulted in excessive lateral vibrations and discomfort. Lateral lock-in and other human-induced incidents resulted in extensive testing, leading to the development of new guidelines and advancing the study of lightweight footbridges across Europe through both in-situ testing and numerical simulations. However, the literature reveals a considerable variation in assessment methods and verification techniques, which complicates the accurate evaluation of a footbridge’s dynamic behaviour by structural engineers. Nevertheless, a consensus is reached in the literature that design situations must be carefully considered in every footbridge design. Pedestrian comfort and dynamic response are crucial design factors, requiring a thorough understanding of expected traffic patterns and the structure’s dynamic behaviour. Design situations encompass a range of conditions, such as daily pedestrian use or special events, to establish realistic performance limits under ranging circumstances. Studies show that higher pedestrian density leads to reduced walking speeds and restricted movement, which in turn influences the dynamic loads on the structure. Comfort is assessed through acceleration measurements during loading, with predefined ranges to categorize acceptable performance levels. These evaluations stress the importance of a comprehensive analysis of dynamic effects, rather than relying on a single limit criterion.

To mitigate the issues observed in the aforementioned bridge designs, external control devices are applied to offer additional damping and reduce vibrations to acceptable levels. These control devices are applied after footbridge construction, enabling thorough testing of the bridge to determine the structure’s dynamic properties and ensuring the damping system is optimized and properly tuned. External damping has various forms applied in civil engineering structures. Most notably there are three categories to be distinguished, namely: tuned mass/liquid, viscoelastic and viscous fluid dampers. Tuned mass dampers (TMDs) are most commonly used due to their ease of application, allowing for effective control of vibrations post-installation. By tuning the TMD’s eigenfrequency to match the primary structure’s critical natural frequency, energy dissipation is achieved through the mass of the damper and its motion relative to the structure to which it is attached. TMD design is highly effective in controlling the target frequency. However, it should be noted that this localized damping primarily addresses the response of a single frequency, rather than the total response of the structure. If eigenfrequencies are closely spaced, a shift in frequency could lead to a new resonant response in the overall structure, as damping the initially critical mode may consequently amplify nearby modes.

These imposed challenges raise the question if reducing excessive human-induced vibrations within footbridge design can be achieved through other means. A promising method regards the geometric modification of the structural design, providing a change of dynamic characteristics and reducing resonance effects. Modern-day advancements enable engineers to perform more complex problem solving, namely through computational power by utilising optimisation techniques which require many iterations. An optimisation is characterised by its objective function, constraints, design variables and requirements it should satisfy. Evolutionary algorithms, such as genetic behaviour from groups observed by animals in nature provide effective results for optimisation.

To provide context to such an optimisation algorithm, a case study is presented, showcasing how the concept can be utilised. The optimization primarily targets reducing the structure’s mass as an objective, improving cost and sustainability while influencing dynamic performance. Minimizing accelerations is likewise pursued to evaluate the extent of reduction possible and identify the most influential geometric parameters. The structure must meet ultimate limit state requirements in the optimized design to ensure feasibility. Data from the original design, including FEM models, analysis reports, and TMD specifications, informs the optimization process. A parametric model is developed to support geometric optimization. Key design variables, objectives and constraints are carefully selected to maximize the effectiveness of the optimization and achieve a design that either mitigates or eliminates the need for external damping devices.

When footbridge design deviates significantly from conventional girder bridge design will the effectiveness of assessment methods drop, requiring more extensive analysis to address dynamic behaviour. The presented case study shows the closest adherence to measured results via direct time integration, being most costly in time whilst requiring a substantial level of engineering judgment. Furthermore, does the correct assessment of damping in footbridge design play a major role, showing agreement with the proposed mean damping values addressed in the literature.

Optimisation to exclude the need for external damping devices through evolutionary algorithms by conducting a geometric parameter study is a feasible approach. However, it requires a deep understanding of the structural behaviour of footbridges and a robust parametric model capable of performing both static and dynamic analyses to account for geometric changes. In the case study, significant improvements were achieved through this optimization process, resulting in a new design that eliminates the need for TMDs.
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This report evaluates the influence of dynamic motions, more specifically earthquake motions, on the stiffness of offshore soil. As this stiffness reduces over the course of an earthquake, the structural response of offshore technology is affected. The focus of the investigation presented is on the influence of this seismically triggered stiffness degradation on the simplified design procedure of jack-up vessels, a vessel used to install and maintain offshore structures such as wind turbines, in the offshore area of Japan and the East and South Chinese Sea.
A literature study was conducted to outline the shortcomings in the current screening process of a jack-up vessel, as well as to get acquainted with some geotechnical concepts. These concepts were used to develop a soil model with a simplified structure on top. Earthquake motions of different intensity were applied to the base of this soil deposit and the response of the structure was compared to the response of a three-dimensional jack-up model, in which the soil was represented by linear springs and dashpots.
The results show that for lower intensity levels, defined as the earthquake’s level of peak ground acceleration, there is barely any degradation in the soil. For earthquakes with a peak ground acceleration of around 0.1g, there sometimes is degradation in the soil, however, almost never significant enough to alter the structural response. For more intense earthquakes, there is a clear degradation in the soil deposit, which affects the response of the jack-up vessel. For the case presented in this research project, an equivalent stiffness degradation factor is found for these more intense earthquakes, so that soil stiffness degradation can be implemented in the simplified design procedure of a jack-up vessel. Furthermore, the results imply that linking the earthquake’s signal intensity to both the peak ground acceleration and the Arias intensity level will lead to a more accurate subdivision of the equivalent stiffness degradation factors ... Read more

This thesis studies the use of metamaterials for mitigating train-induced ground-borne vibrations, a growing issue with the projected increase in train transportation. Traditional mitigation measures such as trenches often fall short, particularly at low frequencies and small incidence angles. Metamaterials, engineered to alter wave propagation properties, offer a novel solution by creating frequency bands that attenuate vibrations. This study begins with an one-dimensional model of an Euler-Bernoulli beam on a visco-elastic foundation, where metamaterials are modeled as local mass-spring-dash pots and single-degree-of-freedom resonators. This model facilitates an analytical study into wave propagation and band gap formation using Floquet analysis, which identified band gaps arising from both local resonances and the periodicity of resonator arrangements.

The study progresses by examining a finite periodic system using a numerical model. This involves comparing the dispersive properties of the finite system with those observed in its infinite counterpart. The results demonstrate an excellent agreement between the two. A significant focus is on the "metawedge", a metamaterial configuration with unit cells varying in natural frequency, allowing for broadband frequency targeting. This configuration enables elastic rainbow trapping and wave-mode conversion, with detailed three-dimensional analysis performed using FEMIX to explore these phenomena further. The three-dimensional model consists out of a homogeneous elastic half-space with single-degree-of-freedom resonators placed on top of the surface. The results demonstrate that the proposed metamaterial solutions are effective in mitigating low-frequency vibrations caused by trains across all incidence angles. The findings indicate that the classic metawedge configuration traps waves, by slowing them down, while the inverse metawedge accelerates waves, facilitating wave-mode conversion. ... Read more

The objective of the European Green Deal is to reduce net greenhouse gas emissions by at least 55% by 2030 and to achieve climate neutrality by 2050 [1]. Due to a growing global population and increased needs for travelling on the one hand, and progressive bans of short-haul flights by the governments on the other, the need for a more sustainable and fast means of transportation comes in high demand.

The Hyperloop transportation system has emerged as the fifth mode of transportation, offering an energy-efficient, fast alternative for freight and passenger transportation. However, to successfully establish the Hyperloop network, an extensive tube infrastructure would need to be constructed with requirements of being safe, sustainable, and cost-effective. At the time of this project, various tube designs and materials have already been examined and evaluated; given its preliminary stage of development, new design ideas are rapidly emerging. Engineers are faced with two fundamental challenges: firstly, defining safety limits, and secondly, establishing the balance between the safety, environmental footprint, and operational efficiency of hyperloop infrastructure.

The Hyperloop Skeleton tube design is the latest addition to the integral designs that holds great potential in terms of weight efficiency. The aim of this research is to determine the applicability and efficiency of the newly proposed tube design and to evaluate structural performance to imposed loads.
For the design evaluation, the study uses a numerical approach. Skeleton tube design is initially disassembled into individual components, which are analysed separately to identify potential weaknesses of the design as well as to predict their behaviour within the assembly. After that, the study conducts the analysis of the assembly. The initial design lacked rail support design; thus, a design is proposed and implemented in the model for the global analysis. Within the assembly, the research identifies critical sections and design weaknesses. In accordance with this, it proposes and analyses a new ring-to-stringer connection design. Additionally, a comparison study has been conducted with the conventional (plain) tube design, currently used at the European Hyperloop Centre (EHC) [2].

Based on numerical results, the skeleton tube design is conditionally satisfactory in terms of ultimate and serviceability limit states. The design can resist the main load case – vacuum pressure. Nevertheless, the slender components and thin plates make the tube susceptible to plate rupture or penetration if exposed to environmental actions; thus, making the hyperloop system vulnerable to accidental and impact loads. Moreover, the elastic strength capacity of rings, which are primarily in compression and are therefore critical components, is nearly reached. An initiation of local plastic response is observed, yet due to integral design, the stresses distribute among components; thus, it does not progress into a fully plastic response. Based on these findings and considering that dynamic loads are yet to be assessed, it can be projected that a strength capacity will be exceeded in further research.

The proposed steel bracket design for ring-to-stringer connection provides an alternative to welded connections. It improves stress concentrations within the ring, and considering that it is a bolted connection, further contributes to the ease of assembly, maintenance and the demountability aspect. However, the requirement for 288 such connections per 16-meter-long tube section might significantly increase the total cost of skeleton tube design.

Based on the comparison study, it is proven that the conventional tube design performs better in terms of structural performance under the considered loading conditions. However, in a controlled environment with the absence of external actions, the skeleton tube design could efficiently operate. In this case, a material efficiency of 28% can be achieved if the structure supports the rails and the pod, and up to 37.8% if the tube is solely used for vacuum pressure retention.

Emerging technologies, currently in the process of development and yet to demonstrate their contribution to a more sustainable future significantly depend on the performance and success of their initial prototypes and real-world applications. Skeleton design offers a cutting-edge design, which is on the safety – sustainability spectrum drastically leaning to the latter. A secondary protective structure is required for consideration of the skeleton design in the hyperloop application. The design can nonetheless be viable for other applications, which operate in a safe and controlled environment, with the absence of external loads. This research lays a foundation for any further research on the skeleton tube design.
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Insulated rail joints (IRJs) play a crucial role in modern railway systems. They serve the critical function of electrically isolating rail segments through the placement of an insulating material, known as an end plate, between two rail ends. This insulating material is necessary to define track segments, which makes it possible to determine the position of trains within the railway system. Knowing a train’s position is key to ensuring efficiency, reliability, and safety. While these joints are highly important, they are also vulnerable. The interruption in rail geometry results in a complex interaction between wheel and rail, giving rise to high dynamic impact forces. Traditional IRJs, or squared IRJs, have the cut between the rail ends orthogonal to the rail. In this thesis, an alternative design with a non-orthogonal junction angle is analyzed.

The primary goal of this thesis is to determine how the junction angle influences both the global wheel-rail interaction and the local contact pressure at the wheel-rail interface. To achieve this, the thesis is split into two parts: (1) the global wheel-rail interaction analysis, which studies the influence of the junction angle on the interaction between the wheel and rail using simplified geometries in a kinematic approach, and (2) a local wheel-rail interface analysis, which studies the effect of the junction angle on an assumed uniform contact pressure between wheel and rail.

The global analysis revealed the possibility of two distinct contact scenarios, depending on lateral wheel position and dip angles greater than zero. In contact scenario 1, the effective geometry and the resulting vertical impulse remained identical to those of squared joints. However, in contact scenario 2, the active geometry of the joint changes, leading to an increase in vertical impulse of the wheel’s center of mass. Additionally, the introduction of the junction angle increased the likelihood of less favorable contact conditions for contact scenario 1 and guaranteed less favorable contact conditions for contact scenario 2. The local analysis showed that uniform contact pressure between the wheel and rail increases slightly for non-orthogonal junction angles with dip angles near zero. For small junction angles (resulting in a long cut in the longitudinal direction), outside of the practical range, the rate of change of the contact pressure was greatly reduced.

The study has shown that insulated rail joints with non-orthogonal junction angles within the practical range do not provide significant improvements in dynamic performance compared to traditional squared joints. However, due to the assumptions made in this model, the complexity of the rail geometry was significantly simplified, and material elasticity was not considered. These limitations are expected to affect the contact behavior and could affect the results. This should be investigated further. The second model demonstrates that for junction angles within the practical range, the assumed uniform contact pressure increased slightly. However, for very small junction angles, which result in impractically elongated joints, the rate of change in uniform contact pressure can be greatly reduced.

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The maintenance and repairs of transition zones pose significant challenges in the railways industry due to their accelerated degradation rates in comparison to free tracks. These zones, characterized by track property variations, amplify their response when a source travels along the tracks. The resulting amplifications in stress and strain fields lead to differential settlements, affecting both track's stability and passenger comfort. This study investigates the influence of incorporating active control forces and moments at the interface of transition zones to mitigate the excessive degradation of soft domains.

Three 1-dimensional models are developed, which include active control forces and moments as a novel method to minimize the amplification of the response in the soft domain of transition zones, as well as, the derivation of these forces. The purpose of these three models is to give the reader an inside view of the method to derive these active control forces with models that increase in complexity.

The first model involves an Euler-Bernoulli beam resting on a piece-wise inhomogeneous Winkler foundation. The second model extends this by including a shear beam and a second layer of foundation, with the first layer being homogeneous and the second layer piece-wise inhomogeneous (Kerr foundation). The third model is a hybrid model between the first two, on which the soft domain is represented by the description of the second model, and the rigid domain by the description of the first model. Numerical solutions in the time-domain were applied to these models, and the study focused on a transition zone subjected to a constant amplitude moving load with constant velocity, traveling from a soft to stiff domain. The purpose of the first model is to give the reader a general idea on the derivation of a very simplistic model. The second model's purpose is to better represent the different elements of a railway structure, on which the shear beam and the lower layer of springs represent the mobilised soil under the tracks, while the top layer of springs and the Euler-Bernoulli beam represent the ballast, the sleepers and the rail. Finally, the third model was made to represent a transition zones, on which the soil is discontinued due to a man-made structure, e.g. a concrete bridge, which leads the structure under the ballast, in the rigid domain, to be consider infinitely stiff and to be represented just by an Euler-Bernoulli beam on a Winkler foundation.

Findings reveal that the active control forces and moments are capable of fully mitigating the dynamic amplification in soft domains of transition zones, however, they increase the dynamic amplifications in the stiff domain. Moreover, the shape that these forces take over time is dictated by the interaction between both domains of the transition zone, when the interface of the transition zone has continuous elements, the forces take a similar shape to the eigenfield of the system, while when there is discontinuous elements over the interface, the forces take a 'flipping' shape. Furthermore, of the two parameters studied (velocity of the moving load and vertical stiffness), the dominating parameter in the response of the system depends upon the regime that the system is being subjected to. For relatively low and extremely high velocities of the moving load, the system is dominated by the vertical stiffness ratio, while for medium velocities of the moving load, the system is dominated by the velocity of the moving load. Finally, transition zones with discontinuous elements require significantly more energy to be absorbed and added into the system by the active control forces to mitigate the dynamic amplifications in the soft domain of the system.

These thesis offer valuable insights for preliminary designs of active control forces aimed at diminishing the dynamic amplification of soft domains of transition zones railway. ... Read more

This thesis aims to investigate the feasibility of developing a successful unsupervised Structural Health Monitoring (SHM) methodology to detect damage in structures, specifically bridges. Detecting damage, especially in its earliest stages, is challenging, thus prompting the need for robust and effective methods. The success of such a methodology could lead to timely inspections and interventions, resulting in significant economic benefits and preventing further damage, including potential failure of the structure in use.

The approach involves a literature review to establish relevant background knowledge and useful concepts. From this, a methodology is developed utilizing unsupervised machine learning, specifically Gaussian Mixture Models (GMM), to identify abnormal behavior indicative of structural damage.

A Finite Element Method (FEM) model of a simple bridge is created and monitored over a three-year period, serving as a testing ground for the methodology and a primary source for data generation. Temperature data and its effects on the natural frequencies of the bridge model are used to establish a baseline for normal or healthy behavior. Synthetic damage, such as settlement and stiffness reduction, is then introduced to the model to create anomalies or abnormal behavior. The developed methodology is tested using three case studies, each with varying types of synthetic damage. By using both the healthy and unhealthy data generated from the model, the healthy behavior of the bridge is captured using GMM. The model then progressively incorporates unhealthy data into the proposed anomaly detection algorithm. The algorithm evaluates the likelihood of each incoming data point of belonging within the healthy distribution, resulting in data points being classified as either healthy or flagged as abnormal.

The case studies presented in this research underscore the efficacy of the proposed anomaly detection approach. In scenarios involving sudden or abrupt damage, the algorithm swiftly and accurately labels abnormal points. For gradual damage scenarios, such as settlement, the algorithm consistently identifies abnormal points, with the rate of abnormal point detection accelerating over time. This detection rate is contrasted with the rate of erroneous abnormal point labeling when processing an exclusively healthy data set through the anomaly detection algorithm. This comparison reveals a higher rate of abnormal point identification when actual damage is present, affirming the effectiveness of the unsupervised SHM methodology in pinpointing abnormal behavior within the modeled bridge structure. ... Read more

On the 17th of October 2021, a concrete grandstand element collapsed at the Goffert stadium in the Netherlands after a crowd jumped on it for 8 seconds. An investigation by an engineering consultancy firm concluded that the design loads in the building code are too low, raising questions about the safety of grandstand elements. Currently, no method to assess the reliability of grandstand elements exists.

This thesis presents a state-of-the-art method to determine the reliability of concrete grandstand elements. The reliability is assessed by performing a non-linear dynamical analysis. The element is modelled as a non-linear single-degree-of-freedom system. Excitation signals are synthetically generated by consulting the literature and by analyzing a data set of jumping crowds. A bi-linear force- displacement relationship based on technical drawings of the collapsed grandstand element is adopted and extended by a model uncertainty parameter which accounts for both the non-linearity of the analysis and the uncertainty related to the dynamical basis of the analysis. The reliability is determined through a Monte Carlo simulation: almost 100,000 simulations can be performed per assessment.

Out of the 100,000 simulations, 0 failed. This result is not in line with what happened; one failed out of only a few elements. This gives rise to two different investigations. On the one hand, the failure of the Goffert stadium grandstand elements has to be explained. On the other hand, the lifetime reliability of a grandstand element has to be determined.

The first assessment indicated that if the element’s resistance conforms to the technical drawings, there is no cause for concern regarding its reliability. Measurements on 23 other grandstand elements in the same stadium showed a high variation in the concrete cover. The collapsed element was, therefore, also likely subjected to a high variation in the concrete cover. To understand the influence of an increased concrete cover on the reliability, two additional analyses were performed, where the post-yielding resistance of the structure was slightly reduced. This resulted in an increase in the probability of failure, which indicates that this parameter plays a crucial role in determining the reliability of grandstand elements. These points combined make it more plausible that the element failed because the concrete cover was larger than intended rather than the design loads being too low, as concluded by the engineering firm.

When investigating the lifetime reliability of grandstand elements in general, no collapse is expected after 8 seconds but rather after 30 seconds or even longer durations. Therefore, two additional analyses were performed where signals of longer durations (120 seconds and 300 seconds) excited the system. In these analyses, it is assumed that the resistance of the grandstand element conforms to the technical drawings. Signs of a converged reliability were perceived as 120- and 300-second excitation signals led to a probability of failure of the same order of magnitude, indicating that a steady-state solution is obtained after 120 seconds of jumping. In that case, the lifetime reliability of a grandstand element would be equal to the 120-second reliability. The corresponding reliability passes the lifetime reliability requirements for existing structures in consequence class 2 (for a reference period of 15 years).

While the results presented are estimations, and a larger sample size is needed for a converged probability of failure, the proposed method provides a valuable framework for assessing the reliability of grandstand elements. This method can easily be extended to any grandstand element by changing the model parameters, and the true reliability of grandstand elements can be assessed by performing more (1-10 million) simulations. ... Read more

Friction damping is common in engineering structures for the purpose of energy dissipation and vibration control. Examples of applications are bolted connections and earthquake isolation systems. However, there is a shortage of works that investigate the effects of different contact materials on the energy dissipation performance and friction behaviour of friction dampers, which is valuable knowledge for design optimization.

This thesis uses a numerical approach to explore the time response and energy dissipated by friction of the harmonically excited SDOF (single-degree-of-freedom) system with Coulomb friction contact between the sliding mass and a fixed wall. In addition, for the same SDOF system, an experimental investigation of the friction damping performance in terms of friction behaviour and energy dissipation is carried out for (1) steel, (2) rubber and (3) aramid contact
materials. The aim is to get a better understanding of how different contact materials affect the performance of friction dampers. Various time scales, excitation frequencies and friction forces are considered.

The main findings of this research are: (1) the characterization of the friction behaviour of steel-to-steel, rubber-to-steel and aramid-to-steel contacts; (2) the comparative analysis of the energy dissipation performance of the different contact materials; (3) the assessment of the long-term performance of the different contacts; (4) the comparison between numerical results based on the Coulomb friction model and experimental results. The tests have shown that rubber has the highest energy dissipation capacity and fairly unstable behaviour, steel has the second highest energy dissipation and irregular behaviour and aramid has the lowest energy dissipation performance and very consistent behaviour. Finally, the application of a method that calculates the energy dissipation of friction damping based on direct experimental outputs is an important contribution to the field regarding experimental investigations. ... Read more

The offshore wind energy industry is quite literally reaching for the sky to meet the increasing demand for renewable energy in Europe. Offshore wind turbines are sprouting out of the waves off the coast of many European nations and their size is increasing rapidly. As the turbines become larger and the waters in which they are placed become deeper, the foundations that carry these behemoths must grow as well. The most frequently used foundation is the monopile foundation. Over the years, both the length and the diameter of these monopiles have steadily increased. Installing monopile foundations has, as a result of this, become more and more difficult.
An important aspect of the installation of monopile foundations that has become more challenging is the upending of the monopile. When the monopiles are transported to the site of installation, they are sea-fastened to the deck in horizontal orientation. When they arrive, they need to be rotated to a vertical orientation for installation. This can be done with the aid of an upend hinge. This thesis focusses on the modelling of such a hinge for operability studies.
The goal of these operability studies is to determine the weather and wave conditions in which the operation can be safely performed. Conventionally, the stiffness of the upend hinge is approximated by several linear springs between the vessel and the monopile. The aim of this thesis is to apply dynamic substructuring to existing Finite Element models of a hinge to more accurately describe its dynamic behaviour within hydrodynamic simulations. Hereafter, the response of the dynamically substructured model can be compared to the response of the conventional model.
The findings of the research show that it is possible to use dynamic substructuring to reduce the Finite Element models of an upend hinge and implement them into hydrodynamic simulations of an upend operation. When comparing the conventional model to the substructured model, it can be seen that there is a significant difference between the high-frequency response of the models. However, the responses of the models to prevailing ocean waves are very similar. For operability studies, this response is most relevant. Furthermore, the required computation time is significantly higher for the simulations employing the dynamically substructured models than for the conventional models. Therefore, it is not recommended to apply dynamic substructuring to model this upend hinge in operability studies. For situations where the high-frequency response is more relevant, however, dynamic substructuring may prove a valuable tool to more accurately describe the dynamic properties of an upend hinge or other marine equipment. ... Read more

This study presents the structural response of a Submerged Floating Tunnel (SFT) subjected to earthquake loading and other relevant static loading types. The SFT is a competitive solution for crossings of deep seas, canals and fjords, as it is submerged in water and floats at a fixed submersion depth. It is supported by its buoyancy and tethers, connected to the seabed to maintain the structure at an even submersion level. Influence on the environment is low compared to other competitive structures, as the structure does not occupy any surface of the seabed, except for the tether foundations. Moreover, the environment has little influence on the SFT’s operability, as it is insensitive to harsh weather conditions. However, in areas of high seismicity, the SFT’s dynamic characteristics must be carefully tuned to the expected type of earthquake to optimize its performance. Previous research showed that special care should be taken of the transition between the SFT and land tunnels, as this joint has proven itself to be the main challenge.

The purpose of this research is to alter the transition structure between the SFT and adjacent land tunnels, such that an optimal dynamic response of a SFT is found to seismic events (Chapter 1). Initially, its performance is measured by comparing the seismic serviceability limit state (SLS) response to the static ultimate limit state (ULS) response. Subsequently, for more severe earthquakes, it is measured by comparing the SLS seismic stresses with maximum allowed levels of concrete prestress.

To analyse the SFT behaviour, a global model has been created of the SFT+land-tunnel system in Chapter 3, which is built by means of a linear-elastic finite element method in Python. It accounts for dynamic loads through the soil and tethers, as well as static loads by the structure's weight, traffic and buoyancy. The influence of stagnant water is accounted for by the Morison equation. Soil-Structure-Interaction (SSI) is incorporated using a Substructuring method. The properties of the soil and tethers are found in local sub-models, after which the total structural response of the global model is solved in the frequency domain. Later, its response is transformed to the time domain to obtain a time-series of displacements and forces. Its dynamic characteristics are studied by comparing Fourier spectra with SFT natural frequencies, which gives insight in the influence of design choices on the time-domain response.

The global model is validated with a replica model in the finite element software DIANA FEA (Chapter 4). A realistic case study is defined based on a previous TEC project in Chapter 5 and later applied in a parameter study in Chapter 6. Here, the effects of various design choices with respect to the transition structure are monitored using 3 earthquake signals. 5 standard end-joints and 2 special end-joints with seismic base isolation and viscous dampers are tested. The effects of Multi-Support-Excitation is studied by letting earthquakes horizontally approach the SFT with various wave speeds and angles of attack. Finally, the effect of SSI is compared with a non-SSI case, to see its contribution to the research.

In Chapter 7, the results are discussed and in Chapter 8 a conclusion is provided together with recommendations for both TEC and future research.
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With the rise of hydrogen as a green alternative for fossil fuels, the demand for storage capacity of hydrogen increases significantly. Due to the high risk of explosions in urban environments it brings along, the blast analysis of buildings within in range of the explosions becomes more relevant.

The goal of this research is to develop a quick method to analyse the roof of a building subjected to blast load. This is done by first clarifying the blast load definition on a reinforced concrete (RC) structural element through existing design standards and literature. Next, the material behaviour of the concrete and the reinforcement steel is scrutinised by an extensive literature study. Materials behave differently under dynamic loads. The dynamic material properties are increased by the strength increase factor (SIF) and the dynamic increase factor (DIF).

In blast analysis, most energy is dissipated though plastic deformation. Therefore, it is of great importance to accurately describe the nonlinear behaviour of RC elements. The nonlinear behaviour of RC elements is translated in the moment-curvature relationship. This relationship is calculated on cross-sectional level and serves as input for the global beam or slab model. The global structural behaviour of the beam or the slab is calculated using the finite difference method (FDM). The FDM model generates a force-deflection (F-u) relationship which can be used in the single degree of freedom (SDOF) mass-spring system. The SDOF mass-spring system is used in this research to predict the dynamic behaviour of RC elements.

The research method is validated by published experiments and finite element analysis. Three experiments are reported, where the following results are obtained:
• Flexural stiffness may be assumed when the scaled distance is above 1.2 m/kg1/3. This is labelled as the ‘far field design range’.
• When choosing the DIFs carefully, the dynamic behaviour of RC elements can be predicted well.
• The FDM model can provide a good estimation of the nonlinear F-u relationship. The method of incorporating cracks in the FDM model is not previously presented in published literature.
• The unloading stiffness requires additional care. This research briefly covers the unloading stiffness.
• According to the UFC 3-340-02 (Department of Defence, US, 2008), RC elements without shear reinforcement and without the possibility of membrane action, fail at a support rotation of 2 degrees. This is where crushing is supposed to happen. This research shows that this is rather conservative and that the support rotation can go up to 6 degrees before failure.

Finally, the validated research method is applied on a case study. The case study contains a slab supported on two stiff beams on opposing sides. This results in a main span (weak direction) and a secondary span (stiff direction) due to the flexural stiffness of the supporting beams. In most cases, the slab supported by beams can be approached as a SDOF mass-spring system. After occurrence of cracks, the slab reinforcement in the main span direction will absorb most of the energy and is therefore the dominating member in the two degrees of freedom (2DOF) mass-spring system. ... Read more

In the underwater environment, it is all but silent. In most parts of the oceans, sunlight is barely available and thus marine animals have evolved to rely on sound for navigation, foraging and communication. Marine animals are not the only sources of underwater sound. Other natural sources such as earthquakes, waves and rain cause ambient noise, but also loud impulses. Furthermore, human activities consisting of dredging, surveying, construction and shipping cause loud noise in a wide frequency range. Underwater radiated noise (URN) from shipping has severe negative consequences on marine animals. The negative effects include auditory masking, stress, and behavioural and acoustic responses, possibly leading to collision with ships. It is evident that the mitigation of the underwater radiated noise of a ship is advantageous and worth researching.

In the past, plenty of research has been done into the modelling of the acoustic characteristics of vessels. A research gap was identified in the modelling of mitigation methods of the underwater radiated noise from ships with a focus on marine mammals. Up until now, most research has focused on the attenuation of vibrations on board a ship or radiated noise due to the propellers. At all times, the focus was either on human comfort or the radiated noise in general, however, for marine mammals certain frequency bands are of greater importance. It is valuable to assess the URN of a ship in the design phase, such that adjustments can be made to decrease the URN without excessive costs. The research goal of this thesis is:
Predict and mitigate the structure-borne underwater radiated noise of a ship in the design phase caused by onboard machinery.

The research goal and corresponding research questions are answered by first setting up the framework for the models. This framework sets the frequency analysis range to 20 - 200 Hz, formulates a reference ship case for validation of the data and gives the inputs and boundary conditions for the models. The acoustic metric of interest is set to the source level (SL) in dB re 1 μPa2m2.

Secondly, a simplified model is setup in Ansys 2021R2. This model is a 3D solid element model shaped like a beam. The equivalent beam (EB) model has similar global properties as the reference ship case. Around the EB model an acoustic domain is located that is modelled to represent an infinite domain. No physical boundary effects are included as the source level is per definition not dependent on this.
Subsequently, mitigation methods for machinery URN are researched and the resilient mount was found to be the most promising. A resilient mount is applied to the EB model in Ansys 2021R2 and source level spectra for different mount parameters are investigated.
Lastly, a two degree of freedom (2-DOF) schematisation is made that incorporates the Ansys model using a dynamic stiffness. The 2-DOF schematisation allows for faster computations of the complete model and thus a more extensive parameter study of the resilient mount is possible.

Over the frequency analysis range of 20 - 200 Hz, the results show that machinery structure-borne URN can be reduced by 45 - 65 dB re 1 μPa2m2. The reduction oscillates over the frequencies at lower frequencies. A linear SL reduction was observed from 60 Hz and above, which gradually lessened for higher frequencies. The SL reduction increased from 45 dB re 1 μPa2m2 to 60 dB re 1 μPa2m2 when the resilient mount damping ratio was changed from 0.18 to 0.02. In addition, the normalised resilient mount parameter study showed the system's parameter sensitivities and responses. It became clear that the resilient mount does not respond to a change in resilient mount damping as expected. The accuracy of the absolute results is subject to assumptions and limitations, which introduce uncertainties.

The absolute decrease in URN with the resilient mount was computed using acceleration input rather than force input. The acceleration input was found to have overestimated the 'no-mount' case, which was used to compare cases with the resilient mount. The total URN reduction with the resilient mount could thus have been overestimated. Furthermore, an effect of the model boundaries and the model domain size on the results was present in the models. The magnitudes of the results were influenced by this effect, which could not be eliminated due to the computational limitations reached. Finally, there was a scarcity of model input data and reference data. The magnitudes of the results were obtained and compared to limited data in order to determine the accuracy of the results.
Taking these limitations into consideration, the findings of this study should be interpreted with caution. The findings support literature claims that a resilient mount can reduce structure-borne machinery URN by 20 - 40 dB re 1 μPa2m2, with more reduction at higher frequencies.

The effect of the application of the resilient mount on marine mammals was hard to quantify. The structure-borne machinery URN is a part of the total URN of a ship. Due to the logarithmic relation of the noise, the reduction of one part could have very limited effects. Furthermore, the total soundscape in the ocean is formed by the combined noise of many ships. Moreover, the relation between the perceived nuisance of marine mammals and the URN levels is hard to indicate. The effect is undoubtedly positive but could be negligible in the bigger picture. At low speeds and close distances, the machinery URN is governing and the influence of URN from other ships is reduced. In those cases, the reduction of structure-borne machinery URN with resilient mounts could be expected to be the most positive for marine mammals.
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The Haringvlietbrug, which was delivered in 1964 and connects the island of Goeree-Overflakkee to the Dutch mainland, approaches the end of its lifetime. Rijkswaterstaat and Witteveen+Bos investigate the potential use of vibration-based structural health monitoring (SHM) to track deterioration. In vibration-based SHM, a change in the structure’s eigenfrequencies indicates probable damage but most current approaches focus on fundamental modes of the structure which are not or hardly affected by small structural impairments. In this study, vibration-based SHM was employed on local modes of vibration of the Haringvlietbrug, with the hope of detecting small-scale damage. New obstacles arose as a result of this: the influence of environmental and operational variabilities (EOV) on the eigenfrequencies of the structure was often larger than the influence of small damage. As a result, the EOVs should be filtered out of the recorded acceleration data before damage sensitive features can be extracted.
To investigate this, 32 accelerometers and 16 temperature sensors were installed in two segments of the Haringvlietbrug. The sensors yield a large data set which was analysed extensively. This made it clear, among other things, that the dynamic response of the bridge deck showed large variability when comparing different vehicle passages.

The first research objective was to investigate the applicability of similarity filtering (SF) to filter out operational variabilities from the Haringvlietbrug acceleration signals to extract damage-sensitive features. SF amplified similarities and damped differences between samples of vehicle passages. This way, only consequently excited modes should remain in the signals which were subsequently used as damage-sensitive features for SHM.
This study found that using SF to filter the operational variabilities from the Haringvlietbrug data set was ineffective. Three reasons were identified for this. First, the method was not robust as a single deviating sample or a poorly chosen filter coefficient significantly influenced the results. Secondly, missing closely-spaced modes might have caused inconsistency of the results. Lastly, SF was not able to converge to consistent behaviour as the variability of response of the bridge deck might be too great for different passages. The latter reason was investigated further in the remaining of the research.

The second research objective was to improve the understanding of the effect of vehicles on local bridge vibrations of the Haringvlietbrug for the application of vibration-based SHM. First, the eigensystem realisation algorithm (ERA) was used to identify and compare consistent mode shapes in order to better understand bridge deck vibrations and find patterns in the eigenfrequencies. ERA is an operational modal analysis (OMA) and output-only system identification technique.
ERA was able to identify two consistent modes in the data but they had a large variance in both shape and eigenfrequency. The uncertainties of the results were too large to draw firm conclusions based on ERA because two of ERA’s key assumptions were not perfectly met and the input samples were not optimal.

Next, a semi-analytical model of a segment of the Haringvlietbrug was built to simulate the important sources of the variability as found in the acceleration recordings of the Haringvlietbrug. The goal of the model was to investigate the sensitivity of the response of the beam to variations of input parameters. The model was both used for time-history analyses and eigenfrequency analyses. Parametric studies showed that the response of the beam was highly sensitive to the time delay between moving masses (dependent on the axle configuration and vehicle velocity), the unevenness (describing any source of vibration of the interaction between vehicle and bridge deck) and the vehicle velocity. These parameters influenced both the amplitude and the shape of the acceleration response of the Haringvlietbrug bridge deck in the time and frequency domain.
The effect of the three dominant parameters was further investigated by simulating four characteristic cases from the Haringvlietbrug data set. Hypotheses on the source of the measurement variability were formed by qualitatively comparing the results of the model to the measured response of the bridge. The model parameters were able to describe a large part of the variability but it was concluded that it is likely that some factors that were not included in the model also play a role in the variability of the measurements.

The above findings led to the following recommendations for further research. Firstly, it is recommended to only select similar vehicle passages for SF because this would improve the ability to converge to consistent modal behaviour. Secondly, should someone want to further explore ERA, it is recommended to equip a section of the bridge with a high spatial density of accelerometers to improve the reliability of the results.
Next, some recommendations related to the model were made. The first step of follow-up research would be to verify the influence of the model parameters on the dynamic response of the Haringvlietbrug by experimenting with different test vehicles. Subsequently, depending on the importance of the parameters, possible extensions of the measurement set-up for a new campaign were proposed. Secondly, the current model could be improved by introducing more parameters, like acceleration of the moving mass or by implementing a more realistic vehicle model, to be better able to explain the dynamic variability. Thirdly, more parameters could be investigated by building a 3D finite element model. This would make it possible to investigate the influence of the presence of multiple vehicles on the bridge and 3D wave propagation.
Upcoming research into data-driven approaches of vibration-based SHM of bridge decks is recommended to focus on similar passages as not all samples contain the same information on the dynamic behaviour of the structure. Decreasing the variability of the input samples might improve the performance of the algorithms.
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Human-induced rhythmic loading is an increasingly critical aspect in the design process of civil engineering structures such as sports stadiums and floors accommodating gym and aerobic classes. There are two main reasons for this trend. First, structures are becoming more slender with improvements in materials and construction techniques and modern trends in architectural designs. And second, crowds are getting livelier than previously was the case, their activities can become better synchronized due to the presence of various auditory and visual stimuli at above mentioned events.

In recent years there is also a growing discussion on the strength and stability of event structures. A very common type of structure is an event deck structure. Visitors gather on top of these decks during festivals and in some cases festival organizers place bars underneath them to efficiently use the structure. Personnel working in these bars experience the movement of the structure due to a dancing crowd and tend to feel uncomfortable. Engineers at Tentech are aware of this phenomenon through contacts with clients.

Nowadays, in the Netherlands, event deck structures are designed to withstand a vertical static load of 5 $kN/m^2$, prescribed by Dutch design codes. The amplitude of this static load is based on a dense static crowd. But according to existing literature, a synchronically jumping crowd can cause a vertical load which far exceeds the design load prescribed by design codes. This provides a reason to further investigate the extreme load case of a synchronically jumping crowd on an event deck structure.

A missing element in the standard design of structures subjected to a synchronically jumping crowd is the consideration of dynamic interaction between human and structure. In this research the focus is on how human-structure interaction (HSI) can influence the human-induced loading and the internal stresses caused by that loading in the structure. This is done by building a 3D finite element model in Abaqus.

A 3D finite element model is used to easily vary in the position of a jumper on the structure. Modelling group effects such as the coordination factor is also easier when using a 3D model. And in the case of an event deck structure a 3D model will result in more detailed results compared to 2D models because mechanical properties of an event deck can vary over the third dimension.

A mass-spring system is suggested to represent a jumping person. To simulate a synchronically jumping crowd, multiple mass-spring systems are used. By assigning an initial velocity to the mass in the mass-spring system, it is possible to simulate a similar mechanism as a jumping person colliding with a structure. By analysing the force in the spring over time it is possible to draw conclusions on the influence of human-structure interaction on the impact peak force. And by comparing the impact forces with the reaction forces which are measured at the base of the structure, the effects of structural vibrations on the internal stresses are determined.

It is found that taking HSI into account does influence the impact peak force and the internal stresses of the structure. But for an event deck structure with a natural frequency of 20 Hz or higher, this only accounts for an individually jumping person. It is found that the more people jump on a structure, the less significant the effect of HSI will be, even when a crowd tries to jump synchronically. This is caused by the natural time lag between each jumping person. ... Read more