Vertical Damping Research Articles

Development of a Matrix for Seismic Isolators Using Recycled Rubber from Vehicle Tires

Over recent decades, numerous strong earthquakes have caused widespread devastation, including citywide destruction, significant loss of life, and severe structural damage. Seismic base isolation is a well-established method for mitigating earthquake-induced risks in buildings; however, its high cost often limits its implementation in developing countries. Simultaneously, the global rise in vehicle numbers has led to the accumulation of discarded tires, intensifying environmental challenges. In response to these issues, this study investigates the development of a seismic isolator matrix using recycled rubber from vehicle tires, proposed as a sustainable and cost-effective alternative. Ten recycled rubber matrices were experimentally evaluated for their physical and mechanical properties. The matrix with optimal granulometry and binder content, demonstrating superior performance, was identified. This optimized matrix underwent further validation through compression and cyclic shear tests on reduced-scale prototypes of fiber-reinforced isolators, which included five prototype designs, two of which featured flexible reinforcement. The best-performing prototype comprised a recycled rubber matrix with 15% binder and glass fiber, exhibiting vertical stiffness and damping characteristics superior to those of natural rubber. Specifically, this prototype achieved a damping ratio of up to 22%, surpassing the 10% minimum required for seismic isolation, along with a vertical stiffness of 45 kN/mm, critical for withstanding the vertical loads transferred by buildings. These findings suggest that the recycled tire rubber matrix, when combined with glass fiber, is a viable material for the production of seismic isolators. This combination utilizes discarded materials, contributing to environmental sustainability.

Analytical model analysis of suspension bridges with tower-girder-connected dampers

Recently the tower-girder-connected damper has been utilized to suppress multi-mode vertical vortex-induced vibration (VIV) of long-span suspension bridges. In this paper, an analytical solution is proposed for the damping ratio of vertical bending modes of a single-span suspension bridge, with a vertical or/and a rotational damper mounted near the end of the stiffening girder, which significantly simplifies the design procedure for tower-girder-connected dampers on suspension bridges. The damping effect and the accuracy of the analytical solution are validated for Humen Bridge. It is found that both the vertical and rotational damper with an appropriate parameter selected can supply significantly additional damping ratio to multiple bending modes of the suspension bridge. The rotational and vertical dampers work in a similar way and provide nearly the same maximum additional damping ratio for each mode. In particular, for the first two symmetric modes, regions of reduced motion near the ends of the stiffening girder are developed due to the effects of cable geometry and elasticity, and this reduces the effect of the tower-girder-connected damper. Excluding these modes, the damper effect on a suspension bridge is similar to that on a tension beam with the same beam stiffness and horizontal tension forces.

Modelling of air springs for metro vehicles and studies on the effect of orifice damping

With the metro vehicle as the subject, a mathematical model of the main chamber, the auxiliary chamber and the orifice of the air spring were established based on the thermodynamic theory. The lateral nonlinear model is obtained based on the analytical geometry. Establish the four-point levelling valve and differential valve models through theoretical analysis. A complete three-dimensional air spring model is established. The correctness of the model is verified by comparing it with the actual data. The impact of orifice diameters and secondary vertical dampers on the dynamic performance of the metro vehicle is investigated. The results show that the secondary vertical damping configuration has a greater effect on vertical stability and acceleration but a minor impact on operational stability. Metro vehicles equipped only with air springs in the smaller diameter orifice do not need to be configured with a vertical damper, resulting in excellent dynamic performance and savings in production costs.

A robust and fail-safe semi-active vertical damper to improve ride comfort

In recent years, the technical progress in railway engineering has led to the integration of electronic elements in suspension components that once were purely mechanical. Many studies have been carried out, developing active and semi-active suspensions. Among these, semi-active suspensions are particularly attractive due to their simpler design compared to fully active ones. In this context, this paper proposes a semi-active vertical damper to be implemented on the secondary suspension stage of rail vehicles. A prototype is developed by modifying a pre-existing passive damper through the addition of an external servo-valve which manages an additional by-pass channel between the compression and rebound chambers. The prototype is characterised on a dedicated test rig. A reduced vehicle model is then developed as the starting point in developing a sliding mode controller to manage the semi-active feature of the damper. A time-varying sliding surface containing the state of the system and car body accelerations is proposed. Finally, the damper prototype is tested on a hardware-in-the-loop test rig, focusing the experimental campaign on quantifying the damper performance, the evaluation of the controller robustness and a failure analysis to study the behaviour of the proposed solution even in the case of unexpected failures.

Virtual track irregularity establishment for load prediction of heterogeneous bogie frames for virtually coupled trainsets

In this paper, we establish the virtual track irregularity (VTI) considering suspension system dynamics for load prediction of heterogeneous bogie frames for virtual coupled train sets (VCTS). At first, the dynamic characteristics of axlebox spring set and primary suspension vertical damper of A/B-type high-speed trains are analyzed and compared for establishment of frequency-varying parameter simplified vehicle dynamic models (FVP-SVDMs). Then, a frequency-segmented time-domain inversion (FSTIM) of VTI suitable for FVP-SVDMs is conducted, and a quantitative evaluation method for VTI consistency is established. Finally, the consistency of VTIs based on measured loads of A/B-type high-speed train bogie frames is quantitatively assessed, and the agreement between the measured and predicted load spectra based on VTI is evaluated. Based on the FVP-SVDM and the corresponding VTI, the equivalent load amplitude error between the predicted and measured bouncing load is 7%. The VTI technology provides the possibility for VCTS to eliminate the need for conducting the main test before applying the new vehicles on the line. In addition, for the fleet is running on the same track through the VCTS communication, the VTI will provide the theoretical support for implementing active control across the entire fleet.

Improving the energy efficiency and riding comfort of high-speed trains across slopes by the optimized suspension control

As the link between cities, the high-speed train (HST) not only effectively enhances national and regional accessibility, but also induces much energy consumption. On the other hand, passengers have a higher requirement for riding comfort of HST than before. Considering the impacts of slope gradient on energy consumption and vertical carbody acceleration, this paper optimizes the scale factor of the damper controller depending on the running condition to juggle the energy efficiency and riding comfort when HST is across slopes. Firstly, the multibody dynamics simulation model of HST is established to evaluate the energy consumed by motion resistances and carbody vibrations. Then the Skyhook control strategy is applied to the secondary vertical damper of the vehicle model. The effects of vehicle speed, slope gradient, and scale factor of the Skyhook controller on energy saving and vertical carbody acceleration of HST are investigated. Based on the simulation results, the Gaussian process regression model is established to predict the vehicle performance and describe the bi-objective optimization problem. It is demonstrated that the optimized Skyhook control system can at most save energy consumed by motion resistances by 8.52 % or reduce vertical carbody acceleration by 37.14 % without sacrificing the other target. Finally, a comprehensive feasibility and economic analysis of the proposed control system is carried out to promote its practical implementation.

Proposal and Evaluation of Vertical Vibration Theory of Air Caster

Urbanization and human development have increased the exposure of seismic risk. Therefore, engineers need to develop new and more efficient technologies to protect people and objects from the disastrous consequences of earthquakes. Air casters have gained attention and have been utilized in the past decade as effective seismic vibration control devices. Although such active isolation systems perform well in mitigating horizontal input vibrations, they might cause excessive rocking motions, if not designed properly. This fact emphasizes the importance of exploring the vertical dynamic properties of air isolation systems. To gain such an understanding, this research examines and proposes a formula for the vertical stiffness and damping of air caster systems. Theoretical solutions to the vertical stiffness and damping of such systems have been explored. Computer simulations considering fluid-structure interaction have also been performed to understand the dynamic behavior of the supporting air layer. Results have been compared to validate the proposed dynamic quantities within the considered simulation range. It is also concluded that the instantaneous air layer thickness, representing the air chamber pressure, and the bearing inlet flow rate are the key factors in determining the dynamic properties of the air layer. It is concluded that to evaluate the performance of the air caster seismic isolation device and increase the probability that the qualified seismic isolation performance will be exhibited, it is necessary to investigate which parameters are greatly involved in the viscous damping coefficient and the spring constant of amass-spring-damper system equivalent to the air caster isolation system.

A Simulation Approach for Analysis of the Regenerative Potential of High-Speed Train Suspensions

This study primarily investigates the adaptability and performance of hydraulic–electric regenerative dampers for high-speed trains by substituting conventional primary dampers with hydraulic–electric regenerative dampers. The primary objectives are to develop a detailed model of primary suspension regenerative damper (PSRD) energy conversion that incorporates factors such as oil pressure loss, motor efficiency, and overall system efficiency, and to perform a comprehensive comparative analysis of vibration responses, wheel wear, comfort indices, and power generation using an integrated MATLAB and SIMPACK co-simulation platform. The results reveal that at an operational speed of 350 km/h, the dynamic responses of the carbody, bogie, wheelset, and dampers equipped with the proposed PSRD systems closely align with those of conventional primary vertical damper systems. The detailed PSRDs’ hydraulic–mechanical–electrical model effectively captures the subtleties of oil pressure fluctuations and their impacts. The wear distribution and magnitude across the vehicle remain consistent during acceleration, constant, and deceleration speeds, ensuring uniform wear characteristics. Under real-world railway operational conditions, the ride comfort metrics of vehicles fitted with regenerative dampers are comparable to those with conventional primary vertical dampers. Furthermore, each regenerative damper can generate up to 21.72 W of electrical power, achieving a generation efficiency of 45.28%. Finally, a test rig was designed and fabricated to validate the primary suspension regenerative damper (PSRD) model, showing good agreement between predicted and actual damping force and power regeneration, with results indicating a peak damping force of 12.5 kN and approximately 230 W of regenerated power. This research provides a theoretical foundation and experimental validation for implementing power regeneration mechanisms in railway transportation, demonstrating that the hydraulic–mechanical–electrical PSRD model can fulfil the performance criteria of conventional dampers while offering substantial energy harvesting capabilities. This advancement not only enhances energy efficiency but also contributes to the sustainable development of high-speed rail systems.

Structural design and multi-objective optimization of an MR isolator based on flow valve-cone rubber structure

Due to the distinctive working environment of high precision machining and manufacturing field, it poses challenges in meeting the isolation requirements, including limited installation space, multi-dimensional vibration, and a wide range of vibration frequencies. To tackle these obstacles, this paper introduces a magnetorheological (MR) isolator that offers adjustable vertical damping characteristics while guaranteeing three-axis vibration isolation through an inclined cone structure. First, the structure of the isolator was designed by combining a flow valve damper with a conical rubber structure. Second, in pursuit of lightweight design and enhanced magnetic field strength, collaborative simulations using ANSYS and Maxwell are conducted to subject the critical components of the isolator to multi-objective optimization. The optimization results demonstrate that the mass of the isolator has been reduced by approximately 27.7%, while the magnetic field intensity has increased by around 20%. Finally, the performance of the MR isolator was verified through static testing and dynamic testing, respectively. The experimental results demonstrate that the isolator can generate a maximum damping force of approximately 778[Formula: see text]N when exposed to a current of 1.5[Formula: see text]A. Compared to the initial value of 445.06[Formula: see text]N at 0[Formula: see text]A, there has been an approximate increase of 1.74 times.

Basic Characteristics and Vibration-Serviceability-Related Properties of Recent Footbridges in China

Abstract Purpose This study identifies basic characteristics and vibration-serviceability-related properties of recent footbridges in China. Also, it characterizes relations between vibration-serviceability-related properties and basic characteristics. Methods A database is constructed for recent footbridges in China based on systematic literature survey. For each footbridge, it collects basic information (name, function, province, location, service year), structural information (girder cross-section type, main span length, width, bridge type, girder material, deck material, first lateral and vertical natural frequencies, first lateral and vertical damping ratios), response information (crowd density, acceleration responses, mitigation measures), etc. Results Data analysis shows natural frequencies decrease with increasing bridge span. Estimation relations are proposed to quantitatively express fundamental natural frequencies and main spans in vertical and lateral directions. Damping ratios vary from 0.0015 to 0.0325, indicating the low damping capacity of the footbridges. Footbridges with non-solid cross-section are more vulnerable to human-induced excitations. Most footbridges apply mitigation measures, with mitigation efficiency from 18% to 70%. Conclusion This study provides designers with first judgements on feasibility of footbridges’ design scheme, for instance, a first estimation of natural frequency. Also, the reported information may guide them towards right directions of better design scheme, for example, by adjusting structural information.

Experimental Study on the Mechanical Properties of Nylon Fabric-Reinforced Elastomeric Isolators (N-FREIs)

In recent decades, carbon fiber, glass fiber, polyester and Kevlar fiber have been utilized to replace the steel shims in conventional steel-reinforced elastomeric isolators (SREIs). This study chose nylon fabrics owing to their extreme low cost, low elastic modulus and good adhesion to rubber, and nine nylon fabric-reinforced elastomeric isolators (N-FREIs) were manufactured with different design parameters. Compression and compression shear tests were, respectively, conducted to investigate the mechanical properties together with their influential factors of the N-FREIs. Results show that the vertical load-carrying capacity of the isolator is high enough to sustain a compressive stress of 10[Formula: see text]MPa without visible damage. The compressive stiffness of N-FREI is much smaller than that of SREI, and the vertical damping ratio under cyclic compression reaches up to 7%. In the compression shear tests, the shear stiffness of the isolator first decreases and then increases as the shear strain increases within 300%, and the equivalent damping ratio varies between 9% and 14% for different sizes of the isolator. Additionally, due to the flexibility and extensibility of the low modulus nylon fabric, both vertical and horizontal stiffness decrease a bit with an increase in the number of fabric layers. Finally, a formula for calculating the horizontal stiffness of N-FREI is proposed, it provides a comprehensive mathematical model to predict the behavior of the N-FREI under horizontal shear conditions.

Analysis of Sliding Vibration of an Electric Shoegear Against a Conductor Rail in Medium- and Low-Speed Maglev Trains

In recent years, medium- and low-speed maglev trains have been put into use in China. It was discovered during testing that the electric shoegear and conductor rail system generate significant vibration and noise when the electric shoegear passes through expansion and intermediate joints. By analyzing the sound pressure level (SPL) of the noise signal, it was found that the A-weighted SPL of the noise was between 77.83 dBA and 91.80 dBA, when the maglev trains were running normally, which reached the level of annoyance. Based on the theory of self-excited frictional vibrations, the finite element models of an electric shoegear and conductor rail system (shoe–rail system) were established. The main frequency of the vibration signal calculated by the transient dynamic analysis method was 1510.05 Hz. The self-excited frictional vibrations of the system were further studied using the complex eigenvalue analysis (CEA), and the causes of the noise are analyzed. The results show that the system has unstable vibration when the friction coefficient was greater than or equal to 0.21. The parameter sensitivity analysis showed that the slip shoe material of the electric shoegear, vertical damping of the suspension device, and tuned mass damper (TMD) structure have an important influence on the generation of vibration and noise of the system. Installing an appropriately tuned mass damper structure can suppress or eliminate the unstable vibration of the system.

A Novel Vertical Active Damping System for the Superconducting Electrodynamic Suspension

A Novel Vertical Active Damping System for the Superconducting Electrodynamic Suspension

Shaking table test of vertical isolation performances of super high-rise structure under metro train-induced vibration

Metro systems are integral to improving transportation efficiency and providing convenience to the public; however, they cause environmental vibrations. To analyze the metro vibration propagation law and vibration isolation performance of a 120 m super high-rise structure positioned directly above two metro tunnels, a shaking table test at a 1/30 scale ratio is conducted in this study. First, a model for the shaking table test is designed and manufactured, and measurements of metro train-induced ground vibrations obtained on site are input into the model. Subsequently, vertical vibration tests are performed on the models with and without laminated rubber isolation bearings. Finally, their dynamic characteristics, vibration propagation law, and vibration isolation effect are analyzed, and the vertical vibration isolation mechanism of the structure is discussed. The results indicate that the metro vibration exerts a resonance effect on non-isolated super high-rise structures, thus resulting in the progressive amplification of the metro vibration response along the floors of the structure. The vibration isolation layer formed by the laminated rubber isolation bearings significantly reduces the vertical modal frequency and increases the vertical damping ratio of the super high-rise structure, thus effectively attenuating the vertical metro vibration. Unlike the non-isolated structure, the vibration-isolated structure can avoid severe structural resonance responses in the dominant frequency band of the metro vibration. This study aims to offer insightful considerations for evaluating metro vibrations in super high-rise structures and may serve as essential reference for vertical vibration isolation.

Hydraulic interconnected suspension for rail vehicles: a preliminary analysis

This paper aims at analyzing a preliminary layout for a Hydraulic Interconnected Suspension (HIS) for rail vehicles. The device is intended to replace the primary vertical dampers and its design aims at decoupling the heave and roll responses. HIS solution provides additional tuning possibilities to optimize and refine the primary suspension stage of rail vehicles. A physical numerical model is developed, and the influence of three design parameters on the forces generated by the HIS is studied.

Applications of vertical damping wigglers in an X-ray diffraction limited storage ring

This study presents a lattice design for an X-ray diffraction limited storage ring (DLSR) light source with a circumference of 864 m and achieving an ultralow natural emittance of 25.6 pm·rad (N-IBS). However, the ultra-low emittance and long damping times lead to significant intra-beam scattering (IBS) effects. To address this issue, the study explores the implementation of vertical damping wigglers (VDWs) to decrease damping times, reduce beam horizontal emittance, and generate vertical emittance to achieve a “round beam” in the 864mDLSR. Through theoretical analysis and accelerator toolbox (AT) simulations, the impacts of VDWs with varied parameters were investigated, and the optimal period length, peak field, and total length were determined. Additionally, the twelve quadrupole magnets in both the front and rear cells of the VDWs were employed to correct linear optics. The findings demonstrate that VDWs could significantly reduce the beam's equilibrium emittance and damping times of the 864mDLSR. Furthermore, a comparison between the spectral brightness and flux of the 864mDLSR with and without VDWs revealed that the 864mDLSR employing VDWs yielded higher brightness and flux.

Dynamic Response Analysis of Mega-Sub Isolated Structures under Multiaxial Earthquakes

With the use of seismic isolation techniques on mega-sub structures, several scholars have carried out research on them. However, little research has been carried out on mega-sub isolated structures under multiaxial earthquakes. There have been instances in actual engineering where the peak vertical acceleration exceeded the horizontal direction, and the vertical seismic component will also amplify the dynamic response of the structure in the horizontal direction, so in practice, it is necessary to consider the influence of the vertical component of the earthquake on the structure. To investigate the dynamic response of mega-sub isolated structures under unidirectional earthquake and coupled earthquake, this paper used numerical methods to analyze the influences of the horizontal and vertical damping ratio of the isolation layer, the horizontal and vertical frequency ratio of the main substructure, and the mass ratio of the main substructure on the acceleration and displacement of the main and substructure. The optimum parameter values are finally achieved by analytical calculations, which provide a basis for further optimization and practical design of the structure. Finally, the collision between the main and sub-structures in the mega-sub isolated structure was simulated, and the influences of the peak ground motion, main and subframe spacing, vertical seismic component, and sub-structure height on the collision force and acceleration were analyzed. It was shown that the conflict of the main and sub-structures generates instantaneous, large collision forces, which also instantaneously amplify the acceleration and base shear force response, which should be avoided in practical engineering.

A comprehensive study of viscous damper configurations and vertical damping coefficient distributions for enhanced performance in reinforced concrete structures

A comprehensive study of viscous damper configurations and vertical damping coefficient distributions for enhanced performance in reinforced concrete structures

Analysis on abnormal low-frequency vertical vibration of medium–low-speed maglev vehicle

A newly-developed medium–low-speed maglev test vehicle was used to obtain the vertical dynamic response signals of the vehicle-line coupled system when the test vehicle was standing still on four different types of lines through field tests. It was found that abnormal low-frequency vertical vibration occurred on the car body, so that an excellent ride index of the test vehicle cannot be ensured. As the stability of the vehicle at standstill is the prerequisite to the stability of the vehicle running at a certain speed, it is necessary to investigate the causes underlying the abnormal vibration and propose corrective measures through theoretical studies in combination with the measured results. Therefore, this paper established a coupled vehicle-track system dynamics model considering active feedback control, and investigated the stability and bifurcation behavior of the coupled system through nonlinear dynamics theory and numerical simulation. Field test results show that: the vertical ride index of the test vehicle was rated as “Unqualified” when it was standing still; the vertical vibration eigenfrequency of the car body is basically the same (between 2.10 and 2.20 Hz) when the test vehicle was standing still on the four different lines, indicating that the abnormal vibration was basically independent of the line type; the vertical dynamic response of each measurement point on the electromagnet, F-rail and bridge was normal. The theoretical and simulation studies show that: the numerical simulation of the theoretical model can effectively reproduce the abnormal vibration; the malfunction in the nonlinear characteristics of the air spring vertical damping (i.e. the damping malfunction) is the main reason for this vibration, and the abnormal vibration corresponded to the supercritical Hopf bifurcation dynamics behavior in nonlinear dynamics; after the air spring was restored to normal, the equilibrium point of the coupled system was stable under the influence of different initial disturbances. This study may provide an important reference for reducing the abnormal low-frequency vertical vibration of the test vehicle at standstill.

Design and Analysis of Driver Seat Suspension System

Abstract: Over the years, the vehicle driver has endured a great deal of agony and anguish as a result of poor road conditions or lengthier travel lengths that they must complete within a certain time limit. It is a misery to them that the standard or budget vehicles do not feature a good suspension system for their wellbeing. This research article demonstrates a unique design of scissor seat suspension for vehicles, as well as models for manufacturing and testing the system to eliminate low-frequency and high-amplitude vibrations that might cause health problems for vehicle drivers or passengers. Although scissor seat suspension is frequently utilized in commercial vehicles to reduce interior vibrations, a common optimization difficulty emerges because designs often involve a compromise between seat acceleration and suspension travel. The stiffness and damping characteristics of the scissor seat suspension are also investigated, and a simplified model of the scissor seat suspension is presented. The effect of damping force and mass on a human is investigated in preparation for future design and testing. The ideal vertical stiffness damping response is then cascaded into a performance-oriented model, and the design parameters are optimized with a multibody kinematics model focused on the scissor seat suspension structure.