Damping Research Articles

Frequency-independent damping models for a high-rise building with simultaneous horizontal and vertical seismic motions

Recent seismic analyses indicate that the structural damping ratio should be considered frequency-independent, for safe and accurate estimations. In response, damping models like the Wilson–Penzien (WP) damping model, that is one of the modal damping, provide frequency independence across all modes; however, these models require considerable computational resources, especially for large-scale models. While Rayleigh damping is computationally efficient, it maintains a nearly constant damping ratio only within a limited frequency range. To address these limitations, several alternative damping models have been introduced, such as uniform (UN), causal hysteretic (CH), and extended Rayleigh (ER). We use the factor Wξ to represent the frequency range where the damping ratio remains approximately constant, defined as the ratio of maximum to minimum frequencies (fmax/fmin), within a specified tolerance of the target damping ratio. For Rayleigh damping, Wξ = 3.7, while the CH and ER models achieve Wξ values greater than 20. Although the UN model achieves a high Wξ, it demands large computational resources in the implicit analyses, commonly used for seismic response studies. In this study, we address the simultaneously inputting horizontal and vertical seismic motion into a large-scale dynamic analysis model of a high-rise building. In this analysis, horizontal, vertical, and local beam vibration modes spanning a wide frequency range appeared. Considering that these modes require the same damping ratio, damping models with Wξ values of 50 or higher are desirable. However, this threshold considerably exceeds Wξ values achievable with the existing models, rendering these models unsuitable for the intended application. Therefore, we propose and validate the efficiency of two new damping models (ER-W and CH19) that meet this requirement by improving existing models. Using these damping models, it is possible to analyze the horizontal and vertical modes and local vibration modes of the beam, assuming a simultaneous horizontal and vertical input to a high-rise building.

Correlations between spectrum-based and other ground-motion intensity measures considering various damping ratios

Spectral acceleration at a given period, SA( T), is usually combined with other intensity measures (IMs) for vector-valued ground-motion selection and seismic hazard assessment. The correlations between SA( T) and other IMs have been extensively studied, based on the SA-related IM pairs with a damping ratio ( ξ) of 5%. Yet, ξ varies notably with various types of structures. This article thus investigates the correlations of SA( T, ξ) with 10 commonly used non-SA IMs (e.g. Arias intensity), and the correlations of damping-specific acceleration spectrum, spectrum, and displacement spectrum intensities, namely ASI( ξ), SI( ξ), and DSI( ξ), with the other IMs. Comprehensive correlation analyses are conducted to derive the correlations for the IM pairs considered based on the NGA-West2 database and compatible ground-motion models. The results indicate that increasing ξ generally yields stronger correlations, and the difference between the ξ-specific and 5%-damped correlation coefficients could be larger than 0.2. The neural network and polynomial regressions are subsequently used to develop parametric models for estimating the correlations of SA( T, ξ)-containing pairs and the other IM pairs, respectively. All the models developed exhibit good performance in terms of predictive accuracy. The application of the proposed models is demonstrated within the generalized conditional IM approach. The models proposed could be useful for ground-motion selection and seismic demand or risk assessment for structures with various ξ values.

Modal Frequency and Damping Identification of the FAST Cabin-Cable System

The Five-Hundred-Meter Aperture Spherical Radio Telescope (FAST) faces challenges in establishing high-precision rigid connections between the receiver and the reflective surface due to its vast spatial span. Innovatively, FAST suspends the feed cabin in mid-air using six supporting cables. The precise positioning of the feed focal point is achieved through the coordinated control of cable extension and retraction, along with the A-B axis and the Stewart platform within the cabin. The cables and the feed cabin form a large parallel mechanism. Since the cables are flexible, and the feed cabin remains at a high altitude during observations, it is inevitably subject to internal and external disturbances. To quickly dissipate these disturbances, the system requires a certain level of damping, which directly affects the pointing and tracking accuracy of FAST. During the 2022–2023 operational period, there were multiple instances where the pulleys of the curtain mechanism on the supporting cables became stuck and were carried to the top of the towers by the cables. This also led to the phenomenon where the pulleys, after being stuck, would rapidly slide down the cables due to accumulation. At such moments, the cabin-cable system would experience instantaneous excitation, causing vibrations. This study uses the intrinsic time-scale decomposition (ITD) method to analyze the inertial navigation data installed in the cabin during these events, identifying modal frequencies and damping ratios. The analysis results show that the lowest primary vibration frequency of the FAST cabin-cable suspension system ranges from approximately 0.12 to 0.2 Hz, with a damping ratio of no less than 0.004. These data indicate that the current structure of FAST has a strong energy dissipation capability, providing important reference points for improving the control accuracy of FAST and for the upgrade of the feed support system.

Development and experimental study of a replaceable double stage coupling beam damper

A double stage coupling beam damper (DSCBD) was proposed and tested in this paper. The DSCBD comprises a viscoelastic damper and a metallic damper connected in series. Deformation of the DSCBD in the first stage was concentrated on the viscoelastic damper, which provided initial stiffness and energy dissipation capacity. With the increase in displacement and the initiation of the second stage, the deformation of the viscoelastic damper was constrained by the limiting mechanism and triggered the deformation concentrating in the metallic damper. These further increased the stiffness and energy dissipation capacity and the DSCBD exhibits the double stage behavior. The DSCBD proposed in this paper can simultaneously satisfy the seismic requirements of the main structure under different levels of seismic excitation, without installing different types of traditional dampers to achieve the same effect. A performance-based design method was proposed. Two full-scale DSCBD specimens were subjected to quasi-static multi-stage cyclic loading tests to investigate the effects of different aspect ratios. The test results showed that DSCBD with an aspect ratio of 3.2 exhibited ideal shear failure mode, and the minimum equivalent viscoelastic damping ratio in the second stage was 22.58 %, while the DSCBD with an aspect ratio of 4.4 exhibited unexpected bending failure mode, and the maximum equivalent viscoelastic damping ratio in the second stage was 19.42 %. In addition, the DSCBD with an aspect ratio of 3.2 showed better low-cycle fatigue capacity, whose degradation of bearing and energy dissipation capacities can be controlled within 5 % after 30 additional loading cycles. The accuracy and the correction scheme of the design method were verified by the test results.

An analytical model for estimating aerodynamic damping of wind turbines in the shutdown state

As wind farms are constantly being constructed, the risk of tower failure for wind turbines increases significantly under strong winds. Compared with the extensively concerned wind-induced behaviors during the operating state, those ones during the shutdown state attract little attention but may lead to serious problems of damages or even collapse. To clearly grasp the aero-structure interaction in the shutdown state, this paper develops an analytical model for estimating aerodynamic damping of wind turbines. In this method, an analytical expression of aerodynamic damping coupling matrix is derived via the combination of multibody dynamics and first-order Taylor expansion. This matrix is further quantified as the ratio of modal aerodynamic damping with the aid of state-space equation and complex eigenvalue analysis. This treatment can facilitate the straightforward application of efficient calculation methods, such as frequency domain analysis and uncoupled analysis. More importantly, the developed model is able to simultaneously consider multiple realistic factors, such as blade flexibility, tower top rotation, yaw error, wind shear, and pitch angle. This model may have the high calculation efficiency and accuracy, as well as strong applicability for estimating the aerodynamic damping. Numerical examples based on a typical 5 MW wind turbine are employed to validate the effectiveness of the developed model. Experimental analyses demonstrate that this model outperforms the existing formula and presents a high consistency with OpenFAST in the estimation of aerodynamic damping. Meanwhile, the influence of multiple realistic factors is quantitatively analyzed, which even makes the estimation error exceed 70%.

Parametric analysis of self-excited aeroelastic instability of an isolated single-axis two-dimensional flat solar tracker

The escalating global energy demand is driving a transition towards sustainable energy sources, particularly solar power, which is experiencing significant growth. Single-axis, horizontally mounted photovoltaic (PV) solar trackers are emerging as one of the most cost-effective methods for solar energy generation. However, the reduction in structural stiffness has led to an increase in aeroelastic issues, some of which have resulted in catastrophic failures around the world, posing significant challenges. Recent aerodynamic studies have attributed these instabilities to stall flutter. The absence of a validated theory hampers early estimation of these aeroelastic phenomena. The primary aim in this work is to develop a semi-empirical framework to predict aeroelastic instabilities in isolated two-dimensional solar trackers, focusing on dynamic self-excited responses. This effort aims to improve the reliability and efficiency of solar tracker designs, optimizing energy utilization in the context of the evolving renewable energy landscape. The semi-empirical formulation developed here reveals the influence of geometric and mechanical characteristics on the critical wind speed at which aeroelastic instabilities set in. The effects of reduced inertia (m⁎) and mechanical damping coefficient (ξmech) of the structure on the critical wind speed at which aeroelastic instabilities arise are analyzed here. It is shown that increasing either inertia or damping has a minor impact on the critical speed when the initial values of these parameters are large, while the changes are significant when these initial values are small.

Experimental study on the seismic behavior of all-steel buckling-restrained brace with constrained coupler

This study proposes a novel all-steel buckling-restrained brace (BRB), in which cross-shaped (or H-shaped) steel members and double steel tubes are employed for the core members and buckling-restraining members, respectively. The core members are equipped with a constrained coupler in the central region. The square outer tube, welded to one end of the bracing system, uses spacers to prevent buckling of the inner tube. The hexagonal inner tube is connected to a constrained coupler by welding, thereby preventing the buckling of the core members. The constraint system provides a quadruple restraint mechanism comprising the inner tube, outer tube, constrained coupler, and spacers. Global and local stability are analyzed based on Eulerian theory, the principle of virtual work, and yield line theory, respectively. Cyclic loading tests were performed on four test specimens of the proposed BRB and four traditional BRBs without constrained couplers. Comparative analysis, through cyclic loading tests, reveals that the proposed BRB exhibits a stable energy dissipation performance post-yielding under compression, outperforming the specimens without constrained couplers in terms of the equivalent viscous damping ratio, cumulative plastic deformation, and the compression-strength adjustment factor. Furthermore, the numerical model was constructed and validated using the test results. The effects of the core width-to-thickness ratio and the gap size between the core member and inner tube on hysteretic behaviors were investigated. The contributions of this study can provide a reference for the application of BRBs in the engineering of more complex high-rise buildings and mega-spatial structures.

Experimental investigation of damping ratio of sand-laponite and sand-bentonite mixtures using one-dimensional bender elements

Damping ratio and dynamic shear modulus are fundamental parameters for assessing the seismic response of geotechnical structures such as retaining walls, dams, tunnels, foundations, landfill covers, and embankments. Numerous seismic wave sources can substantially impact the stability and integrity of geotechnical structures, influencing design choices and the implementation of alternative solutions. In this study, the damping ratio of sand mixed with small quantities of laponite was determined by an experimental set-up using bender elements meticulously constructed for this study. Comparative tests were conducted with pure sand (i.e., control test) and sand mixed with bentonite to evaluate the effects of two types of nanoparticles. The results revealed that the damping ratio (ξ) of pure sand was approximately 7.48 %, which is generally compatible with values reported in the literature, taking into account the variations of sand and errors associated with laboratory equipment and electronic devices. Over time, the damping ratio of pure sand gradually decreased, reaching equilibrium at 0.99 % after 3–4 days of continuous shaking. The highest observed damping ratios for sand-laponite mixtures were 59 %, 69.7 %, and 98.6 % for sand+1 % laponite, sand+2 % laponite, and sand+3 % laponite, respectively. After reaching the peak, the damping ratio gradually decreased to equilibrium at 11 %, 16 %, and 19.4 %, respectively. The higher damping values for sand-laponite specimens reflect a viscous damping contribution from the presence of laponite at sand grain contacts, with higher laponite content resulting in increased damping. In comparison, the peak damping ratios for sand-bentonite mixtures were 21.9 %, 42.7 %, and 67.9 % for sand+1 %, +2 %, and +3 % bentonite, respectively. The findings highlight the potential of laponite to enhance the damping capacity of sands, which could be valuable for seismic design applications requiring improved energy dissipation.

Dynamic characterization of permanent magnet electrodynamic suspension system with a novel passive damping magnet scheme

In the paper, a 3D electromagnetic force analytical model incorporating the vertical vibration velocity of the permanent magnet is derived using the virtual magnetic charge method, which is used to examine the system’s dynamic properties. Then, a novel passive damping scheme based on permanent magnets is developed to enhance the system stability without increasing the complexity of the system. Finally, the dynamic experiment is carried out on the rotating platform employing a dynamic test apparatus, where the validity of the analytical model is checked and the effect of the damping magnet is explored. The results exhibit that the permanent magnet electrodynamic suspension system is self-stabilizing yet underdamped, and the vertical damping coefficient decreases as the velocity and airgap increase. The system has favorable stability in the absence of disturbance with a fluctuation of roughly 0.5 mm. The proposed damping scheme reduces the vibration overshoot from 41.18% to 32.47% and shortens the settling time from 3.29 s to 0.97 s. Meanwhile, the system is especially sensitive to long-wave irregularities in the high-speed range throughout the experiment with the track irregularity, where the vibration amplitude of the guidance system can be reduced by approximately 8 times from 4.6 mm to 0.57 mm by applying the damping magnet scheme. As a result, the proposed passive damping magnet scheme offers a pretty damping effect, which is capable of significantly improving the stability of the permanent magnet electrodynamic suspension system.

Modal analysis of concrete gravity dam incorporating pre-stress condition along with soil–structure interaction

Purpose The fundamental period of the structure plays an important role in the seismic analysis. This study aims to analyze the modal response of dam, the two-dimensional (2D) FEM model is developed by using ANSYS 2022 R1 software. Design/methodology/approach To examine the optimized mesh size to achieve grid independence, the variable element size has been considered, and its optimal value is calculated using the technique of response surface optimization. Further, the effect of damping ratios of 5%, 8% and 10% is also considered for the free vibration analysis of the dam structure. Findings The results show that the natural frequencies of the dam decrease with a reduction in stiffness of the whole structure. Further, the effect of pre-stress conditions is analyzed and the study has proved that the natural frequency increases after considering the pre-stress as initial condition during modal analysis. Further, it is found that the damping has a substantial effect on frequency for higher modes of vibrations. Research limitations/implications The study only focused on modal analysis of the gravity dam, and this study’s results can be used further to evaluate the dynamic behavior of the dam including hydrodynamic conditions. Originality/value The finite element tool is used to evaluate the modal response of gravity dam incorporating pre-stress and damping ratio along with soil–structure interaction. Moreover, to the best of the authors’ knowledge, no earlier study has been conducted to evaluate the effect of damping and pre-stress conditions on the stability and natural frequency of the system.

Experimental and numerical investigation on the influence of bilge keel shape on roll damping

Excessive roll amplitudes due to roll motion are undesirable in marine ships. Consequently, it is imperative to conduct a detailed analysis of roll motion and the associated roll damping characteristics. This study experimentally and numerically investigates the roll damping characteristics of bilge keels with various geometric shapes on a ship model under different roll amplitudes. By comparing the non-dimensional roll damping coefficients obtained from experiments and numerical analyses, it is observed that bilge keels with geometries differing from the conventional plate shape exhibit distinct roll damping coefficients. Specifically, bilge keels with sharper tip ends demonstrate higher roll damping coefficients. Based on these findings, it is recommended that the corners and tip end of bilge keels be sharpened to enhance the roll damping coefficient.

Wind-Induced Vibration Control of High-Rise Buildings with Double-Skin Façades Using Distributed Multiple Tuned Façade-Dampers-Inerters

To address the shortcomings of tuned mass dampers (TMD), such as excessive internal space occupation and overlarge physical mass, this paper proposes a tuned façade damper inerter (TFDI) that utilizes parts of the outer façades of double-skin façades (DSF) as damping mass, capitalizing on the lightweight and efficient characteristics of inerters. The TFDI effectively resolves the challenge of multi-layer connections of inerters in high-rise buildings by utilizing corridor space. By vertically distributing TFDIs, a distributed multiple TFDI (d-MTFDI) system is formed. The configuration and motion of equations of this system are presented, and the control effectiveness is validated using wind tunnel test data. Two tuning modes are further proposed: unified tuning mode and distributed tuning mode. For the unified tuning mode, analytical expressions for optimal tuning frequency and damping ratio are derived; for the distributed tuning mode, numerical optimization methods are employed to determine the optimal tuning frequency range and damping ratio. Comparative results indicate that the distributed tuning mode achieves higher control efficiency than the unified tuning mode, with a significant reduction in the required optimal damping ratio. Furthermore, comparisons with d-MTMD demonstrate that d-MTFDI significantly enhances wind-induced vibration control performance.

Topology and size optimization of viscous dampers with discrete design variables by outer approximation

This article proposes a novel seismic retrofitting approach for the topology and size optimization of fluid viscous dampers using discrete design variables. The design variables are the damping coefficients of the dampers, and they are chosen from catalogues, leading to practical optimal design solutions. The optimization problems considered are formulated as 0–1 nonlinear programming problems. An algorithm based on outer approximation and that relies on first-order information is proposed to find optimized designs with modest computational resources and time. The effectiveness of the proposed approach is demonstrated through optimal seismic retrofitting of three-dimensional irregular frame structures. In the optimization problem formulation, the retrofitted structures are subjected to realistic seismic ground acceleration records with constraints on inter-storey drifts and total storey accelerations.

Sensing equivalent kinematics enables robot-assisted mirror rehabilitation training via a broaden learning system.

Robot-assisted mirror therapy has been widely developed to help remodeling of premotor cortex for patients suffering from motor disability of limbs. Nevertheless, it is difficult to achieve real-time adaptive control in robot-assisted mirror rehabilitation training, particularly for patients with varying levels of limb impairment. This paper proposes an equivalent kinematics control framework based on the Broaden Learning System model for active robotic mirror rehabilitation, where people's bilateral upper limbs actively perform mirror movements to enhance the impaired limb's participation. The framework accommodates a broaden learning model from sensing multi-kinematic features to adjust the robotic damping coefficient in assisting human participants to complete mirror-symmetry training. Besides, in order to adapt to inter-patients' variability with different disability levels, a challenge-level modification interface is also fused for safer training. This model is verified by additional symmetry indicator such as position trajectory error and force. Experimental results show that the weaker subjects can also maintain mirror movement with the stronger subjects under the help of this model and verify the performance of framework in mirror-symmetry effects and movement smoothness. This leads us to believe that the framework can safely and efficiently assist human participants in completing mirror-symmetry movement. The framework has the potential to improve outcomes in smoother and safer mirror-symmetry training by sensing multi-kinematic features. Future studies are necessary to involve clinical trials with actual patients.

Integral Sliding Mode‐Composite Nonlinear Feedback Control Strategy for Microgrid Inverter Systems

To enhance the dynamic performance and robustness of the voltage control system of islanded microgrid inverters, a new control strategy combining integral sliding mode (ISM) control and composite nonlinear feedback (CNF) control is proposed. In ISM control, firstly, a new reaching law is designed to improve movement quality in the reaching phase by improving the power term and introducing the inverse tangent function. Then, to improve disturbance observation accuracy, a variable gain extended state observer is designed by improving the regulation mechanism of the state variables according to deviation control. Using the idea of variable damping, linear and nonlinear feedback are combined into CNF control. Specifically, linear feedback provides a small damping ratio for faster system response, while nonlinear feedback increases the damping ratio to improve steady‐state performance. Simulation results show that the integral sliding mode‐composite nonlinear feedback (ISM‐CNF) control strategy cam balances convergence speed and chattering better and achieves higher steady‐state accuracy than conventional strategies. Moreover, ISM‐CNF control has better robustness to reference voltage variations and disturbances caused by sudden load changes. Therefore, the ISM‐CNF control strategy can accomplish voltage control of islanded microgrid inverters quickly and steadily, effectively suppressing system disturbances and enhancing stability and power quality. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Investigation on the variations of dynamic characteristics of anchor bolts considering transverse inertia effects under tensile loads

Abstract In the case where tunnel anchor bolts are located in strata with limited surrounding rock boundaries, the response signals of the anchor bolts are affected by the tensile load and the transverse inertia effect, resulting in a decrease in the reliability of the non-destructive testing (NDT) results. To accurately assess the anchorage quality under these disturbances, a vibration energy loss model for anchor bolts after excitation was proposed. NDT experiments and numerical simulation studies were conducted on intact and defective anchor bolts under different conditions, analyzing the variation patterns of structural dynamic characteristics such as the the first-order natural frequency, the first-order damping ratio, and the vibration energy loss under the influence of tensile load and transverse inertia effect. The results show that during the gradual increase of the tensile load, the first-order natural frequency and the first-order damping ratio exhibit an overall trend of first increasing and then decreasing, while the rate of the energy loss initially decreases and then increases. The presence of anchorage defects leads to a reduction in the first-order natural frequency, the first-order damping ratio, and the energy loss of the anchor bolt. As the transverse inertia effect intensifies, the first-order natural frequency initially increases and then decreases, the first-order damping ratio decreases, and the energy loss initially decreases slightly before increasing. The numerical simulation verifies the applicability of the theoretical model and explores the influence of defect location on energy loss. The results indicate that the closer the defect location is to the free end, the less the vibration energy loss of the anchor bolt.

Exact Solution of Nonlinear TVMD Based on Maximizing Damping Enhancement Effect for Acceleration Response Control

The tuned viscous mass damper (TVMD) exhibits superior control effect and energy dissipation capability compared to the viscous damper (VD). Existing literature has primarily focused on the control of absolute acceleration response in structures by linear TVMD, with limited research on nonlinear damper for controlling structural performance and efficiency. This study proposes a methodology for determining the optimal parameters of linear TVMD. The closed-form solution of the nonlinear TVMD is derived through stochastic linearization based on the linear TVMD, aiming to minimize the damping ratio of TVMD by utilizing the damping enhancement effect of the system. For lightly damped structures, the closed-form solution remains a reliable method for accurately approximating TVMD design parameters. Compared to traditional fixed-point theory, the TVMD developed through the proposed methodology demonstrates superior control performance, especially in terms of absolute acceleration, with a smaller damping ratio and minimal deviation from the optimal state of the TVMD. Additionally, the study investigated the influence of the damping index on the optimal parameters and the efficacy of the TVMD in vibration control. It is observed that reducing the damping index can improve structural performance, particularly in long-period structures with small mass ratios, although it may reduce the efficiency of the TVMD. Notably, TVMDs with lower mass ratios maintain higher efficiency regardless of the structural natural period. The damping index does not affect the optimal frequency ratio or the mean square response. Ultimately, the effectiveness of the optimization method is displayed through the examination of response spectra following 22 real seismic events, showcasing its adaptability across various structural types. The comparison of the root-mean-square response between the VD and TVMD across different periods shows consistent results, with a maximum deviation of only 10%. The TVMD is highly effective at regulating the structural response, excelling particularly in controlling the absolute acceleration of long-period structures, where it reduces maximum absolute acceleration by 20% more than displacement. The proposed exact solution rapidly and precisely identifies the design parameters of nonlinear TVMD by the desired specifications, thereby offering theoretical guidance for practical engineering applications.

Experimental Investigations of Seismic Performance of Girder–Integral Abutment–Reinforced-Concrete Pile–Soil Systems

Integral abutment bridges (IABs) have been widely applied in bridge engineering because of their excellent seismic performance, long service life, and low maintenance cost. The superstructure and substructure of an IAB are integrally connected to reduce the possibility of collapse or girders falling during an earthquake. The soil behind the abutment can provide a damping effect to reduce the deformation of the structure under a seismic load. Girders have not been considered in some of the existing published experimental tests on integral abutment–reinforced-concrete (RC) pile (IAP)–soil systems, which may not accurately represent real conditions. A pseudo-static low-cycle test on a girder–integral abutment–RC pile (GIAP)–soil system was conducted for an IAB in China. The experiment’s results for the GIAP specimen were compared with those of the IAP specimen, including the failure mode, hysteretic curve, energy dissipation capacity, skeleton curve, stiffness degradation, and displacement ductility. The test results indicate that the failure modes of both specimens were different. For the IAP specimen, the pile cracked at a displacement of +2 mm, while the abutment did not crack during the test. For the GIAP specimen, the pile cracked at a displacement of −8 mm, and the abutment cracked at a displacement of 50 mm. The failure mode of the specimen changed from severe damage to the pile top under a small displacement to damage to both the abutment and pile top under a large displacement. Compared with the IAP specimen, the initial stiffness under positive horizontal displacement (39.2%), residual force accumulation (22.6%), residual deformation (12.6%), range of the elastoplastic stage in the skeleton curve, and stiffness degradation of the GIAP specimen were smaller; however, the initial stiffness under negative horizontal displacement (112.6%), displacement ductility coefficient (67.2%), average equivalent viscous damping ratio (30.8%), yield load (20.4%), ultimate load (7.8%), and range of the elastic stage in the skeleton curve of the GIAP specimen were larger. In summary, the seismic performance of the GIAP–soil system was better than that of the IAP–soil system. Therefore, to accurately reflect the seismic performance of GIAP–soil systems in IABs, it is suggested to consider the influence of the girder.

Investigation of a novel magnetic inerter-based absorber under shock load

Inerter-based absorbers have proven exceptionally effective in dampening vibrations within a specific low-frequency range, thus finding widespread application in engineering. However, their performance under shock loads poses a more intricate challenge, demanding the development of structures that can encompass a broader spectrum of vibration reduction frequencies. This paper introduces the magnetic inerter shock absorber (MISA), a groundbreaking approach that addresses this challenge. The cornerstone of the MISA lies in the ingenious linkage of its additional mass to the base. This design minimizes the influence on the payload while achieving an astounding amplification factor of thousands. Once integrated into a single-degree-of-freedom system, comprehensive nonlinear motion differential equations are formulated to capture the dynamics triggered by shock loads. Utilizing Fourier analysis, the shock loads are decomposed, and the harmonic balance method is employed to obtain the analytical structure of the system. Following this, numerical solutions are derived via the shock alternating frequency time method, providing insight into the ultimate dynamic response. The results demonstrate that the MISA swiftly suppresses residual vibrations while attenuating transient responses. Finally, an experimental verification confirms the MISA’s ability to reduce shock vibrations. This work not only introduces a novel solution for mitigating the shocks of transient vibrations and residual oscillations induced by shock loads, but also provides guidance for implementing advanced vibration control by adjusting the rotational damping ratio.

Evolution of modal properties in the non-proportionally damped coupled vehicle–bridge system

The modal properties of bridges are crucial parameters in engineering applications, and their variation caused by moving vehicles has been increasingly recognized in recent years. However, existing closed-form analytical expressions for the varying modal properties during vehicle passage exist only for simple structural configurations. This paper proposes an innovative method for analyzing the instantaneous modal properties of the system, considering general boundary conditions and the damping effect. First, only general boundary conditions are considered, and the results show that the location of the maximum system frequency shift depends on the mode shape. Then the damping effect is considered, observing that the system is non-proportionally damped in most cases, making it difficult to obtain a closed-form solution using existing methods. To solve this, we transform the system of second-order ordinary differential equations into a set of fourth-order ordinary differential equations and derive the closed-form solution for system’s modal properties. Based on this solution, we introduce the concept of Critical Coupling Damping (CCD), which defines the transition between the coupled description and the moving mass case. This work deepens understanding of changing modal properties during the traverse of sprung masses, and so has numerous potential engineering applications.