Multi-mode Vibration Control Research Articles

Passive structural control for wind turbine towers using a novel dual-track nonlinear energy sink

With larger rotors and taller towers developed to capture more wind energy, the tower structures become slenderer and more sensitive to wind loads, resulting in vortex-induced vibration (VIV) in both downwind and crosswind directions. The vibration control is faced with the challenges of broadband and multi-directional dynamic responses. Thus, this paper proposed a new type of dual-track nonlinear energy sink (NES) aimed to achieve the multi-mode and multi-direction vibration control of wind turbine towers. The two-degree-freedom coupled governing equations of the wind turbine tower with the dual-track NES are established and solved numerically, with full considerations of aerodynamics and fluid–solid interactions. Then, an optimized design of the dual-track NES is performed theoretically. To evaluate the vibration mitigation performance of the dual-track NES, a series of wind tunnel tests are carried out and analyzed further, in terms of the acceleration time-history response, statistical characteristics, frequency and damping ratio. It is demonstrated that the proposed NES functioning as an energy-dissipating device is efficient and robust in mitigating the dynamic response of wind turbine towers, even enabled to address the vortex resonance. It is remarkable that the dual-track NES can synchronously realize the vibration control in multi-mode and multi-direction by increasing the damping ratio of primary structure.

Auxetic enhancement of the shunted piezoelectric effect for vibration suppression

Shunted piezoelectric patches connected to passive electric circuits can be attached to a host structure for effective vibration attenuation. The effect of an auxetic layer to enhance the electromechanical coupling and subsequently the vibration suppression is studied here. Three different configurations are considered for the layer: a classical, a homogeneous auxetic and a layer with microstructure leading to auxetic behavior. First, is presented a modification of the “current-flowing” shunt circuit for multimode vibration control. Two finite element models have been validated, the frequency response graph of the system and the most suitable values of the electric parameters are calculated and a comparison is provided. Furthermore, it is shown that the vibration reduction of the second and third eigenmodes can be enhanced, provided that an auxetic of significant thickness is used. The results demonstrate the effect of the auxetic boosting on vibration suppression.

Multi-Mode Vibration Control of Super-Long Stay Cables with Negative Stiffness and Stockbridge Dampers

Installing mechanical dampers near the cable anchorage is a commonly used measure for suppressing rain-wind-induced vibrations (RWIVs) of stay cables. However, the high-mode vortex-induced vibrations (VIVs) are still observed on super-long stay cables installed with dampers. To this end, the study presents the combination of a negative stiffness damper (NSD) and Stockbridge dampers (SDs) to simultaneously suppress cable RWIVs and VIVs. In the proposed cable–NSD–SDs system, the NSD is installed near the cable anchorage to suppress cable RWIVs, and the SDs are installed at a higher location to suppress cable VIVs. First, the generalized characteristic equation of the cable–NSD–SDs system is derived for computing the coupled damping effect. Subsequently, a novel design method of an NSD and two SDs for mitigating cable multi-mode vibrations is proposed, and its effectiveness is numerically verified on an ultra-long stay cable of the Sutong Bridge. Finally, the control performance of an NSD and two SDs for the cable under white noise and harmonic excitations is emphatically evaluated and compared. Results indicate that the NSD–SDs system is quite effective for mitigating high-mode vibrations of super-long stay cables. Compared with the cable–NSD system, the cable acceleration response of the cable–NSD–SDs system is reduced by over 35%.

Robustness Evaluation of Negative Stiffness Damper for Cable Vibration Mitigation Based on Interval Model with Experimental Validation

The negative stiffness damper (NSD) has emerged as a promising passive vibration control device for cable structures due to its simplicity and effectiveness. However, uncertainties stemming from both internal and external environmental factors can potentially compromise the NSD’s performance in real‐world applications, posing risks to cable safety. In response, this paper conducts a robustness evaluation on an integrated cable‐NSD system, taking into account various potential uncertainties. Specifically, the uncertain parameters are described by interval variables. Consequently, an interval model is constructed to delineate the boundaries of cable dynamic responses when subjected to these uncertainties. The model’s accuracy is validated against experimental results. Subsequent simulations involve assessing interval responses for both single‐ and multimode cable vibrations under varying uncertainties. Finally, the NSD’s robustness concerning cable vibration control is evaluated using the model, which incorporates the first‐passage theory. This analysis delves into the relationships among confidence levels, performance measures, and the variation range of uncertainties. The results indicate that for single‐mode vibration control, there is a 90% confidence level that the damping ratio reduction remains within 10%. As for multimode vibration control, a 90% confidence level is established that the amplification falls within 17%.

Spanwise layout optimization of aerodynamic countermeasures for multi-mode vortex-induced vibration control on long-span bridges

Aerodynamic countermeasures are widely used to control vortex-induced vibration (VIV) on long-span bridges. However, due to the lack of appropriate three-dimensional (3-D) VIV analysis approach, these countermeasures are usually installed along the entire span of the bridge deck, leading to excessive costs. This study proposes an optimization method for the spanwise layout of aerodynamic countermeasures, aiming to achieve an economical control scheme for multi-mode VIV. An improved mode-by-mode 3-D VIV analysis approach is developed based on the generalized polynomial model to predict the VIV responses of the bridge with different spanwise layouts of aerodynamic countermeasures. The genetic algorithm (GA) is then employed to search for the most economical layout scheme with constraints of limited multi-mode VIV responses. Two alternative types of search spaces for the optimization are presented. The effectiveness of this optimization method is demonstrated on a long-span suspension bridge in conjunction with finite element simulation and wind tunnel tests. The results show a noteworthy reduction in the use of aerodynamic countermeasures, thus highlighting the necessity of countermeasure layout optimization.

Discrete viscous dampers for multi-mode vortex-induced vibration control of long-span suspension bridges

Multi-mode vertical vortex-induced vibrations have been observed on several long-span suspension bridges, where several vertical modes of stiffening girder are excited in turn with increasing of wind velocity. This paper proposed a discrete viscous dampers solution and its optimization targeting multi-mode vortex-induced vibration control for long-span suspension bridges. The minimal modal damping ratio was used to evaluate the performance of the damper system. The wind tunnel test verified that the modal damping ratio is an alternative to the resonance response amplitude and can be obtained by complex modal analysis. The ternary search algorithm was adopted to find the optimal damper parameter for the Yingwuzhou Yangtze River Bridge, which is a suspension bridge that suffered excessive vortex-induced vibrations. Using linear damper elements to connect the bridge tower and the bridge girder directly turned out to be a feasible method of increasing multiple modal damping ratios. Four torsional eddy current dampers have been installed in the Yingwuzhou Yangtze River Bridge, based on the numerical optimization results calculated in this paper. Although the measured modal damping ratios were smaller than the numerical results, the structural damping increased by three times after dampers were installed, and the requirement of the current specification was satisfied.

Study on enhanced performance of CuFe alloy's eddy current damping and its advantages in multi-mode vibration control of stay-cable

This study presents an innovative solution to address the performance degradation of eddy current dampers (ECD) at high speeds. It replaces the traditional copper conductor with a magnetically and electrically conductive CuFe alloy. The damping force equation for this CuFe alloy-based ECD (CuFe-ECD) is derived and validated through rotor experiments and a simplified finite element model. Results confirm that CuFe alloy enhances damping performance, with CuFe20 exhibiting outstanding quasi-bilinear characteristics, particularly at higher speeds. CuFe10, CuFe15, and CuFe30 also demonstrate similar behavior. The study explores the impact of CuFe alloy properties (conductivity, permeability, and thickness) on the bilinear damping curve. CuFe alloys notably reduce magnetic reluctance, especially in thicker conductors, mitigating skin effect and armature reaction in the electromagnetic field. Finally, the CuFe-ECD is utilized for multi-mode vibration control using the long cable of the Sutong Bridge. The results indicate that the modal damping ratios of modes 1st-20th can reach 5‰, which is superior to other schemes. In high-order modes, the damping ratio of the 35th-40th modes still stabilizes at 3.72–3.90‰. It can be concluded that the bilinear damper has significant advantages in multi-mode vibration control: compared with the single linear damper scheme, it can improve the vibration reduction effect of multi-mode control, and compared with the dual linear damper scheme, it can reduce the number of dampers and achieve better economic benefits.

Multimode Vibration Control Strategies of Long-Span Bridges Subjected to Multi-hazard: A Case Study of the Runyang Suspension Bridge

Multimode Vibration Control Strategies of Long-Span Bridges Subjected to Multi-hazard: A Case Study of the Runyang Suspension Bridge

Modal analysis and vibration control of a vertical cable with dual tuned mass dampers

This paper proposes a vibration model for modal analysis and vibration control of a vertical cable-dual tuned mass damper (C-DTMD) coupled system. The proposed model introduces several non-dimensional parameters to describe the in-plane vibration of the coupled system. Moreover, the phenomenon of modal split is comprehensively studied to present the complex vibration modes. Parameter analysis is conducted to show the influence of length ratio, mass ratio, damping ratio, and frequency ratio on vibration reduction. In addition, the theoretical model is verified using finite element methods. A practical vertical cable in Jiangyin Bridge with designed wind loads is chosen as a numerical example. The results show that DTMD devices can effectively reduce the modal vibration and have great potential for multi-mode vibration control of vertical cables in suspension bridges. The proposed model can accurately describe the in-plane vibration modes of C-DTMD systems and provides a basis for the optimal design of damper parameters.

Multimode vibration control of stay cables using pseudo negative stiffness MR damping system

At present the vibration control of stay cable suffers from low damping effectiveness in single mode vibration caused by the limitation of damper installation position as well as the poor modal compatibility, that is, a rapid degradation performance when the actual mode deviates from the designed optimal mode. In this paper, one practical semi-active magnetorheological (MR) damper based control solution is proposed to address the problems faced in multi-modal vibration control of stay cables. The semi-active pseudo negative stiffness (PNS) control strategy takes full account of the MR damper’s mechanical characteristics and the demands of the stay cable vibration control. Compared with the linear equivalent model, the proposed time-varying model exhibits more details of the damping force and the nonlinear response of the damped stay cable, which shows its essential role in the optimal design of MR-PNS scheme. Then the optimal design method of MR-PNS multi-modal vibration control for stay cable is summarized by taking the first three modes vibration control of the J20 cable in Nanjing Baguazhou Yangtze River Bridge as simulation examples. The simulations of cross-modal, multi-modal and wind-induced vibration cases are conducted respectively, while the results show that the optimal designed multi-modal MR-PNS scheme can simultaneously exceed the passive maximum modal damping ratio within first three modes. The advantages of the proposed MR-PNS method in high damping efficiency and modal compatibility could be verified by comparing with the passive multi-modal damping solution.

A magnetic negative stiffness eddy-current inertial mass damper for cable vibration mitigation

Previous studies have shown superior control performance in mitigating vibrations of stay cables by using passive control devices such as negative stiffness dampers (NSDs) and inertial mass dampers (IMDs). Integrating the advantages of the two dampers, we propose a novel passive control device termed magnetic negative stiffness eddy-current inertial mass damper (MNS-ECIMD) for cable vibration mitigation. A mechanical model of the MNS-ECIMD is proposed and validated against dynamic test data of a small-scale prototype. A parametric analysis is conducted based on the finite difference model of the cable-damper system to investigate the effects of the magnetic negative stiffness coefficient, inertance coefficient, and eddy-current damping coefficient of the MNS-ECIMD on cable vibration mitigation performance. The MNS-ECIMD performance is further validated using a small-scale cable test, of which the results illustrate its superior performance for the first two modes compared with the ECIMD. A simple parameter optimization procedure is then presented for cable multi-mode vibration control, which is then demonstrated via numerical simulation of a 306 m-long stay cable of Stonecutter Bridge in Hong Kong. Numerical results illustrate that the MNS-ECIMD significantly outperforms conventional viscous dampers and the ECIMD for cable multi-mode vibration control, owing to the additional negative stiffness effect.

Analytical study on the effects of flexural rigidity and negative stiffness in the optimal tuning of inerter-based damper for cable vibration mitigation

The control performances of inerter-based dampers on stay cables, usually governed by relevant damper parameters (such as inertance, stiffness, and damping coefficients), are sensitive to parameter variation around the optimal range. Further given these inerter-based dampers amplify the vibration amplitude at the damper location, the effects of cable’s flexural rigidity, which is often ignored in previous studies, are examined in this study. The results suggest an approximate 10% increase in all three design parameters (i.e., inertance, stiffness, and damping coefficients) is required to achieve optimal control compared with the case ignoring the flexural rigidity. In addition, the potential combination of inerter-based dampers with negative stiffness elements is also discussed in this study, which offers a more flexible layout and enhances multi-mode cable vibration control performance. Consequently, the tuning procedures are updated, and the revised optimal tuning formulas taking account of both the cable’s flexural rigidity and the introduction of negative stiffness are presented in this paper.

Dynamic behavior and damping enhancement of cable with negative stiffness inerter damper

To improve the control performance of stay cables, a novel negative stiffness inerter damper (NSID) that consists of a negative stiffness device in parallel with an eddy current inerter damper is proposed in this study. The novelty of the NSID is that the damper can utilize the damping enhancement of the negative stiffness and inerter for cable vibration control, simultaneously. A further novelty is to carefully explore the modal behavior of the cable based on optimum parameters of the NSID. On this basis, the damping enhancement principle and conditions of the NSID for cable vibration control are demonstrated. In addition, the closed-form equation of the cable modal damping ratio and the design equation of the NSID for multi-mode cable vibration control are derived. And the control efficacy of the NSID is evaluated through the damping enhancement of the design cable modes. The results show that the modal behavior in the nth cable mode can be divided into three distinct regimes according to the negative stiffness and the corresponding optimum inertance, which are underdamped mode, subcritical damped mode, and the (n − 1)th underdamped mode. In the first regime, the inerter and negative stiffness have similar effects on enhancing damping ratio of the cable and reducing the optimum damping coefficient of the NSID. In the second and third regimes, the mode crossover phenomenon is observed, and the actual damping ratio of the nth cable mode decreases as the negative stiffness or inertance increases. The NSID performs better than the VD, VID, and NSD in mitigating multi-mode cable vibrations. Increasing negative stiffness can further improve the control performance and reduce the optimum inertance and damping coefficient of the NSID.

Modal vibration decomposition method and its application on multi-mode vibration control of high-speed railway car bodies

The vibration of a railway car body is a superposition of the vibrations of its various modes. It is typically easy to obtain the physical vibration of the car body using sensors in an in situ or a simulated test vehicle. However, it is difficult to determine the modal vibration of the body and its contribution. There are no effective multi-mode vibration control methods for the car bodies. This study proposes a modal vibration decomposition method (MVDM) based on singular value decomposition (SVD) and least squares fitting (LSF). Accordingly, the physical vibration of a railway car body is decomposed into modal vibrations. A method for calculating the modal contribution factor (MCF) is presented, and the dominant flexible modes of the car body are determined and considered the target for the vibration control method. Several pieces of equipment are considered as dynamic vibration absorbers (DVAs) to control the multi-mode vibration of the car body using the dynamic vibration absorption theory and determine the installation parameters of the individual equipment. Finally, the effectiveness of vibration control is verified through dynamic simulations. The results demonstrate the effective decomposition of the physical vibration of the car body into various modal vibrations using the MVDM. This provides accurate data for the MCF calculation and determination of the flexible modes of the car body. The proposed method reduces the vibration of the target modes and improves the ride quality of the railway vehicle. At the optimal damping ratio, the vibration of the DVA-based equipment itself is acceptable. This allows for multi-mode vibration control without requiring extensive modification to the car body structure or suspension system parameters of the vehicle.

A novel eddy current damper system for multi-mode high-order vibration control of ultra-long stay cables

Recently, the multi-mode high-order wind-induced vibration of the ultra-long stay cables has been observed on several cable-stayed bridges, which may result in a visual panic of the users and the fatigue of the stay cables at anchorage ends. In order to investigate the multi-mode high-order wind-induced vibration characteristics of ultra-long stay cables, a vibration monitoring system (VMS) of the stay cables is established on the Sutong Bridge (STB). Furthermore, to suppress the in-plane and out-of-plane vibration responses of the stay cables simultaneously, a novel eddy current damper system (ECDS) is proposed in this study. The damping coefficients of the ECDS for multi-mode high-order vibration of the stay cables are determined via a modified method. Moreover, laboratory tests are conducted to evaluate the performance of the developed dampers. Furthermore, the field tests of seven stay cables of the STB are carried out to identify the modal damping ratios of the cable-damper system via the free vibration method. The results show that it is feasible to provide sufficient additional modal damping ratios for multi-mode high-order vibration of ultra-long stay cables applying the ECDS proposed in this study. Finally, the one-year field measurements of the wind-induced vibration responses of the seven stay cables of the STB are carried out to validate the ECDS suppress effects on multi-mode high-order vibration control of ultra-long stay cables. The measurement results show that the multi-mode high-order vibration responses of the monitored stay cables of the STB are effectively suppressed.

Influence of Internal Rubber Damper on Cable External Viscous Damper Effectiveness

In practice, the internal rubber dampers are widely installed inside the cable guide pipe between the external viscous damper and the cable anchorage. In order to study the effect of the internal damper on the performance of the external viscous damper, the theoretical analysis model of a taut cable with an internal rubber damper and an external viscous damper is established in this paper, where the internal damper is assumed to be a high damping rubber damper with a flexible support and the external damper is considered to be a linear viscous damper. Then, the numerical iterative formula and approximate solution expression for the cable modal damping ratio are derived. Based on the approximate solution, the parameters of the internal rubber damper are analyzed comprehensively, and its influence on the cable modal damping in cable multimode is studied as well. Results show that, except for the support flexibility of the internal rubber damper, other parameters will have a negative effect on external viscous damper effectiveness. From the perspective of cable multimode vibration control, the installation of an internal rubber damper significantly weakens the modal damping, and this effect is more pronounced in lower frequency modes.

Multi-mode vortex-induced vibration control of long-span bridges by using distributed tuned mass damper inerters (DTMDIs)

Tuned mass damper inerter (TMDI) has been proved to be a feasible device for vibration control of long-span bridges due to its excellent space performance. However, existing design method for TMDI is conducted mode-by-mode. When applied to multi-mode control of the bridge through multiple TMDIs, it cannot consider the synergistic effect among the TMDIs and thus leading to a suboptimum design result. This paper presents an efficient method for multi-mode vortex-induced vibration (VIV) control of long-span bridges by using spatially distributed TMDIs (DTMDIs). The governing equations of the bridge-DTMDIs system are established in modal coordinate. A global optimization method considering the synergistic effect among the DTMDIs is proposed and compared with conventional mode-by-mode approach through a numerical case study. The robustness of the control schemes against variations in structural and aerodynamic parameters is investigated. The influence of inerter span length on the control efficiency is also discussed. The results show that the proposed global design method can achieve a better control efficiency with even less TMDIs as compared with conventional mode-by-mode approach. The proposed method can also be extended to VIV control of some other line-like structures.

A robust optimised shunted electrodynamic metamaterial for multi-mode vibration control

This paper presents a design approach for a shunted electrodynamic metamaterial (EDMM) for broadband robust vibration control. A unit cell of 12 inertial electrodynamic transducers is proposed, where the response of each transducer is tuneable via a connected resistive and inductive shunt circuit. The variations in the parameters of an off-the-shelf transducer are characterised experimentally, before the effect of this variation on the shunted response is investigated. It is shown that instability of the system is a limiting design factor. A problem is proposed whereby the resistive and inductive shunt values of an EDMM attached to a parametrically uncertain structure are to be found, and given the complexity of the design problem, a Particle Swarm Optimisation (PSO) is utilised to find a solution using an analytical model of the system. The results of the optimisation show that the effects of uncertainty in the actuators must be included, otherwise, the solution can be unstable. However, it is also shown that it is sufficient to ignore the uncertainty in the structure and optimise the EDMM considering actuator uncertainty alone, since the EDMM motion is then highly damped and, therefore, inherently robust to structural uncertainties.

An improved multi-mode seismic vibration control method using multiple tuned mass dampers

Multiple vibration modes of an engineering structure might be excited by earthquake ground motions. Multiple tuned mass dampers (MTMDs) are widely used to control these multi-mode vibrations. However, in the commonly used MTMD system, the mass element in each tuned mass damper (TMD) is normally assumed to be the same. To improve the performance of MTMDs for seismic-induced vibration control, non-uniform MTMD masses are adopted in the present study to improve the mass utilization of TMD, and a location factor is proposed to determine the best location of each TMD in the MTMD system. The effectiveness of the proposed method is validated through numerical study. The results show that the proposed method effectively reduces the seismic responses of the structure induced by multiple vibration modes.

Optimized negative stiffness damper with flexible support for stay cables

The negative stiffness damper (NSD) has been gaining increasing attention for cable vibration control owing to its superior energy dissipation capacity. Recent research has implied that a flexible support, rather than a rigid support, might be advantageous to improving the performance of an NSD. This study further simplifies the design of an NSD for multimode cable vibration control by leveraging the potential advantages of a flexible support. First, an equivalent model is established for the NSD support system. The deformation across the support is illustrated. Through parametric analysis, the parameter ranges for which the support flexibility exhibits various types of impacts on the damping force are obtained. Thereafter, to ensure rigidity, the lower limit of the support stiffness is determined. An optimization procedure is proposed for the single-mode cable vibration. The method of determination of the optimized NSD and its corresponding support is presented. On this basis, a simplified method is eventually developed for multimode cable vibration. A full-scale cable on a real bridge is adopted as the design prototype. A series of performance evaluations is conducted for validation. The theoretical and numerical results indicate that a small-sized NSD with a flexible support is capable of realizing the required damping. An optimized support stiffness is found to be independent of the vibration mode. Therefore, it may be concluded that only the highest mode should be taken into consideration and it considerably simplifies the design of the NSD for multimode cable vibration.