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Stay cables are becoming slender and their fundamental frequencies are becoming lower with the span of bridges increasing, thus leading to the occurrence of multi-modal vibration under various excitations. As a simple and effective strategy for cable vibration mitigation, the external damper is widely used in practice. However, one damper normally can target only fewer modes and poses limited effects on the control of multi-modal vibration. This paper proposed the use of a joint control system combining a viscous damper and a tuned mass damper for mitigating the multi-modal vibration of stay cables, followed by the optimization methodology of tuning and positioning. The control performance of the joint system was evaluated by numerical simulations. The feasibility of the joint control system was validated by analyzing the results of the comparative study, therefore providing a possible solution to multi-modal and high-modal vibration of stay cables.

Steel–concrete hybrid towers (SCHTs) have been adopted as a popular supporting structure for wind turbines with the increasing hub height and rotor diameter. The excessive transverse vibration of the supporting tower adversely compromises the turbine’s operation and leads to structural deteriorations. The tuned mass damper (TMD) has been validated as an efficient device integrated with high-rise structures in vibration suppressions. This study aims to provide a reliable method for determining the key parameters of the TMD to obtain the optimal performance in vibration suppressions. This study begins with a rigorous theoretical analysis to investigate the dynamic responses of the SCHT. The dynamic analysis serves as a basis for developing a dynamics model of the SCHT integrated with a TMD, which provides a programmable method to analyze the effect of the TMD on the dynamic responses of the SCHT. Then, an optimization model based on the genetic algorithm (GA) is established to obtain the optimal parameters of the TMD. Finally, a numerical test comprising 12 loading conditions is conducted to analyze the vibration mitigation effect of the TMD. The validation process also provides discussions about the influence of the wind turbine operation states and the fitness function adopted in the GA on the efficiency of the TMD. Those findings demonstrate the effectiveness and limitations of the TMD for mitigating vibrations of the SCHT. It thereby contributes to the understanding and improvement of vibration control strategies for SCHT structures and can guide future design and optimization efforts.

Tuned mass dampers (TMDs) are a useful control of vibrations for tall buildings and can be considered equal to burdens such as breezes and earthquakes. The better limits for TMD are to reduce the earthquake vibrations of tall buildings including soil–structure interaction (SSI) influences. This study proposes the multi-objective Black Widow Optimization (BWO) with Elman neural network (ENN) computation that is brought on to find the optimal limits of TMD. Considering that this proposed model analyzed the mass, stiffness, and damping ratio of TMD to get the maximum accelerations and displacement of 40 story building model, from the execution results, starting from this proposed BWO–Elman model to the expected methodology, the most outrageous TMD limits are better, likewise, the reduction of acceleration and displacement are 25% and 19.86% in the proposed study. This study assists the researchers with a better understanding of earthquake vibration and leads the fashioners to achieve superior TMD for tall designs. The impact of vibration control on the displacements and accelerations of both controlled and uncontrolled buildings is investigated in this work. It uses a MATLAB software technique to analyze their modal replies, moreover, this proposed optimal TMD model is compared with conventional techniques by acceleration and stiffness parameters.

The optimum parameters of multiple tuned mass dampers (MTMD) for suppressing the dynamic response of a base-excited damped main system are investigated by a numerical searching technique. The criterion selected for the optimality is the minimization of the steady state displacement of the main system under harmonic base acceleration. The parameters of the MTMD that are optimized include: the damping ratio, the tuning frequency ratio and the frequency bandwidth. The optimum parameters of the MTMD system and corresponding displacement are obtained for different damping ratios of the main system and different mass ratios of the MTMD system. The explicit formulas for the optimum parameters of the MTMD (i.e. damping ratio, bandwidth and tuning frequency) are then derived using a curve-fitting scheme that can readily be used in engineering applications. The error in the proposed explicit expressions is investigated and found to be negligible. The effectiveness of the optimally designed MTMD system is also compared with that of the optimum single tuned mass damper. It is observed that the optimally designed MTMD system is more effective for vibration control than the single tuned mass damper. Further, the damping in the main system significantly influences the optimum parameters and the effectiveness of the MTMD system.

In contrast with the odd number based multiple tuned mass dampers (ON-MTMD) used conventionally, which is targeted at the central natural frequency, the arbitrary integer based multiple tuned mass dampers (AI-MTMD) is proposed for the convenient applications of MTMD by giving up the central natural frequency hypothesis. The total number of the TMD units constituting the AI-MTMD may be selected as an arbitrary integer according to the practical requirements. In terms of the dynamic magnification factors (DMF) of the AI-MTMD structure system, the criterion for evaluating the optimum parameters and effectiveness of the AI-MTMD is selected as the minimization of the minimum values of the maximum DMF of the structure with the AI-MTMD. Employing the maximum DMF of every mass block in the AI-MTMD, the stroke of the AI-MTMD is simultaneously evaluated. The results indicate that both the AI-MTMD and the ON-MTMD can practically render the same performance, thus demonstrating that the former can be more convenient in mitigating structural oscillations with respect to the ON-MTMD stuck to the central natural frequency hypothesis.

Active multiple tuned mass dampers (AMTMDs) consisting of several active tuned mass dampers (ATMDs) with uniform distribution of natural frequencies have been proposed for vibration mitigation of structures under wind loads. In this regard, the optimum parameter criterion is defined as the minimization of the root-mean-square (RMS) displacement and acceleration responses of the structure with the AMTMD. Meanwhile, the effectiveness criterion is defined as the ratio of the minimum RMS displacement and RMS acceleration of the structure with the AMTMD to those without the devices, respectively referred to as the displacement and acceleration reduction factors (DRF and ARF). With these two criteria, the influences of the selective parameters on the effectiveness and robustness of the devices for vibration control under wind loads are studied. In addition, the stroke of the AMTMD is examined by quantitatively assessing the RMS displacement of each ATMD. Results indicate that in comparison with a single ATMD, the AMTMD can cause more reduction in the displacement and acceleration responses of the structure under wind loads. The stroke of the AMTMD is greater based on the ARF than the DRF criterion. In particular, the simulation results in the time domain confirm that by resorting to the AMTMD, a large control force can indeed be decentralized into many smaller control forces without losing the level of response reduction.

This study investigated the effect of a pendulum tuned mass damper (PTMD) on the vibration of a slender two-dimensional (2D) rigid body with 1:2 internal resonance. Focus is placed on the damping effect of various parameters of the PTMD on preventing the internal resonance of the system. The instruments used include fixed points plots, time response and Poincaré maps, which were compared for confirmation of accuracy. The Lagrange's equation is employed to derive the equations of motion for the system. The method of multiple scales (MOMS) is applied to analyzing this nonlinear vibration model. The internal resonance conditions of the rigid body in vibration are obtained by the eigen-analysis. Moreover, a 3D internal resonance contour plot (3D-IRCP) aided by various amplitude analysis tables is proposed for identification of the parameter combinations of the PTMD for preventing internal resonance. This approach enables the designers to evaluate the effectiveness of various parameter combinations of the PTMD prior to the design process. The present study indicates that without changing the main configuration, the vibration amplitudes in the main body can be greatly reduced under certain parameter combinations of the PTMD.

Displacement- and reliability-based designs of tuned mass damper (TMD) for a shear building are studied herein. Different sources of uncertainties such as earthquake records and their peak ground accelerations (PGA), masses of floors, cross-sectional dimensions of structural members, damping of the structure and modulus of elasticity are considered. Monte Carlo simulation (MCS) is used for evaluating the performance of the designed TMD. A method for generating artificial earthquake record by using wavelet packet transform (WPT) and particle swarm optimization (PSO) is proposed to generate artificial records for areas without sufficient strong ground motion records. An illustrative example is used to study the displacement- and reliability-based designs of TMD, which are related to minimizing the structural displacement and maximizing the performance of TMD, respectively. In addition, the performance of TMD on mitigating the response of structure and its reliability under uncertain parameters of loading and structural properties are investigated. The results show that a displacement-based designed TMD could reduce the lateral displacement of a structure. Furthermore, it illustrates that the reliability-based designed TMD has a better performance in real condition of loading and structural parameters.

Tuned mass dampers (TMDs) have been widely used to suppress or absorb vibration. Optimum tuning of the TMD parameters using metaheuristic algorithms demands numerous numerical analyses which is a tedious and time-consuming task. Recent advances in data processing systems have attracted great attention towards the creation of intelligent systems to evolve models in engineering applications. The present paper implements the least squares support vector machine (LS-SVM) to build up models which predict the optimum TMD parameters. The performance of the proposed models is largely dependent on the quantity and the accuracy of databases used for training the models. Therefore, a wide-range numerical tuning of the TMD system, attached to a single-degree-of freedom (SDOF) main system, is done using a novel metaheuristic algorithm, called the cuckoo search (CS), to obtain the tuning frequency and damping ratio of the TMD system for a main system subjected to three types of excitations: external white-noise force, harmonic base acceleration and white-noise base acceleration. The superior performance of the LS-SVM models in prediction of optimum TMD parameters is proved in comparison to other studies in the literature. Furthermore, it is found that the optimum TMD parameters are not influenced by the predominant frequency of the filtered white-noise excitation.

Failures of transmission tower-line systems have frequently occurred during large earthquakes. It is essential to control the excessive vibrations of transmission tower-line systems to ensure their safe operation in such events. This paper numerically investigates the effectiveness of using a novel bidirectional pounding tuned mass damper (BPTMD) to control the seismic responses of transmission tower-line system when subjected to earthquake ground motions. A finite element model of a typical transmission tower-line system with BPTMD is developed using the commercial software ABAQUS, with the accuracy of the results verified against a previous study. The seismic responses of the system with and without BPTMD are calculated. For comparison, the control effect of using the conventional bidirectional tuned mass damper is also calculated and discussed. Finally, a parametric study is performed to investigate the effects of the mass ratio, seismic intensity, gap size and frequency ratio on the seismic response of the system, while optimal design parameters are obtained.

Dynamic response control of a wind-excited tall building installed with distributed multiple tuned mass dampers (d-MTMDs) is presented. The performance of d-MTMDs is compared with those of single tuned mass damper (STMD) and MTMDs installed at top of the building. The modal frequencies and mode shapes of the building are first determined. Based on the mode shapes of the uncontrolled and controlled building, the most suitable locations are identified for the dampers, in that the TMDs are placed where the modal amplitude of the building is the largest/larger in a particular mode, with each tuned to the modal frequency of the first five modes. The coupled differential equations of motion for the system are derived for the cases with the STMD, MTMDs, and d-MTMDs and solved numerically. Extensive parametric studies are conducted to compare the effectiveness of the three control schemes using STMD, MTMDs, and d-MTMDs by examining the variations in wind-induced responses. The mass ratios, damping ratios of the devices, number of TMDs, and robustness of the TMDs are the parameters of investigation. It is concluded that the MTMDs exhibit improved performance when compared with the STMD. The use of d-MTMDs is most efficient among the three schemes because it can effectively control wind-induced response of the building, while reduced space is required in the installation of the TMDs, as they are placed at various floors.

This paper presents the field tests and vibration performance assessment of two long-span floors with tuned mass dampers (TMDs). The floors considered are made of steel beams and concrete slabs, as part of a gymnasium with composite floors spanning 36 m in each direction and equipped with 30 TMDs. Operational modal analysis based on ambient acceleration measurements is performed to extract the modal parameters of the floors. Ambient vibration tests were conducted at three stages of construction for each floor, namely (i) after the concrete slab was completed, (ii) after one layer over the concrete slab was added, and (iii) after the flooring (surfacing) was fully finished. The effects of the layers making up the flooring system and of the TMDs on the dynamic properties of the floors are studied. The finite element models of the floors are validated using the identified modal parameters. The effects of natural frequency of TMDs on the dynamic properties of the floors are investigated using the validated model. Finally, the effects of flooring on the vibration serviceability of the two floors are studied with TMDs in operation, when the floors were subjected to crowd-induced rhythmic loading, from which the efficiency of TMDs is assessed numerically. The results show that the coupled vibrations of the two floors with TMDs turned off occur in the first two modes, while the natural frequencies of the floors decrease with the addition of layers. The TMDs in operation break the first mode of the floor into two modes with similar mode shapes, resulting in smaller vibration response and larger damping ratios, which vary with the natural frequency of TMDs. Also, the wood flooring significantly increases the human-induced vibration of the floor, while the plastic flooring shows basically no effect.

A passive tuned mass damper (TMD) fabricated using the Reid damping, referred to as the Reid-TMD, is proposed. First, the characteristics of the Reid damping model are introduced, followed by the presentation of a passive variable friction damper to achieve this model. Next, the steady-state response of single-degree-of-freedom structures with the Reid-TMD under a harmonic load is solved by the harmonic balance method (HBM), together with an error analysis of the results. Subsequently, the optimization and control effect of the Reid-TMD damping system are analyzed and compared with the traditional viscous damping TMD. The results show that under the action of a harmonic load or seismic load, the vibration suppression effect of the Reid-TMD with the same mass ratio is essentially equivalent to the traditional viscous damping TMD. In addition, the damping control effect increases with the increase in mass ratio. When the mass ratio is less than 0.05, the energy dissipation coefficient is less than 0.5 and the frequency ratio is less than 0.95. For parameters within this range, the steady-state response of the seismic reduction structure with the Reid-TMD is solved by the HBM. If the parameters of the Reid-TMD are outside this range, the error of the HBM becomes large, and recourse should be changed to general numerical methods. The optimum parameters of the Reid-TMD are determined through an optimization analysis for the mass ratio in the range of 0.005–0.1. While using the Reid-TMD for the vibration absorption design, the optimum parameters can be acquired directly by using the established tables. Because the passive variable friction damper has good durability and economy, the application of the Reid-TMD is beneficial to shock absorption technology.

High and slender towers may experience excessive vibrations caused by both wind and seismic loads. To avoid excessive vibrations in towers, tuned mass dampers (TMDs) are often used as passive control devices due to their low cost. The TMDs can absorb part of the energy of vibration transmitted from the main structure. These devices need to be finely tuned in order to work as efficient dampers; otherwise, they can adversely amplify structural vibrations. This paper presents the optimal parameters of a pendulum TMD (PTMD) to control the vibrations of slender towers subjected to an external random force. The tower is modeled as a single-degree-of-freedom (SDOF) mass–spring system via an assumed-mode procedure with a pendulum attached. A genetic algorithm (GA) toolbox developed by the authors is used to find the optimal parameters of the PTMD, such as the support flexural stiffness/damping, the mass ratio and the pendulum length. The chosen fitness function searches for a minimization of the maximum frequency peaks. The results are compared with a sensibility map that contains the information of the maximum amplitude as a function of the pendulum length and the mass ratio between the pendulum and the tower. The optimal parameters can be expressed as a power-law function of the supporting flexural stiffness. In addition, a parametric analysis and a time-history verification are performed for several combinations of mass ratio and pendulum length.

Piping systems are typical nonstructural components of a building. Previous investigations have reported many cases that earthquake causes damages or failures of piping system, resulting in secondary disasters. Therefore, this paper conducts a survey of the seismic damage of the piping systems of buildings and then reviews the state-of-the-art of the passive seismic protection methods. This paper proposes to classify the building piping system into rigid connected pipes, flexible connected pipes and semi-rigid connected pipes. Typical seismic damages of building pipes are presented following this classification. Then, several current seismic protection methods (including constructional measures, seismic braces, damping techniques and base isolation methods) are discussed regarding the theoretical mechanism and feasibility. Furthermore, the state-of-the-art of the building piping system and the passive protection methods with application prospects are evaluated. Based on the review, the flexible piping systems are most commonly used in existing old buildings and are more vulnerable in earthquakes due to their high flexibility. New buildings prefer the rigid connections which tend to restrain the motion of the pipe. However, the excessive stiffness of the rigid connection may cause overlarge internal stresses in both the connection and the pipe. Semi-rigid piping systems have sufficient overall stiffness and a degree of local deform ability and thus have the best seismic performance. In future studies, more research should be devoted to propose and develop new dampers suitable for piping systems, which will improve the seismic safety of building piping systems.

Tuned Mass Damper (TMD) with magneto-rheological elastomer isolators (MRE-TMD) is a novel control device for suppressing structural vibration caused by earthquakes. It is a nonlinear hybrid vibration absorber and the stiffness & damping can be controlled by changing the current of isolators’ coil. Using MRE-TMD as an adaptive frequency TMD to mitigate vibration and treating it as only a passive damper is the focus of most nowadays researches. In this paper, semi-active control theory is introduced to the MRE-TMD-structure system which means that the control force can be obtained through variable stiffness & damping technology, and MRE-TMD is a semi-active damper instead of a passive one. A control system sketch, as well as principles and control strategies of a semi-active MRE-TMD-structure system for vibration control is designed. An improved limited sliding (ILSL) algorithm based on linear quadratic optimal theory is also introduced. Numeric simulations of a five-story benchmark building model equipped with semi-active MRE-TMD subjected to several benchmark earthquake records are conducted to investigate the control performance of the proposed semi-active MRE-TMD. Control force characteristics of the structural MRE-TMD systems are also evaluated. The results indicate that semi-active MRE-TMD can provide control force to the system and it shows superior ability to suppress the structural vibrations of comparing to the passive MRE-TMD.

A vibration amplifier is first proposed for adding to a test vehicle to enhance its capability to detect frequencies of the bridge under scanning. The test vehicle adopted is of single-axle and modeled as a single degree-of-freedom (DOF) system, which was proved to be successful in previous studies. The amplifier is also modeled as a single-DOF system, and the bridge as a simple beam of the Bernoulli–Euler type. To unveil the mechanism involved, closed-form solutions were first derived for the dynamic responses of each component, together with the transmissibility from the vehicle to amplifier. Also presented is a conceptual design for the amplifier. The approximations adopted in the theory were verified to be acceptable by the finite element simulation without such approximations. Since road roughness can never be avoided in practice and the test vehicle has to be towed by a tractor in the field test, both road roughness and the tractor are included in the numerical studies. For the general case, when the amplifier is not tuned to the vehicle frequency, the bridge frequencies can better be identified from the amplifier than vehicle response, and the tractor is helpful in enhancing the overall performance of the amplifier. Besides, the amplifier can be adaptively adjusted to target and detect the bridge frequency of concern. For the special case when the amplifier is tuned to the vehicle frequency, the amplifier can improve the vehicle performance by serving as a tuned mass damper, as conventionally known. This case is of limited use since it does not allow us to target the bridge frequencies. Both bridge damping and vehicle speed are also assessed with their effects addressed.

Owing to the increasing span of pedestrian bridges and the use of new lightweight and high-strength materials, the natural frequency of pedestrian bridges has been reduced significantly. A pedestrian bridge experiences a wide range of vibrations while being walked on by large crowds. This type of vibration affects the comfort of people walking on the footbridge and also the safety of the footbridge. This paper proposes a dynamic design method that is suitable for long-span composite footbridges. The footbridge considered in this study comprises a composite steel box girder with self-anchored suspensions and has a main span of 70.5m. The dynamic characteristics of the long-span footbridge were analyzed using the finite element model, and the first 10 frequencies and mode shapes were obtained. Based on the global analysis of comfort standards, the comfort index for a practical evaluation was proposed, along with the walking excitation load. Meanwhile, a tuned mass damper (TMD) was adopted for the vibration reduction of the long-span footbridge constructed using a composite box girder with self-anchored suspensions in order to determine its applicability. Furthermore, the TMD layout was optimized using a GA. The results demonstrated that the proposed method can provide a theoretical basis and reference for the dynamic design of long-span composite pedestrian bridges.

Tuned mass damper (TMD) is a type of energy absorbers that can mitigate the vibrations of the main system if its frequency and damping ratios are well adjusted. By adopting simple assumptions on the structure and loadings, many analytical and empirical relationships have been presented for the estimation of the parameters for TMDs. In this research, methods based on the artificial intelligence (AI) techniques are proposed for optimal tuning of the TMD parameters of the main damped-structure for three kinds of loadings: white-noise base acceleration, external white-noise force, and harmonic base acceleration. For this purpose, a dataset using the cuckoo search (CS) optimization algorithm is created. The performance of the proposed methods based on the radial basis function (RBF) neural network, feed-forward neural network (FFNN), adaptive neuro-fuzzy inference system (ANFIS), and random forest (RF) techniques are evaluated by some statistical indicators. The results show the proper performance of these methods for the optimal estimation of the TMD parameters. Overall, the ANFIS method results in best matching with the observed dataset. Moreover, the simulation results indicate that the TMD’s optimal frequency ratio is reduced, while its optimal damping ratio is increased, against the increase in the TMD mass ratio of the main structure subjected to harmonic base acceleration. This trend with a less slope is observed for the optimal frequency ratio of the TMD in the main structure subjected to external white-noise force; however, the optimal damping ratio of the TMD is independent of its mass ratio in this case. Similar results are obtained for the main structure subjected to white-noise base acceleration.

Wind turbines are slender and flexible structures which can undergo large amplitude vibrations when subjected to external loads and, an important way to reduce these excessive vibrations is to apply structural control. In this work, the vibration control of the coupled wind tower–blade system subjected to external lateral loads and rotating blade is studied. To model the tower and blade, the nonlinear Euler–Bernoulli beam theory was applied, and the structural control device considered is a nonlinear inverted tuned mass damper pendulum (ITMDP), located at the top of the tower. The Rayleigh–Ritz method, together with Hamilton’s principle, is applied to obtain a set of coupled nonlinear ordinary differential equations of motion which are in turn solved by the Runge–Kutta method. First, the dynamic instability of the system is studied by considering the variation of the natural frequencies of the tower, as a function of the speed of rotation of the blade and the veering phenomenon is observed. The optimum parameters for the ITMDP are obtained and, a nonlinear dynamic analysis is performed to evaluate the influence of the tuned mass damper (TMD) in the nonlinear regime, by obtaining the time responses, resonance curves, Poincaré maps and basins of attraction. The obtained results show the importance of considering the coupled system and the good performance of the structural control in the dynamic behavior of the system.