Mass Damper Inerter Research Articles

Analysis and experimental evaluation of an inertial eddy current damper for vibration control

Electromagnetic damping features non-contact operation, easy adjustability, convenient processing, and high energy consumption. Combined with the damping efficiency enhancement effect of the inertial system, it is conducive to further improving its damping effect. This paper proposes an inertial mass damper, named the Inertial Eddy Current Damper (IECD). The proposed IECD has the advantage of adjustability, meaning that the eddy current damping force can be adjusted by regulating the current in the coil. First, the mechanical model of the IECD was proposed through theoretical methods. Secondly, performance tests were conducted to verify the accuracy of the proposed mechanical model. Finally, numerical models of structures employing various applications of the IECD were established to conduct seismic response analysis. The results show that the proposed mechanical model effectively reflects the actual performance of the IECD. When used for energy dissipation and vibration reduction, the IECD demonstrates superior control performance in terms of displacement and velocity compared to the LVD, and the switch control strategy can address the issue of poor acceleration control performance. Combining the IECD with isolation bearings not only further reduces the seismic response of the superstructure but also enhances the safety of the isolation bearings, preventing excessive deformation.

Spectral Analysis of a Sagged Cable with an Optimal Viscous Inertial Mass Damper under Random Wind in a Generalized State-Space Formulation

In this study, a spectral analysis method is proposed for a sagged cable with an optimal viscous inertial mass damper (VIMD) under random wind loads based on a generalized state-space formulation. The frequency response functions of the cable responses were evaluated for the wind force vector using complex modes orthogonal to the system matrices, from which the power spectral densities of the cable responses were readily obtained for the spectral matrix of the wind force. The accuracy and efficiency of the proposed method were verified by comparing the root mean square responses with those obtained from the time-domain and covariance analyses. The performance of two VIMDs optimized by the fixed-point method and the maximum damping ratio method was investigated for various cases of cable sag and wind properties. Serviceability failure probability analysis was also conducted using the first-passage problem. The results show that the proposed spectral method is computationally more efficient than the other two analysis methods. The VIMDs optimized for the first original cable mode were found to be highly effective in reducing cable vibration and the probability of serviceability failure.

Stochastic Optimization of Electromagnetic Inertial Mass Dampers in Nonlinear Hybrid Base Isolation Systems Under Seismic Excitations

Recently developed inerter-based dampers have been installed at the base layer to reduce base displacement and simultaneously improve the superstructure’s performance. However, in the existing research on optimizing damper parameters, the nonlinear property of base isolation is simplified and stochastic linearization technique is introduced to approximate such nonlinearity, which would inevitably introduce errors. In this paper, an improved method is proposed for stochastic optimization of electromagnetic inertial mass dampers (EIMD) in nonlinear hybrid isolation systems subject to seismic excitations. First, a stochastic seismic excitation is represented by one elementary random variable adopting the dimension-reduction spectral representation method. Then, statistical moments of nonlinear base-isolated structural responses are estimated using two-point estimation method (2PEM). Finally, the EIMD optimal parameters are obtained via the modified directional bat algorithm (MDBA) recently proposed by the authors through minimizing base layer response moments. This proposed improved method could fully consider the base isolation nonlinearity compared with the previous stochastic linearization technique. Moreover, the proposed stochastic optimization of the EIMD only requires two dynamic analyses to achieve its efficiency. A seven-story base-isolated frame building equipped with an EIMD is investigated in the numerical simulation, and results indicate that EIMD optimized by this proposed method obviously outperforms the results by the stochastic linearization technique and the conventional viscous damper (VD) in the base layer displacement reduction.

ダイナミック・マスを用いたTMDに関する最適設計条件の導出及び振動実験による検証

This paper derives the optimal design conditions by the relational expression of natural period and propose the design method for the tuned mass damper (TMD) using a rotary inertial mass damper called DTMD. It shows the design example for the multi degree of freedom (MDOF) system, and confirms the damping effect of DTMD by the response analysis. In addition, it verifies the proposed theory and confirms the control effect on the actual structure by the vibration tests.

Stochastic Optimization of a Nonlinear Base Isolation System with LRB and EIMD for Building Structures

Base-isolated structures achieve superior seismic performance but with the cost of large deformation of the base floor, which possibly causes superstructure collapse during severe earthquakes. Hence, it is of great interest to develop hybrid base isolation systems that can reduce the base deformation and simultaneously improve the superstructure’s performance. Recently, several hybrid base isolation systems using inerter-based dampers have emerged; however, the nonlinear performance of the isolators has rarely been considered in these studies. In this paper, we conduct a nonlinear stochastic optimization of a novel hybrid base isolation system with lead-rubber bearings (LRB) and electromagnetic inertial mass dampers (EIMD). Based on the Bouc–Wen hysteretic model of the LRB, we derive the semianalytical solutions of the response variances of a simplified base-isolated model subjected to stationary seismic excitations. Then, based on the semianalytical solutions, we propose a procedure for optimizing the EIMD aimed at minimizing the superstructure interstory drift. In addition, we investigate the effect of site conditions and postyielding to preyielding stiffness ratios of the LRB on the optimal EIMD parameters and corresponding seismic performance. It is found that the hybrid base isolation system achieves better performance at a soft site than at a firm site. Results of a hybrid base-isolated building under artificial and real earthquake excitations illustrate that the EIMD can reduce both the base deformation and superstructure response, which outperforms the hybrid base-isolated building with conventional viscous dampers (VD).

TWO-STEP OPTIMIZATION OF TUNED INERTIAL MASS DAMPERS FOR ELASTIC-PLASTIC MDOF STRUCTURES USING TIME-FREQUENCY DUAL DOMAIN PERFORMANCE EVALUATION

The purpose of this paper is to propose a two-step optimization method to design tuned inertial mass dampers for elastic-plastic MDOF structures using the time-frequency dual domain performance evaluation. Although the frequency-domain-based approach allows us to obtain the optimal design independent of the characteristics of disturbances, it cannot consider the elastic-plastic response of structures. On the other hand, the time-domain design is highly dependent on the characteristics of design earthquake ground motions. The proposed two-step method resolves these issues by use of dual-domain information. Finally, the response analysis for recorded ground motions demonstrates the effectiveness of the proposed design method.

Reliability‐based robust design optimization for building‐connecting inertial mass damper

AbstractThis paper proposes an accurate and efficient reliability evaluation method for robust design optimization using a probabilistic approach. First, the validity of this method is verified using two benchmark functions. This method is then applied to the robust design optimization problem of building‐connecting damper parameters, and the effect of robust design is verified. The variation in the natural period and structural damping ratio of buildings is considered, and the criteria satisfaction rate (CSR) are directly evaluated using the response value calculated by time history response analysis.

Performance of Supplemental Inertial Devices for Base-Isolated Structures

The seismic response of base-isolated structures with supplemental inertial devices subjected to stationary and real earthquake excitation is presented. Three types of devices, namely inertial mass damper (IMD), tuned mass damper-inerter (TMDI), and clutching inerter damper (CID), are considered. The seismic response of the base-isolated structure with and without inertial devices is compared to assess their effectiveness. Under stationary white-noise excitation, the optimum parameters of these devices were obtained. The criterion selected for optimality is the minimization of the mean-square relative displacement and absolute acceleration of the isolated structure. An equivalent linearization method was used for base-isolated structures with CID under stochastic excitation. It was observed that the IMD is not very effective in controlling the response of base-isolated structures. Optimally designed TMDI, on the other hand, was found to be effective in controlling the displacement and acceleration response of the isolated structure, with the effectiveness increasing as the inertance mass ratio increased. The CID involved in the base-isolated structure reduces the structural natural frequency and increases structural damping, thereby reducing isolator displacement and structural acceleration. The high-frequency components were present in the absolute acceleration of base-isolated structure with inertial devices (more pre-dominating for IMD and CID), which may have detrimental effects on installed high-frequency sensitive equipment.

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.

Design Approach and Practical Formulas of Electromagnetic Inertial Mass Dampers for Cable Multimode Control

Design Approach and Practical Formulas of Electromagnetic Inertial Mass Dampers for Cable Multimode Control

Two-step online identification of in-service cable-inertial mass damper systems under nonstationary wind excitations

Recently developed inertial mass dampers (IMDs) exhibit superior performances in vibration attenuation of stay cables due to the introduction of large inertial masses. However, physical parameters of in-service IMD systems tend to vary with operation time and inappropriate parameters would affect vibration mitigation effect. So far, very few researches have been conducted on the online parametric identification of in-service dampers using on-site monitoring data and such evaluation is essential for performances of dampers. To solve such a problem, a novel method is proposed in this paper for online parametric identification of in-service cable-IMD systems under nonstationary wind loads. The identification is a two-step and output-only approach. In the first step, an energy spectrum transmissibility (EST) approach is developed to detect system poles under nonstationary excitation and identification results are not influenced by inputs. By combining covariance-driven stochastic subspace identification (SSI-COV) method with the developed EST approach, spurious modes in SSI-COV estimation are eliminated to obtain reliable modal parameter identification results. In the second step, the errors between the identified modal parameters (i.e., frequencies and damping ratios) and the estimated modal parameters through complex modal analysis are used to construct objective function, and the modified directional bat algorithm (MDBA) recently developed by the authors is utilized to estimate the physical parameters of cable and IMD by minimizing the objective function. Online parametric identification results of a numerical cable-IMD system model under nonstationary wind loads using limited accelerometers demonstrate the effectiveness of the proposed method.

Response control of a transmission tower-line system under wind excitations by electromagnetic inertial mass dampers

Structural vibration of transmission tower-line systems under wind excitations may induce damage and even destruction of the overall system. The control of transmission towers is conducted in the past decades by dynamic absorbers and dampers. Recently, a new type of passive control device, namely electromagnetic inertial mass dampers (EIMD), has been proposed and applied in structural vibration control However, the EIMD has not yet been systematically investigated in the vibration control of power transmission towers. In this regard, the vibration control of wind-disturbed transmission towers using EIMDs is conducted. The analytical model of a real tower-line system is established in line with the Hamilton principles. The response control approach using EIMDs is proposed and the control performance of different methods is compared in both the time and frequency domain. Detailed parametric studies are carried out to examine the effects of electromagnetic damping, inertial mass, and wind load intensity on EIMD performance. The assessment of the system energy responses without and with control is also conducted. The made observations demonstrate that the application of EIMDs can significantly reduce the structural dynamic responses under wind loading and the control performance of the EIMDs is quite robust and versatile under different wind load intensities.

Damping of a stay cable with two eddy‐current inertial mass dampers: Theoretical analysis, experimental study, and parameter optimization

Damping of a stay cable with two eddy‐current inertial mass dampers: Theoretical analysis, experimental study, and parameter optimization

Seismic Vibration Control of Atrium Buildings Using a Truss-Nonlinear Inertial Mass Damper System

Atrium building is a common structural type that can be found in most of the big cities. For seismic vibration control of buildings with large atria, this paper proposes a novel approach of using a core structure inside the atrium building in combination with a truss-inertial mass damper (IMD) system to form a passive control mechanism. The proposed system utilizes the unsynchronized vibrations between the tops of the building and the core structure to activate the IMD for seismic energy dissipation. To evaluate the effectiveness of the proposed truss-IMD system, a numerical time-history method is first developed to compute structural response of the atrium building under an earthquake input, followed by parametric studies of the system. Effects of truss stiffness, inertance, and nonlinearity of the IMD on seismic performance of the atrium building are investigated. Results from a simple structural model and a six-story building indicate that the truss-IMD system can significantly alleviate the dynamic responses of the building, and the overall seismic performance improvement brought by the truss-IMD surpasses a truss-viscous damper system. Results also show that for a given set of truss stiffness and damper nonlinearity, there exists an optimal combination of inertance and damping coefficient for the IMD to achieve a maximum structural performance.

Performance enhancement of FPS-isolated buildings using an inerter-based damper: Stochastic seismic analysis and optimization

Enhancing the seismic performance of based-isolated structures during a major earthquake event using inerter-based dampers emerges as a prominent research direction. However, analysis and optimization of based-isolated structures incorporated with inerter-based dampers considering both system nonlinearity and excitation uncertainty have rarely been reported. An electromagnetic inertial mass damper (EIMD) is a high-performance passive damper that consists of an inerter element and a damping element in parallel, and its superior control performance has been validated when applied to stay cables and frame structures. This paper presents a stochastic seismic analysis and parameter optimization of a friction pendulum system (FPS)-isolated structure with an EIMD considering the Kanai-Tajimi earthquake model. Considering the nonlinear damping of the FPS system, we derive the semi-analytical solutions of the FPS-isolated structure with an EIMD under stationary stochastic excitations based on a two-degree-of-freedom model using the statistical linearization technique. The effect of the EIMD on the FPS-isolated structure is systematically investigated via parametric study. A numerical procedure is proposed for optimizing the parameters of the EIMD and the FPS for minimizing the seismic response variances. Numerical simulation of a seven-story FPS-isolated building subjected to both artificial and real seismic excitations illustrates the effectiveness of the optimization procedure based on the semi-analytical solutions. Numerical results also reveal that the EIMD is capable of reducing both the base floor responses and superstructure responses, which outperforms tuned inerter dampers and conventional fluid viscous dampers. This study might shed light on the applications of inerter-based dampers in based-isolated structures in the years to come.

Effectiveness of damping and inertance of two dampers on mitigation of multimode vibrations of stay cables by using the finite difference method

Stay cables of several cable-stayed bridges with a span of nearly 1000 m are confronted with the simultaneous actions of low-mode rain-wind induced vibration and high-mode vortex-induced vibration. It is difficult to effectively reduce these two kinds of cable vibrations by installing one damper at the end of the stay cable. In this paper, the effectiveness of two dampers attached at the lower end of the stay cable, including viscous dampers and viscous inertial mass dampers, is investigated by the finite difference method. First, the stay cable was simplified as an inclined cable with sag, and equation of motion governing the stay cable attached with two dampers was derived. This equation was then numerically solved by the finite difference method. Second, taking Cable A30 of the Suzhou-Nantong Yangtze River Bridge as a reference, a series of numerical simulations were carefully conducted to obtain the damping ratios of the first fifty modes. The results show that it is impossible to enhance the damping ratios of all of the concerned modes up to the minimum target value only by installing a single viscous damper or a single viscous inertial mass damper at the end of the stay cable. However, two viscous dampers installed at the lower end of the cable (l1/l = 2%, l2/l = 5%) can overcome the shortcoming of a single viscous damper or viscous inertial mass damper to enhance the damping ratios of the first 34 modes up to the minimum target value (0.5%). In general, the optimized relative location of the two dampers (l2/l1) should be near 2. The optimized ratio of the damping coefficients (η1/η2) should be lower than l2/l1, and the lower limit of η1/η2 is determined by the minimum target values for modal damping ratios. Moreover, it appears that a lower installation position of two viscous dampers can realize the mitigation of higher modes even up to the 40th ∼ 50th modes.

Design of a Semiactive TMD for Lightweight Pedestrian Structures Considering Human–Structure–Actuator Interaction

Lightweight pedestrian structures constructed with high strength-to-weight ratio materials, such as fiber-reinforced polymers (FRP), may experience large accelerations due to their lightness, thus overcoming the serviceability limit state. Additionally, uncertainties associated with human–structure interaction phenomena become relevant. Under these circumstances, variations in pedestrian actions could modify the modal properties of the coupled human–structure system and classical approaches based on passive Tuned Mass Dampers (TMD) do not offer an effective solution. An alternative solution is to use a Semiactive TMD (STMD), which includes a semiactive damper that, when properly designed, may be effective for a relatively broad frequency band, offering a robust solution when significant uncertainties are present. Thus, this paper presents a design methodology for the design of STMDs applied to lightweight pedestrian structures including human–structure and actuator–structure interaction. A multiobjective optimization procedure has been proposed to simultaneously minimize structure acceleration, inertial mass, and maximum damper force. The methodology has been applied to a lightweight FRP footbridge. Realistic simulations, including system uncertainties, interaction phenomena, nonlinear damper model, noise-contaminated signals, and the practical elements (in-line digital filters) needed for the successful implementation of the control law, validate the methodology. As a conclusion, the STMD is more effective than its passive counterpart in both, canceling the response or achieving similar performance with significant lower inertial mass.

Nonlinear rotational inertial double-tuned mass damper for reducing human-induced floor vibration with frequency detuning

This study proposes a novel nonlinear rotational inertial double-tuned mass damper (NRIDTMD), which introduces a cubic stiffness element into the inerter-based passive control system RIDTMD, by exploiting the frequency insensitivity of nonlinear energy sink to overcome the frequency detuning problem in human-induced floor vibration control. Due to its nonlinear nature, the complexification-averaging technique is adopted to obtain the approximate steady-state response of the coupled floor-NRIDTMD system, and the number of the solutions and stability of the responses are discussed. Based on the genetic simulated annealing algorithm, the design parameters of the proposed NRIDTMD are optimized, and the empirical design formulation and response prediction equation are further proposed. Considering the effect of frequency detuning caused by human-structure interaction, floor stiffness degradation and mass increase, a numerical model of an experimental floor is used to verify the vibration mitigation performance of the proposed NRIDTMD, and compared with those of TMD and RIDTMD. The results reveal that the empirical formulation and prediction equation exhibit excellent accuracy and applicability, and the proposed NRIDTMD can minimize the acceleration response increment of the floor in frequency detuning, exhibiting better frequency robustness than those of conventional linear dampers.

Design Formulas of Electromagnetic Inertial Mass Dampers for Cable Vibration Mitigation

Abstract This study proposes the design formulas of an inerter-based damper termed electromagnetic inertial mass damper (EIMD) for bridge stay cables. To maximize the modal damping ratio for a spec...

Stochastic seismic analysis of base-isolated structures with electromagnetic inertial mass dampers considering different soil conditions

Stochastic seismic analysis of base-isolated structures with electromagnetic inertial mass dampers considering different soil conditions