Mass Damper Inerter Research Articles

Dynamic behavior and seismic performance of base-isolated structures with electromagnetic inertial mass dampers: Analytical solutions and simulations

The newly-developed electromagnetic inertial mass damper (EIMD) consisting of an inerter element and a damping element can significantly enhance the seismic performance of frame structures. However, whether an EIMD can enhance the seismic performance of a base-isolated structure (BIS) remains largely unknown. This paper presents a comprehensive theoretical study of the BIS with an EIMD, stressing on the dynamic behavior, parameter optimization, and seismic performance. Based on a simplified two-degree-of-freedom model, we derive the closed-form solutions of the dynamic characteristic parameters, modal participation factors, and dynamic amplification factors. A parametric study is conducted to investigate the effects of the EIMD parameters on the dynamic behavior of the system, through which the seismic response control mechanism of the EIMD in BIS is comprehensively analyzed. When the BIS subjected to a total of 20 earthquake records, the parameters of the EIMD are optimized for minimizing the interstory drift of the superstructure, the absolute acceleration response of the superstructure, and the relative displacement response of the base floor, individually. The effectiveness of the EIMD in enhancing the seismic performance of base-isolated structures is validated via numerical simulation of a five-story isolated building structure. Under a typical earthquake ground motion, the peak relative displacement of the base floor is reduced by up to 56.57% in comparison to traditional BIS; whereas the peak relative displacement and the absolute acceleration of the superstructure are reduced by up to 60.00% and 52.11%, respectively. Both analytical and numerical results demonstrate that the EIMD can significantly reduce the dynamic responses of both the base floor and the superstructure.

Performance enhancement in cable vibration energy harvesting employing inerters: Full‐scale experiment

Harvesting cable vibration energy via electromagnetic dampers has been demonstrated as potential power supplies for wireless sensor networks or semi-active control devices. However, how the inerter enhances the energy harvesting performance of the electromagnetic damper when applied to a bridge stay cable remains largely unknown. This paper presents a full-scale experimental study on harvesting the vibration energy of a 135 m-long cable using an electromagnetic inertial mass damper (EIMD). The EIMD integrates an electromagnetic damper and an inerter. A numerical model of the cable-EIMD system was also established using Matlab/Simulink for performance analysis. In the free vibration test, the EIMD could achieve the peak output power of 61.52 W and average output power of 13.80 W, when the inerter and the load resistance are optimized, considering an initial displacement of 100 mm near the mid-span of the cable. The corresponding energy harvesting efficiency was up to 25.31%. However, the energy harvesting performance of the EIMD degrades under ultra-small-amplitude vibration conditions due to the overlarge parasitic damping induced by Coulomb friction. Besides, experimental data uncover a 53.08% increase of average output power due to the inerter used, while numerical results indicate a tremendous increase of output power up to 126.1% because of assuming low parasitic damping. The EIMD with the optimal parameters (inertance, damping coefficient, and load resistance) can provide superior energy harvesting performance owing to the energy amplification mechanism induced by the inerter.

Interaction Phenomena to Be Accounted for Human-Induced Vibration Control of Lightweight Structures

Inertial mass controllers, including passive, semi-active and active strategies, have been extensively used for canceling human-induced vibrations in lightweight pedestrian structures. Codes to check the vibration serviceability and current controller design approaches assume that both excitation forces and controller forces are the same on a flexible structure and on a rigid structure. However, this fact may not be assumable since interaction phenomena arise even for moderately lightweight structures. Analyzing two case studies in this paper, interaction phenomena involved in the frequency-domain-based design of passive and active inertial mass dampers are discussed. Thus, a general vibration control problem including the interaction phenomena is set hereby. Concretely, this paper deeply discusses the following issues: (i) how the structure to be controlled is affected when human-structure interaction is presented for deterministic and stochastic conditions, (ii) the closed-loop transfer function of the controlled structure including a passive inertial mass damper, and (iii) the closed-loop transfer function of the controlled structure including an active inertial mass damper. In addition, the performed analysis considers the actuator dynamics and the actuator-structure interaction.

Optimal Design of Dampers for Multi-Mode Cable Vibration Control Based on Genetic Algorithm

Cables in cable-stayed bridges are subjected to the problem of multi-mode vibrations. Particularly, the first ten modes of long cables can have a frequency less than 3[Formula: see text]Hz and hence are vulnerable to wind-rain induced vibrations. In practice, mechanical dampers are widely used to mitigate such cable vibrations and thus they have to be designed to provide sufficient damping for all the concerned vibration modes. Meanwhile, the behaviors of practical dampers are complicated and better to be described by mechanical models with many parameters. Furthermore, additional mechanical components such as inerters and negative stiffness devices have been proposed to enhance the damper performance on cables. Therefore, it is increasingly difficult to optimize the damper parameters for suppressing multi-mode cable vibrations. To address this issue, this study proposes a novel damper design method based on the genetic algorithm (GA). The procedure of the method is first introduced where the damper performance optimization is formulated as a single-objective multi-parameter optimization problem. The effectiveness of the method is then verified by considering a viscous damper on a stay cable. Subsequently, the method is applied to optimize three typical dampers for cable vibration control, i.e. the positive stiffness damper, the negative stiffness damper, and the viscous inertial mass damper. The results show that the GA-based method is effective and efficient for cable damper design to achieve best multi-mode control effect and it is particularly useful for dampers with more parameters.

Viscous inertial mass damper (VIMD) for seismic responses control of the coupled adjacent buildings

Many research studies have focused on a novel kind of damper involved with an inertial/gyro mass component, called the inertial mass damper (IMD). Different realizations of the IMD share common standard features: a sizeable apparent mass and the pseudo-negative dynamic stiffness. The connected control method (CCM) has been proven effective for mitigating vibration between adjacent flexible structures. This paper explores the efficacy of using an IMD in parallel with a viscous damper (termed VIMD) configured in the sky bridge to control the vibration of two adjacent towers under random earthquake excitation. First, numerical models of two buildings are developed using a Timoshenko beam model, which can accommodate both bending and shear deformation. Key damper parameters are explored through a parametric study. Then, stochastic optimization is performed to determine optimum damper parameters and the most effective configuration. The optimization results are analyzed in detail, and guidelines for the damper configuration are recommended. By comparing the optimal control performance between the VIMD and traditional viscous damper (VD), the following conclusions can be drawn: due to its pseudo-negative stiffness characteristics and large damper force, the VIMD can achieve better control performances for a wide range of the axial stiffness of the sky bridge; the VIMD requires a smaller damping coefficient and axial stiffness, which can result in smaller damper sizes and member sections of the sky bridge. Therefore, the VIMD is demonstrated to be a useful alternative for engineering practice in CCM vibration mitigation strategies.

Semi-active vibration control of structural systems by an inertial mass damper

Semi-active vibration control of structural systems by an inertial mass damper

Semi-active vibration control for structural systems with a variable inertia mass damper

Semi-active vibration control for structural systems with a variable inertia mass damper

Vibration mitigation of stay cables using electromagnetic inertial mass dampers: Full-scale experiment and analysis

Previous numerical study has shown tremendous improvements in increasing the modal damping of bridge stay cables using inerter-based dampers. This article presents an experimental and numerical study on the vibration mitigation of a 135 m long full-scale cable using a novel inerter-based damper termed electromagnetic inertial mass damper (EIMD). The effect of the inerance and damping coefficient of the EIMD on the dynamic characteristics of the cable-EIMD system were systematically investigated using total 133 sets of free vibration data. A numerical model of the cable-EIMD system was established using finite difference method for implementing complex eigenvalue analysis. The relation between the first modal damping ratio and the EIMD parameters was observed in the experiment, which matches well with the prediction by the complex eigenvalue analysis. When installed at 2.5% of cable length away from the anchorage, the EIMD has achieved the maximum first modal damping ratio up to 3.66%, which is 192.8% larger than the theoretical upper limit (1.25%) of a viscous damper (VD). We also observed that the inerter element of the EIMD amplified the damper vibration amplitude and caused approximate π/2 phase lag of damper response. Such unique mechanism remarkably increases the energy dissipation of the EIMD. The inerter element significantly reduces the optimal damping coefficient required for cable vibration mitigation compared to that of the VD. The vibration mitigation performance of the EIMD for higher modes is also validated via harmonic vibration test using sine sweep excitations. The EIMD is capable of achieving superior vibration mitigation performance for bridge stay cables if both the inertance and damping coefficient were set as their optimal values.

Free Vibration of a Taut Cable with Two Discrete Inertial Mass Dampers

Recently, inertial mass dampers (IMDs) have shown superior control performance over traditional viscous dampers (VDs) in vibration control of stay cables. However, a single IMD may be incapable of providing sufficient supplemental modal damping to a super-long cable, especially for the multimode cable vibration mitigation. Inspired by the potential advantages of attaching two discrete VDs at different locations of the cable, arranging two external discrete IMDs, either at the opposite ends or the same end of the cable is proposed to further improve vibration mitigation performance of the cable in this study. Complex modal analysis based on the taut-string model was employed and extended to allow for the existence of two external discrete IMDs, resulting in a transcendental equation for complex wavenumbers. Both asymptotic and numerical solutions for the case of two opposite IMDs or the case of two IMDs at the same end of the cable were obtained. Subsequently, the applicability of asymptotic solutions was then evaluated. Finally, parametric studies were performed to investigate the effects of damper positions and damper properties on the control performance of a cable with two discrete IMDs. Results showed that two opposite IMDs can generally provide superior control performance to the cable over a single IMD or two IMDs at the same end. It was also observed that attaching two IMDs at the same end of the cable had the potential to achieve significant damping improvement when the inertial mass of the IMDs is appropriate, which seems to be more promising than two opposite IMDs for practical application.

A general vibration control methodology for human‐induced vibrations

This paper proposes a general methodology for the design of vibration control of human-induced vibrations. This uses a feedback loop for the design of control parameters and accounts for the nature of human excitation and how humans feel the vibration. The methodology developed considers not only single-input single-output control systems but also multi-input multi-output control systems, especially useful to cancel vibrations coming from modes with closely spaced natural frequencies. The strategy finds simultaneously the optimal placements of a set of inertial mass dampers and the design parameters (control gain matrix for active vibration control, damping ratios and tuning frequencies of tuned mass dampers for passive vibration control). To make this strategy implementable and suitable to human-induced vibrations, elements such as input-output frequency weighting, output time weighting, band-pass filters, actuator dynamics, and nonlinearities are considered within the design. The proposed methodology is illustrated in an application example on a realistic open-layout floor by designing single-input single-output and multi-input multi-output active and passive strategies with one and two dampers. Simulation tests are carried out to evaluate the performance of the controllers in terms of their vibration reduction capacity using a performance index indicator.

Impact of cable sag on the efficiency of an inertial mass damper in controlling stay cable vibrations

Passive negative stiffness dampers (NSDs) that possess superior energy dissipation abilities, have been proved to be more efficient than commonly adopted passive viscous dampers in controlling stay cable vibrations. Recently, inertial mass dampers (IMDs) have attracted extensive attentions since their properties are similar to NSDs. It has been theoretically predicted that superior supplemental damping can be generated for a taut cable with an IMD. This paper aims to theoretically investigate the impact of the cable sag on the efficiency of an IMD in controlling stay cable vibrations, and experimentally validate superior vibration mitigation performance of the IMD. Both the numerical and asymptotic solutions were obtained for an inclined sag cable with an IMD installed close to the cable end. Based on the asymptotic solution, the cable attainable maximum modal damping ratio and the corresponding optimal damping coefficient of the IMD were derived for a given inertial mass. An electromagnetic IMD (EIMD) with adjustable inertial mass was developed to investigate the effects of inertial mass and cable sag on the vibration mitigation performance of two model cables with different sags through series of first modal free vibration tests. The results show that the sag generally reduces the attainable first modal damping ratio of the cable with a passive viscous damper, while tends to increase the cable maximum attainable modal damping ratio provided by the IMD. The cable sag also decreases the optimum damping coefficient of the IMD when the inertial mass is less than its optimal value. The theoretically predicted first modal damping ratio of the cable with an IMD, taking into account the sag generally, agrees well with that identified from experimental results, while it will be significantly overestimated with a taut-cable model, especially for the cable with large sag.

Refined Study on Free Vibration of a Cable with an Inertial Mass Damper

To accurately predict the optimum supplemental modal damping ratio of the cable and the corresponding size of the inertial mass damper (IMD), combined effects of the cable sag, the cable flexural rigidity, and the boundary conditions on the control performance of the cable with the IMD are well investigated in this refined study. An analytical model of the cable-IMD system considering these effects is developed. The equation of motion of the cable-IMD system is transformed into a complex eigenvalue problem through the finite difference method. Experimental results from a scaled cable model with an IMD are then used to verify theoretical solutions. Three typical cables in actual cable-stayed bridges are selected for case studies. The results show that the theoretically predicted modal damping ratios of the cable with an IMD, taking into account the sag and the flexural rigidity, agree well with those identified from experimental results, while would be often overestimated with a taut-cable model. Moreover, experimental damping ratios of the cable always fall between those theoretically calculated with fixed ends or pinned ends for each case. Finally, to be conservative in actual design, it is recommended to use the cable-IMD system model with fixed ends to calculate the required damper size and predict the resulting modal damping ratio of the cable, since the corresponding theoretical solution often gives the lower bound of supplemental damping ratio of the cable.

Experimental evaluation of an inertial mass damper and its analytical model for cable vibration mitigation

Cables are prone to vibration due to their low inherent damping characteristics. Recently, negative stiffness dampers have gained attentions, because of their promising energy dissipation ability. The viscous inertial mass damper (termed as VIMD hereinafter) can be viewed as one realization of the inerter. It is formed by paralleling an inertial mass part with a common energy dissipation element (e.g., viscous element) and able to provide pseudo-negative stiffness properties to flexible systems such as cables. A previous study examined the potential of IMD to enhance the damping of stay cables. Because there are already models for common energy dissipation elements, the key to establish a general model for IMD is to propose an analytical model of the rotary mass component. In this paper, the characteristics of the rotary mass and the proposed analytical model have been evaluated by the numerical and experimental tests. First, a series of harmonic tests are conducted to show the performance and properties of the IMD only having the rotary mass. Then, the mechanism of nonlinearities is analyzed, and an analytical model is introduced and validated by comparing with the experimental data. Finally, a real-time hybrid simulation test is conducted with a physical IMD specimen and cable numerical substructure under distributed sinusoidal excitation. The results show that the chosen model of the rotary mass part can provide better estimation on the damper

Equivalent Linearization Methods for a Control System with Clutching Inerter Damper

Inerter-based dampers have gained great popularity in structural vibration control. In this paper, equivalent linearization methods (ELMs) for a single-degree-of-freedom (SDOF) system with a clutching inerter damper (CID) are studied. The comparison of a SDOF system with a CID and an inertial mass damper (IMD) shows the advantage of the CID. Considering that the system with the CID is nonlinear, which is problematic for its performance evaluation and the integrated design of the structure and control system, three equivalent linearization methods based on different principles are proposed and discussed in this paper. The CID is considered to be equal to a combination of an IMD and a viscous damper. The equivalent inertance and damping can be calculated using the obtained formulas for all methods. In addition, all methods are compared in a numerical study. Results show that the ELM based on period and energy is recommended for small inertance-mass ratios.

Semi-active Vibration Control of Structural Systems with a Variable Inertia Mass Damper

Semi-active Vibration Control of Structural Systems with a Variable Inertia Mass Damper

Inertial mass damper for vibration control of cable with sag

It has been theoretically predicted that superior supplemental damping can be generated for a taut cable with an inertial mass damper. This paper extends previous studies to investigate the effect of the cable sag on the efficiency of an inertial mass damper. The general dynamic characteristics of an inclined sag cable with an inertial mass damper installed close to the cable end are theoretically investigated. The parametric analysis of the inertial mass and the damping coefficient of the inertial mass damper are conducted to evaluate the control performance of the cable with different sags. The results show that the inertial mass damper can alleviate the negative effect induced by the cable sag, and the cable sag can even increase modal damping ratios provided by the inertial mass damper. Sags of stay cables used in actual bridges only affect nearly symmetric vibrations of cables, while having little impact on nearly antisymmetric vibrations. The effect of cable sags will reduce the optimal damping coefficient and inertial mass of the inertial mass damper for the first symmetric mode of the cable.

Mechanical and energy-harvesting model for electromagnetic inertial mass dampers

Abstract Recently, a novel inerter-based damper termed electromagnetic inertial mass damper (EIMD) that is capable of generating a large inertance and providing a controllable electromagnetic (EM) damping has been used as an energy dissipation device for seismic response control. Structural vibration energy induced by external loading is converted into electricity via the EIMD, for being dissipated and harvested. In this paper, the EIMD is proposed for simultaneous vibration mitigation and energy harvesting for the first time. A new mechanical model is proposed to predict the nonlinear behavior of the EIMD, and a linearized model is subsequently deduced based on the equal energy dissipation rule. In addition, an energy-harvesting model is presented to predict the output power and energy harvesting efficiency of the EIMD. To maximize the efficiency of the EIMD, this paper derives the corresponding optimal load resistance that can serve as the design criteria for an energy harvesting circuit (EHC). The proposed models are validated by the dynamic test of a prototype EIMD using harmonic excitation.

Real‐time hybrid simulation of semi‐active control using shaking table: Proposal and verification of a testing method for mid‐story isolated buildings

AbstractThis study proposes a real‐time hybrid simulation method for semi‐active control using a shaking table. The method can be used for simulating a mid‐story isolated building. This simulation system uses a test specimen for the upper structure, a semi‐active damper that is installed in the base isolation layer on the shaking table, and a lumped mass system for a lower structure for the computer simulation. A rotary inertia mass damper that contains magnetorheological fluid is used in the semi‐active control. The semi‐active control cannot avoid a control time lag. This time lag is estimated by assuming a first‐order lag system. The experimental and analytical results considering a control time lag are compared in this study. The validity of the real‐time hybrid simulation is verified.

Displacement reduction effect and simplified evaluation method for SDOF systems using a clutching inerter damper

SummaryThis study evaluates the response reduction effect of linear single degree of freedom systems with a clutching inerter damper (CID) via parametric analysis under harmonic excitations and real earthquake records. The cause of the displacement reduction effect of a CID is inherited from the inertial mass damper (IMD)—reducing the nominal load intensity by increasing the mass by inertance. Additionally, the displacement reduction effect is further enhanced by the clutching effect, which speeds up the decreasing of the velocity response from an instantaneous extremum to 0. Thus, the CID is more effective than the IMD at reducing displacement responses. For example, the displacement response for a long‐period structure with a CID can be reduced by approximately 53%, while for an IMD, it can only be reduced by approximately 24%. Additionally, the linear single degree of freedom system with a CID is a weak nonlinear system reserving homogeneity, indicating that the response reduction factor will provide enough information to reveal the seismic reduction effect of the CID and that there is no need to consider the amplitude of the input excitations. To simplify the analysis of such nonlinear systems, an equivalent linearization method and a simplified formula of displacement reduction factors for code‐based designs are proposed and validated by another independent set of records from the European Strong‐motion Database.

Reduction of vibration response of structures to earthquake by inertial mass damper

Reduction of vibration response of structures to earthquake by inertial mass damper