• Title/Summary/Keyword: Inerter

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An inerter-system chain and energy-based optimal control of adjacent single-degree-of-freedom structures

  • Chen, Qingjun;Zhao, Zhipeng;Zhang, Ruifu
    • Smart Structures and Systems
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    • v.28 no.2
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    • pp.245-259
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    • 2021
  • Because of the limited land resources and preference of centralized services, more structures are often built close to each other, correspondingly yielding a demand that mitigates the dynamic responses of adjacent structures. Utilizing the intrinsic potential of the inerter to improve structural energy performances, an inerter-system chain is proposed for the adjacent single-degree-of-freedom structures, which forms a novel configuration featuring the reduction in input energy transmitted to the adjacent structures. The inerter-system chain is realized by two end-placed inerter-dashpot dampers and inter-placed spring-inerter-dashpot elements arranged in parallel. Stochastic energy balance analysis is conducted to derive a closed-form energy equation that reveals the energy basis of the inerter-system chain. An energy-based and bi-objective optimization strategy is developed with simultaneous consideration of displacement and energy performances, particularly easy-to-use design formulae being derived. The findings of this study show that a complete inerter-system chain exhibits a significant multi-reduction in the structural displacement, shear force, and dissipation energy burden. Particularly, the effectiveness of reducing the input power and vibrational energy transmitted into the entire structures counts on the series inerter-chain, which differentiates the proposed chain from alternative layouts. The proposed energy-based design framework is capable of minimizing the energy dissipation cost, with target displacement control demand satisfied.

Damping enhancement of the inerter on the viscous damper in mitigating cable vibrations

  • Gao, Hui;Wang, Hao;Li, Jian;Wang, Zhihao;Ni, Youhao;Liang, Ruijun
    • Smart Structures and Systems
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    • v.28 no.1
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    • pp.89-104
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    • 2021
  • This paper systematically investigates the effect of the inerter on the damping enhancement of a cable with a viscous damper (VD) installed close to the cable end. Three cases are considered, including the inerter installed parallel with the VD (PVID), the inerter placed in series with the VD (SVID), and the inerter installed at a higher location of the VD (HVID). The asymptotic solutions of the three cases are derived, which can predict the cable modal damping ratio when the inerter and the VD cause minimal perturbation in the undamped frequency of the cable. The effect of the inerter on the modal behavior of the cable with the VD is investigated. Based on the constrained static output LQR method, the effects of the inerter on the damping enhancement of the VD in mitigating cable multi-mode vibrations are further evaluated. The results show that the inerter can improve the control performance of the VD when the inertance is less than the optimum value. Further increasing the inertance beyond the optimum value, the optimum modal damping ratio of the cable decreases, and mode crossover is observed for the cable with PVID and HVID. Compared with the case where the VD and the inerter are located at the same location, the case of the HVID is more effective in mitigating cable multi-mode vibrations.

Performance evaluation of inerter-based damping devices for structural vibration control of stay cables

  • Huang, Zhiwen;Hua, Xugang;Chen, Zhengqing;Niu, Huawei
    • Smart Structures and Systems
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    • v.23 no.6
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    • pp.615-626
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    • 2019
  • Inerter-based damping devices (IBBDs), which consist of inerter, spring and viscous damper, have been extensively investigated in vehicle suspension systems and demonstrated to be more effective than the traditional control devices with spring and viscous damper only. In the present study, the control performance on cable vibration reduction was studied for four different inerter-based damping devices, namely the parallel-connected viscous mass damper (PVMD), series-connected viscous mass damper (SVMD), tuned inerter dampers (TID) and tuned viscous mass damper (TVMD). Firstly the mechanism of the ball screw inerter is introduced. Then the state-space formulation of the cable-TID system is derived as an example for the cable-IBBDs system. Based on the complex modal analysis, single-mode cable vibration control analysis is conducted for PVMD, SVMD, TID and TVMD, and their optimal parameters and the maximum attainable damping ratios of the cable/damper system are obtained for several specified damper locations and modes in combination by the Nelder-Mead simplex algorithm. Lastly, optimal design of PVMD is developed for multi-mode vibration control of cable, and the results of damping ratio analysis are validated through the forced vibration analysis in a case study by numerical simulation. The results show that all the four inerter-based damping devices significantly outperform the viscous damper for single-mode vibration control. In the case of multi-mode vibration control, PVMD can provide more damping to the first four modes of cable than the viscous damper does, and their maximum control forces under resonant frequency of harmonic forced vibration are nearly the same. The results of this study clearly demonstrate the effectiveness and advantages of PVMD in cable vibration control.

High performance active tuned mass damper inerter for structures under the ground acceleration

  • Li, Chunxiang;Cao, Liyuan
    • Earthquakes and Structures
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    • v.16 no.2
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    • pp.149-163
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    • 2019
  • By integrating an active tuned mass damper (ATMD) and an inerter, the ATMDI has been proposed to attenuate undesirable oscillations of structures under the ground acceleration. Employing the mode generalized system, the dynamic magnification factors (DMF) of the structure-ATMDI system are formulated. The criterion can then be defined as the minimization of maximum values of the DMF of the controlled structure for optimum searching. By resorting to the defined criterion and the particle swarm optimization (PSO), the effects of varying the crucial parameters on the performance of ATMDI have been scrutinized in order to probe into its superiority. Furthermore, the results of both ATMD and tuned mass dampers inerter (TMDI) are included into consideration for comparing. Results corroborate that the ATMDI outperforms both ATMD and TMDI in terms of the effectiveness and robustness. Especially, the ATMDI may greatly reduce the demand on both the mass ratio and inerter mass ratio, thus being capable of further miniaturizing both the ATMD and TMDI. Likewise the miniaturized ATMDI still keeps nearly the same stroke as the TMDI with a larger mass ratio. Hence, the ATMDI is deemed to be a high performance control device with the miniaturization and suitable for super-tall buildings.

A negative stiffness inerter system (NSIS) for earthquake protection purposes

  • Zhao, Zhipeng;Chen, Qingjun;Zhang, Ruifu;Jiang, Yiyao;Pan, Chao
    • Smart Structures and Systems
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    • v.26 no.4
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    • pp.481-493
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    • 2020
  • The negative stiffness spring and inerter are both characterized by the negative stiffness effect in the force-displacement relationship, potentially yielding an amplifying mechanism for dashpot deformation by being incorporated with a series tuning spring. However, resisting forces of the two mechanical elements are dominant in different frequency domains, thus leading to necessary complementarity in terms of vibration control and the amplifying benefit. Inspired by this, this study proposes a Negative Stiffness Inerter System (NSIS) as an earthquake protection system and developed analytical design formulae by fully utilizing its advantageous features. The NSIS is composed of a sub-configuration of a negative stiffness spring and an inerter in parallel, connected to a tuning spring in series. First, closed-form displacement responses are derived for the NSIS structure, and a stability analysis is conducted to limit the feasible domains of NSIS parameters. Then, the dual advantageous features of displacement reduction and the dashpot deformation amplification effect are revealed and clarified in a parametric analysis, stimulating the establishment of a displacement-based optimal design framework, correspondingly yielding the design formulae in analytical form. Finally, a series of examples are illustrated to validate the derived formulae. In this study, it is confirmed that the synergistic incorporation of the negative stiffness spring and the inerter has significant energy dissipation efficiency in a wide frequency band and an enhanced control effect in terms of the displacement and shear force responses. The developed displacement-based design strategy is suitable to utilize the dual benefits of the NSIS, which can be accurately implemented by the analytical design formulae to satisfy the target vibration control with increased energy dissipation efficiency.

The tuned mass-damper-inerter for harmonic vibrations suppression, attached mass reduction, and energy harvesting

  • Marian, Laurentiu;Giaralis, Agathoklis
    • Smart Structures and Systems
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    • v.19 no.6
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    • pp.665-678
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    • 2017
  • In this paper the tuned mass-damper-inerter (TMDI) is considered for passive vibration control and energy harvesting in harmonically excited structures. The TMDI couples the classical tuned mass-damper (TMD) with a grounded inerter: a two-terminal linear device resisting the relative acceleration of its terminals by a constant of proportionality termed inertance. In this manner, the TMD is endowed with additional inertia, beyond the one offered by the attached mass, without any substantial increase to the overall weight. Closed-form analytical expressions for optimal TMDI parameters, stiffness and damping, given attached mass and inertance are derived by application of Den Hartog's tuning approach to suppress the response amplitude of force and base-acceleration excited single-degree-of-freedom structures. It is analytically shown that the TMDI is more effective from a same mass/weight TMD to suppress vibrations close to the natural frequency of the uncontrolled structure, while it is more robust to detuning effects. Moreover, it is shown that the mass amplification effect of the inerter achieves significant weight reduction for a target/predefined level of vibration suppression in a performance-based oriented design approach compared to the classical TMD. Lastly, the potential of using the TMDI for energy harvesting is explored by substituting the dissipative damper with an electromagnetic motor and assuming that the inertance can vary through the use of a flywheel-based inerter device. It is analytically shown that by reducing the inertance, treated as a mass/inertia-related design parameter not considered in conventional TMD-based energy harvesters, the available power for electric generation increases for fixed attached mass/weight, electromechanical damping, and stiffness properties.

Response control of wind turbines with ungrounded tuned mass inerter system (TMIS) under wind loads

  • Zhang, Ruifu;Cao, Yanru;Dai, Kaoshan
    • Wind and Structures
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    • v.32 no.6
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    • pp.573-586
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    • 2021
  • Wind turbine towers are sensitive to wind loads and lose efficiency when suffering excessive wind-induced vibrations. Structural control techniques such as tuned mass dampers (TMD) can be used to reduce the vibration response of the tower. However, the additional mass of this system would occupy a large amount of space within the wind turbine device, which can inconvenience installation and maintenance. An inerter is a high-efficiency two terminal mechanical element for vibration control with the characteristic of mass and damping enhancements. An ungrounded tuned mass inerter system (TMIS) - composed of a tuned mass, a tuned spring and an inerter subsystem - has potential to control wind-induced vibration efficiently. In this study, a simple design method for wind turbine towers equipped with a TMIS under wind loads is proposed, based on structural performance demand as well as control cost. A 1.5 MW wind turbine tower benchmark model is adopted to exemplify the proposed design method. Comparative analyses are conducted between a conventional TMD and the TMIS. Results show that the TMIS can achieve the same vibration control effect as the TMD while using a smaller tuned mass. A sensitivity study of the TMIS is also carried out to investigate the impact of mechanical element parameters on the performance of the vibration mitigation system. It is concluded that the optimal designed TMIS has the advantage of lightweight tuned mass over TMDs in wind-induce vibration control of wind turbine towers.

Parametric optimization of an inerter-based vibration absorber for wind-induced vibration mitigation of a tall building

  • Wang, Qinhua;Qiao, Haoshuai;Li, Wenji;You, Yugen;Fan, Zhun;Tiwari, Nayandeep
    • Wind and Structures
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    • v.31 no.3
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    • pp.241-253
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    • 2020
  • The inerter-based vibration absorber (IVA) is an enhanced variation of Tuned Mass Damper (TMD). The parametric optimization of absorbers in the previous research mainly considered only two decision variables, namely frequency ratio and damping ratio, and aimed to minimize peak displacement and acceleration individually under the excitation of the across-wind load. This paper extends these efforts by minimizing two conflicting objectives simultaneously, i.e., the extreme displacement and acceleration at the top floor, under the constraint of the physical mass. Six decision variables are optimized by adopting a constrained multi-objective evolutionary algorithm (CMOEA), i.e., NSGA-II, under fluctuating across- and along-wind loads, respectively. After obtaining a set of optimal individuals, a decision-making approach is employed to select one solution which corresponds to a Tuned Mass Damper Inerter/Tuned Inerter Damper (TMDI/TID). The optimization procedure is applied to parametric optimization of TMDI/TID installed in a 340-meter-high building under wind loads. The case study indicates that the optimally-designed TID outperforms TMDI and TMD in terms of wind-induced vibration mitigation under different wind directions, and the better results are obtained by the CMOEA than those optimized by other formulae. The optimal TID is proven to be robust against variations in the mass and damping of the host structure, and mitigation effects on acceleration responses are observed to be better than displacement control under different wind directions.

Performance of multiple tuned mass dampers-inerters for structures under harmonic ground acceleration

  • Cao, Liyuan;Li, Chunxiang;Chen, Xu
    • Smart Structures and Systems
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    • v.26 no.1
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    • pp.49-61
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    • 2020
  • This paper proposes a novel high performance vibration control device, multiple tuned mass dampers-inerters (MTMDI), to suppress the oscillatory motions of structures. The MTMDI, similar to the MTMD, involves multiple tuned mass damper-inerter (TMDI) units. In order to reveal the basic performance of the MTMDI, it is installed on a single degree-of-freedom (SDOF) structure excited by the ground acceleration, and the dynamic magnification factors (DMF) of the structure-MTMDI system are formulated. The optimization criterion is determined as the minimization of maximum values of the relative displacement's DMF for the controlled structure. Based on the particle swarm optimization (PSO) algorithm to tune the optimum parameters of the MTMDI, its performance has been investigated and evaluated in terms of control effectiveness, strokes, stiffness and damping coefficient, inerter element force, and robustness in frequency domain. Meanwhile, further comparison between the MTMDI with MTMD has been conducted. Numerical results clearly demonstrate the MTMDI outperforms the MTMD in control effectiveness and strokes of mass blocks. Additionally, in the aspects of frequency perturbations on both earthquake excitations and structures, the robustness of the MTMDI is also better than the MTMD.

Input energy spectra and energy characteristics of the hysteretic nonlinear structure with an inerter system

  • Wang, Yanchao;Chen, Qingjun;Zhao, Zhipeng;Hu, Xiuyan
    • Structural Engineering and Mechanics
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    • v.76 no.6
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    • pp.709-724
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    • 2020
  • The typical inerter system, the tuned viscous mass damper (TVMD), has been proven to be efficient. It is characterized by an energy-dissipation-enhancement effect, whereby the dashpot deformation of TVMD can be amplified for enhanced energy dissipation efficiency. However, existing studies related to TVMD have mainly been performed on elastic structures, so the working mechanism remains unclear for nonlinear structures. To deal with this, an energy-spectrum analysis framework is developed systematically for classic bilinear hysteretic structures with TVMD. Considering the soil effect, typical bedrock records are propagated through the soil deposit, for which the designed input energy spectra are proposed by considering the TVMD parameters and structural nonlinear properties. Furthermore, the energy-dissipation-enhancement effect of TVMD is quantitatively evaluated for bilinear hysteretic structures. The results show that the established designed input energy spectra can be employed to evaluate the total energy-dissipation burden for a nonlinear TVMD structure. Particularly, the stiffness of TVMD is the dominant factor in adjusting the total input energy. Compared with the case of elastic structures, the energy-dissipation-enhancement effect of TVMD for nonlinear structures is weakened so that the expected energy-dissipation effect of TVMD is replaced by the accumulated energy dissipation of the primary structure.