Damping enhancement principle of inerter system

Zhang, Ruifu; Zhao, Zhipeng; Pan, Chao; Ikago, Kohju; Xue, Songtao

doi:10.1002/stc.2523

Cited by 101 publications

(77 citation statements)

References 77 publications

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“…Substituting Equation 8 into Equation 7, a closed‐form displacement distribution equation of the structure‐GTMDI system is finally obtained:

γ^{2} + γ_{d}^{2} \frac{ξ}{ζ} = θ

where

θ = {(1 + β)}^{2} + \frac{β^{2}}{κ}

is defined as the displacement response factor of the entire structure‐GTMDI system. Note that, if the tuned mass ratio β is assumed zero, the form in the derived displacement distribution Equation 9 is in consistent with that for the TID in Zhang et al 52 …”

Section: Theoretical Study Of Generic Tuned Mass Damper Inertersupporting

confidence: 73%

“…κ is defined as the displacement response factor of the entire structure-GTMDI system. Note that, if the tuned mass ratio β is assumed zero, the form in the derived displacement distribution Equation 9 is in consistent with that for the TID in Zhang et al 52…”

Section: Stochastic Response Analysis and Displacement Distributionsupporting

confidence: 73%

“…Figure 5 reports the results of γ d / γ and

α_{d}^{2} / α^{2}

, simultaneously providing a unit reference plane with γ d / γ = 1 and

α_{d}^{2} / α^{2} = 1

marked in a transparent form. For the GTMDI with a small nominal damping ratio ( ξ < 0.05), the deformation of the dashpot in GTMDI is amplified and is larger than those of the entire GTMDI, which is a similar phenomenon discovered for the TID 52 . It is proved in this study that the amplification of the dashpot yields the enhanced dissipation power of the GTMDI in Figure 5b, which refers to another benefit of the GTMDI for dissipating energy in an efficient way.…”

Section: Energy‐based Design Frameworksupporting

confidence: 72%

“…For the GTMDI with a small nominal damping ratio (ξ < 0.05), the deformation of the dashpot in GTMDI is amplified and is larger than those of the entire GTMDI, which is a similar phenomenon discovered for the TID. 52 It is proved in this study that the amplification of the dashpot yields the enhanced dissipation power of the GTMDI in Figure 5b, which refers to another benefit of the GTMDI for dissipating energy in an efficient way. Comparing the values of γ d /γ and α 2 d =α 2 in (a) and (b), a small inertance is preferential to pursue the maximum enhanced dissipation power for the dashpot.…”

Section: Minimization η With Enhanced Dissipation Powermentioning

confidence: 61%

“…Solving this parameter design constraint, the maximum value of γ d / γ or

α_{d}^{2} / α^{2}

can be finally obtained, and the optimal parameters β = 0, μ , κ , and ξ and the distribution pattern of the inerter δ = 0.5 are simultaneously obtained. This proposed optimal design basically developed the damping enhancement design in Zhang et al 52 by additionally considering the dissipation power

α_{d}^{2} / α^{2}

. More important, the balanced inerter of the GTMDI makes itself effective to reduce the input power in comparison with the TID.…”

Section: Energy‐based Design Frameworkmentioning

confidence: 99%

See 4 more Smart Citations

Input energy reduction principle of structures with generic tuned mass damper inerter

Zhao

Zhang

Pan

et al. 2020

Struct Control Health Monit

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The incorporation of the inerter with tuned mass damper yields the inerterbased tuned mass damper that has been verified as effective lightweight or performance-enhanced control devices. This study theoretically proved an intrinsic effect, namely, the input energy reduction, that the inerter reduces the input energy transmitted into the controlled structures from ground motion. A generic tuned mass damper inerter (GTMDI) including two separating inerters (the total inertance keeps constant) is analyzed to facilitate a universal analysis of typical inerter-based tuned mass dampers. Closed-form displacement and power equations are derived for the GTMDI to reveal and

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“…Substituting Equation 8 into Equation 7, a closed‐form displacement distribution equation of the structure‐GTMDI system is finally obtained:

γ^{2} + γ_{d}^{2} \frac{ξ}{ζ} = θ

where

θ = {(1 + β)}^{2} + \frac{β^{2}}{κ}

Section: Theoretical Study Of Generic Tuned Mass Damper Inertersupporting

confidence: 73%

Section: Stochastic Response Analysis and Displacement Distributionsupporting

confidence: 73%

“…Figure 5 reports the results of γ d / γ and

α_{d}^{2} / α^{2}

, simultaneously providing a unit reference plane with γ d / γ = 1 and

α_{d}^{2} / α^{2} = 1

Section: Energy‐based Design Frameworksupporting

confidence: 72%

Section: Minimization η With Enhanced Dissipation Powermentioning

confidence: 61%

“…Solving this parameter design constraint, the maximum value of γ d / γ or

α_{d}^{2} / α^{2}

α_{d}^{2} / α^{2}

. More important, the balanced inerter of the GTMDI makes itself effective to reduce the input power in comparison with the TID.…”

Section: Energy‐based Design Frameworkmentioning

confidence: 99%

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Input energy reduction principle of structures with generic tuned mass damper inerter

Zhao

Zhang

Pan

et al. 2020

Struct Control Health Monit

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show abstract

Effectiveness and robustness of an asymmetric nonlinear energy sink‐inerter for dynamic response mitigation

Wang

Zhang

et al. 2021

Earthq Engng Struct Dyn

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Nonlinear energy sinks (NESs) have outperformed tuned mass dampers in mitigating undesired responses against changes in structural frequencies. However, the dilemma of gaining frequency robustness at the cost of energy sensitivity as well as the large masses of devices required for civil engineering structures impede the applications of existing NESs. To solve the issue of lacking energy robustness and take advantage of inerters to reduce physical mass, an asymmetric NES‐inerter (Asym NESI) is developed in this study. This passive inerter‐based nonlinear mass damper is configured based on an energy‐robust NES with an inerter added between the auxiliary mass and a fixed point. The paper commences with the formulation of the Asym NESI through mathematical derivations. Then an Asym NESI is designed and evaluated on a three‐story structure in comparison with other counterpart mass dampers. The effectiveness of the Asym NESI can be attributed to its unique dynamics which are revealed analytically using the harmonic balance method through free vibrations and harmonically forced vibrations. The ensuing numerical validations show that due to the integrated linear and nonlinear dynamics of the Asym NESI, the proposed device exhibits strong robustness against changes in both structural frequency and energy level. Moreover, driven by the large inertial effect induced by the auxiliary inerter, the Asym NESI shows flexibility in choosing a practical installation location without sacrificing excellent control capacity. Importantly, the benefits of the Asym NESI are further confirmed by the responses subjected to a suite of ground motions. This study provides analytical insights into the effectiveness and robustness of Asym NESIs and demonstrates substantial performance enhancement by the inerter in structural response mitigation.

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Seismic control of multidegree‐of‐freedom structures using a concentratedly arranged tuned viscous mass damper

Kang,

Ikago

2023

Earthq Engng Struct Dyn

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Connecting a flexible supporting element to an inerter arranged in parallel with a viscous element yields a tuned‐mass damper‐like system, designated as a tuned viscous mass damper (TVMD). The advantage of a TVMD is that it exploits the flexibility of the supporting member, which is usually considered to compromise the energy‐dissipating performance, and the inerter and soft spring form a supplemental oscillator to enhance the damping performance with resonance to the primary structure. The fixed‐point method for the optimal design of a single‐degree‐of‐freedom structure containing a TVMD is further expanded to a multidegree‐of‐freedom structure, in which a TVMD is arranged concentratedly. Furthermore, approximated closed‐form formulae for a concentratedly arranged TVMD are derived under the assumption that the primary structure is undamped, remains in an elastic range, and the target mode dominates the response of the structure. An analytical example illustrates that installing a TVMD spanning three stories in a concentrated manner based on the proposed design methods ensures the efficiency of the damping system, which demonstrates a damping effect similar to that of stiffness‐proportionally distributed TVMDs with less demand for inertance and total control force, thus resulting in a lower cost.

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Damping enhancement principle of inerter system

Cited by 101 publications

References 77 publications

Input energy reduction principle of structures with generic tuned mass damper inerter

Input energy reduction principle of structures with generic tuned mass damper inerter

Effectiveness and robustness of an asymmetric nonlinear energy sink‐inerter for dynamic response mitigation

Seismic control of multidegree‐of‐freedom structures using a concentratedly arranged tuned viscous mass damper

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