Analysis and optimisation for inerter-based isolators via fixed-point theory and algebraic solution

Hu, Yinlong; Chen, Michael Z. Q.; Shu, Zhan; Huang, Lixi

doi:10.1016/j.jsv.2015.02.041

Cited by 181 publications

(110 citation statements)

References 31 publications

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“…There are mainly two approaches to optimally control the response of a linear system: minimizing the peak modulus of the system's transfer function, which is known as H ∞ optimization, and directly minimizing the system's response, which is known as H 2 optimization. In this study, the H 2 optimization scheme was adopted because of the following: (1) For random excitations such as wind or earthquakes, instead of harmonic excitation, the H 2 optimization scheme would be more practical. (2) The peak modulus of the transfer function does not change smoothly as parameters change; therefore, the H ∞ optimization scheme may cause numerical instability as optimizations in this study would involve numerical approaches.…”

Section: Theoretical Analysis Of Oscillator With Pvidmentioning

confidence: 99%

“…However, parallel layouts, which are the focus of this study, are completely different from TMDs, and fixed‐point theory may therefore not be applicable to performing the parametric design. Although the fixed‐point theory has been used to the design of a VID with a parallel layout, that is, parallel VID (PVID), the unsuitability of this approach is obvious, as discussed in detail in the following section of this paper. Furthermore, for the fixed‐point method, the inherent damping of the primary structure is neglected, and an empirically equivalent mass ratio must be provided before conducting the parametric design, which is an added limitation of the fixed‐point method.…”

Section: Introductionmentioning

confidence: 99%

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Demand-based optimal design of oscillator with parallel-layout viscous inerter damper

Pan

Zhang

Luo

et al. 2017

Struct Control Health Monit

112

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SummaryIn this study, a demand-based optimal design method is proposed for an oscillator (a single-degree-of-freedom system) with a parallel-layout viscous inerter damper (PVID). The proposed design method overcomes some deficiencies of the existing method, which is based on the fixed-point theory and is mainly suitable for tuned mass dampers. Moreover, for the fixed-point method, the inherent damping of the primary structure is neglected, and the global optimal solution cannot be obtained.The proposed method can obtain a more rational and practical design for the actual design by minimizing both the response and the cost. The design problem of a PVID-equipped oscillator is transformed into a multi-objective optimization problem that can be solved using the ε-constraint approach, which is consistent with the concept of demand-based design. The dynamic response of the oscillator and the force of the PVID (i.e., the cost factor) are evaluated according to theories of random vibration to reduce the number of calculations required. A computer program is developed to perform demand-based parametric design of a PVID-equipped oscillator. Several design cases were examined under different excitation conditions using the computer program, and dynamic time history analyses were then conducted to verify the designs obtained. The results show that the proposed optimal design method identifies satisfactory designs more effectively than the existing method by obtaining PVID design parameter values that better meet the performance demand and simultaneously minimize the cost. | INTRODUCTIONStructural vibrations induced by earthquake or wind loads can be attenuated by various means, including modifying the stiffness, masses, damping, or shape of the structure, and by providing passive or active counter forces.[1] Among numerous available methods, passive mitigation measures are the most widely used in building and bridge engineering. Passive vibration mitigation involves providing a structure with additional damping by installing dampers, and the effectiveness of damping has been confirmed by extensive scientific studies and practical applications. Many types of dampers are used in the passive vibration mitigation of building structures all over the world, such as metalyield dampers, friction dampers, viscoelastic dampers, viscous fluid dampers, tuned mass dampers, and tuned liquid dampers. The concept of tuned mass dampers dates back to the 1900s, when Frahm [2] introduced a tuned mass damper (TMD) to absorb the energy of vibrations, thereby reducing the amplitudes of motions. Den Hartog [3] modified the original TMD concept in the

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Section: Theoretical Analysis Of Oscillator With Pvidmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Demand-based optimal design of oscillator with parallel-layout viscous inerter damper

Pan

Zhang

Luo

et al. 2017

Struct Control Health Monit

112

View full text Add to dashboard Cite

show abstract

“…However, as the adaptive‐configuration TMD is a semiactive damper, its performance depends strongly on its control algorithm . Hu et al analytically derived the optimal parameters of different configurations of inerter‐based isolators, including the TVMD and TID, based on an isolated single degree of freedom (SDOF) system with H∞ and H2 optimizations. Wen et al evaluated the performance of tuned inerter‐based dampers, TVMD and TID, for the seismic control of MDOF structures.…”

Section: Introductionmentioning

confidence: 99%

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

Wang

Sun

2018

Earthq Engng Struct Dyn

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Summary This 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.

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“…An appealing property of inerters is that they can be designed and realized in practice having their inertance significantly larger than their mass [1,2]. This opens many interesting possibilities so that many authors reported on how to design and use inerters to suppress mechanical vibrations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

“…In vibration isolation problems it is often necessary to tune the impedance of the isolator elements based on some optimization criteria. This can be done by either minimizing maxima of the response (minimax or H∞ optimization), or by minimizing the energy in the response signals (H2 optimization) [12].…”

Section: Introductionmentioning

confidence: 99%

An inerter-based active vibration isolation system

et al. 2018

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Abstract. This paper presents a theoretical study on passive and active vibration isolation schemes using inerter elements in a two degree of freedom (DOF) mechanical system. The aim of the work is to discuss basic capabilities and limitations of the vibration control systems at hand using simple and physically transparent models. Broad frequency band dynamic excitation of the source DOF is assumed. The purpose of the isolator system is to prevent vibration transmission to the receiving DOF. The frequency averaged kinetic energy of the receiving mass is used as the metric for vibration isolation quality. It is shown that the use of inerter in the passive and active vibration isolation schemes considered enhances the isolation effect.

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Analysis and optimisation for inerter-based isolators via fixed-point theory and algebraic solution

Cited by 181 publications

References 31 publications

Demand-based optimal design of oscillator with parallel-layout viscous inerter damper

Demand-based optimal design of oscillator with parallel-layout viscous inerter damper

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

An inerter-based active vibration isolation system

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