Design of structure with inerter system based on stochastic response mitigation ratio

Abstract

Summary An easy‐to‐use method for a practical design of single‐degree‐of‐freedom (SDOF) structures with inerter systems was developed. The method adopts the stochastic vibration response mitigation ratio as the design index, and expressions of the closed‐form stochastic response are used to evaluate the structural response and optimize the design parameters. Three basic types of inerter systems with tuning and damping magnification mechanisms were considered in this study. The closed‐form stochastic responses of SDOF structures with inerter systems under white‐noise excitations were derived on the basis of the equations of motion. In addition, the response variation patterns due to changes in key parameters of the inerter system were investigated, and the parameter optimization approaches for different inerter systems are proposed on the basis of the response variation patterns. The use of the closed‐form stochastic response mitigation ratio as the design index leads to a rational and simple design process, with the tuning or response extremum conditions employed as complementary conditions for determining the key design parameters. Thus, the proposed method involves the solution of a set of nonlinear equations. Fitted empirical design formulae are provided in this paper for quick calculation of the key parameters of the SDOF structure with the inerter system for a given response mitigation ratio and inherent damping ratio. Moreover, design examples are provided to verify the proposed method. The design results show that the proposed method is effective and more convenient than existing methods. Furthermore, the method can be easily extended for considering seismic excitations and design of structures with other complex‐form inerter systems.

Damping enhancement principle of inerter system

“…The ideal mechanical layouts of two representative series–parallel inerter systems, TID and TVMD, are shown in Figure , where m in , c d , and k d are the inertance of the inerter element, the damping coefficient of the EDE, and the stiffness of the spring element, respectively. For these two typical types of inerter systems, the inerter and the spring are connected in series in both systems, whereas the configurations of the EDEs are different; EDEs are mounted in parallel with the spring and inerter in the TID and TVMD, respectively.…”

“…Mechanical models of classic series–parallel layout inerter systems . EDE, energy dissipation element; SPIS‐I, series–parallel layout I inerter system; SPIS‐II, series–parallel layout II inerter system; TID, tuned inerter damper; TVMD, tuned viscous mass damper…”

“…These two responses can be represented by two dimensionless indicators, that is, the response mitigation ratio, γ , and the DDEF α . The response mitigation ratio, γ , is used to evaluate the performance of the SDOF structure with an inerter system: where σ U and σ U ,0 are the RMS displacement responses of the SDOF structure with an inerter system and the original SDOF structure, respectively. For a classic SDOF structure with an inherent damping of ζ , the normalized RMS of the displacement response under white‐noise excitation can be expressed analytically as As defined in Section 2.1, DDEF α can be expressed on the basis of stochastic responses as whose closed‐form expression can be viewed in Appendix A2.…”

“…In this section, the target‐damping‐enhancement‐based approach has been applied to determine parameters of the TVMD in an SDOF structure whose period of free vibration is 0.54 s and inherent damping ratio is 0.02 . To achieve different performance levels, the target vibration mitigation ratio, γ t , is assumed as 0.60, 0.50, and 0.30 (corresponding to reductions of 40%, 50%, and 70% of the displacement compared to the uncontrolled structure, respectively).…”

Analytical research on the dynamic performance of semi-active inerter-based vibration isolator with acceleration-velocity-based control strategy

“…Wang et al defined four performance indices to evaluate the isolation performance of the inerter‐based vibration isolator and showed that it can achieve a better isolation performance compared with the linear spring–damper vibration isolator. The inerter has also been applied in other structures due to its mechanical property, including vehicle suspension, motorcycle steering system, train suspension, building vibration control system, landing gear, dynamic vibration absorber, and tuned mass damper . The researches show that when the inerter is used, these mechanical systems can achieve a superior performance.…”