Analytical solution of seismic response of base‐isolated structure with supplemental inerter

Abstract

Summary Closed‐form solutions are derived for the modal characteristics and seismic response of a base‐isolated structure equipped with additional inerters. By simplifying the structure‐isolator‐inerter system in terms of the two‐degree‐of‐freedom (2DOF) model, the modal frequencies, mode shapes, damping ratios, and participation factors of the system are derived. Consequently, analytical seismic response solutions are formulated by the modal superposition method. Utilizing these analytical solutions, an extensive parametric study has been carried out to investigate the effect of supplement inerters on both the modal characteristics and seismic response of the structure‐isolator‐inerter system. There is a critical inertance leading to the zero second modal participation factor (ie, the disappearance of the second modal response). The associated critical inertance ratio is derived in closed form as well. Moreover, it is observed that the reduction of deformation of isolators by increasing the inertance may be offset by the increase in relative displacements of the superstructure. To circumvent this adverse effect, an optimal range of inertance is identified whereby both the deformation of isolators and the relative displacement of the superstructure are mitigated concurrently.

Damping enhancement principle of inerter system

“…1,2 Many studies have been conducted to propose various device and structural control approaches in order to reduce the vibration response produced by earthquakes, wind, etc. [3][4][5][6][7] As a recently introduced mechanical element for structural control, the inerter has attracted an increasing amount of attention and has been studied in different fields, from the improved suspension system in mechanical [8][9][10][11][12] and railway engineering 13,14 to the protection of building structures, [15][16][17][18][19][20][21][22][23][24][25] storage tanks, [26][27][28] wind turbine towers, 29,30 platforms, 31 and performanceimproved cables [32][33][34][35] and isolation systems [36][37][38][39][40][41][42][43][44][45] in civil engineering. An inerter is a type of two-terminal inertia element, and its relative motion can be produced between the two termi...…”

Performance and optimal design of base‐isolated structures with clutching inerter damper

“…Later, studies on clutching inerter damper (CID) for seismic response control of structures were conducted, and they were found to be quite effective 10–13 . The use of inertial devices to improve the performance of a base‐isolated structure was also reported 14–17 . The performance of base‐isolated structures with supplemental tuned mass damper inerter (TMDI) has recently been investigated, and it has been found that the TMDI is effective in mitigating the seismic response 18–21 .…”

“…[10][11][12][13] The use of inertial devices to improve the performance of a base-isolated structure was also reported. [14][15][16][17] The performance of base-isolated structures with supplemental tuned mass damper inerter (TMDI) has recently been investigated, and it has been found that the TMDI is effective in mitigating the seismic response. [18][19][20][21] De Angelis et al 22 assessed the optimal tuning of the TMDI for base-isolated structures and confirmed the effectiveness of TMDI for seismic vibration control.…”

Structural optimal hybrid control strategies employing dynamic dual units: inerter and spring

“…These systems involve general structural systems including discrete structure system [24,25,[27][28][29][30][31] and distributed-parameter system, [32][33][34] TMD system, [26,35] and base isolation system (BIS) system. [36,37] These inerter-based devices have proved to be effective in improving the performance of the systems considered. However, in many cases, the performance of the inerter seems limited.…”