Generalized optimal design of multiple tuned inerter dampers for control of MDOF structures under stochastic seismic excitation

Abstract

Optimized designs of tuned inerter dampers (TIDs) have been studied by presetting TID locations for the control of structures with multiple degrees of freedom (MDOF). In addition to the stiffness and damping coefficients, the importance of the inerter device constant, termed inertance, has been recognized. However, research on the effect of inertance on the design of multiple TIDs for controlling multimode responses is insufficient. This study investigates the generalized optimal design of the TIDs for controlling MDOF structures subject to stochastic excitation, where all parameters including TID stiffness, damping, inertance, and locations were considered as variables to be potentially optimized. The excitation was modeled as filtered white noise and combined with a model of an MDOF structure attached with multiple TIDs to create an augmented state space representation. Global optimization was performed to identify the modes of tuning the TIDs, with the TID location and inertance fixed, and the design was improved by adding the inertance as a parameter, and the mechanism of the performance enhancement by optimizing the inertance was demonstrated. Using the global optimization results as initial values, localized placement designs of multiple TIDs were realized using topology optimization and optimal TID tests were performed on three-and ten-story buildings. Results show that the control performance was improved by optimizing the inertance, along with the frequencies and damping ratios, and that the localized placement of multiple TIDs with equal total inertance is optimally designed and can achieve comparable performance of the TIDs distributed at the structure.

Adaptive Stiffness Structures with Dampers: Seismic and Wind Response Reduction Using Passive Negative Stiffness and Inerter Systems

“…Particularly, the inerters (Smith 2002), which can amplify inertial effects by rotating mass and gear mechanism, are receiving a lot of attention (Lazar et al 2014). The effects of inerterbased devices on single-or multi-degree-of-freedom systems have been investigated, e.g., Wen et al (2021). Inerters have been introduced into the damping system of stay cables to enhance the damping provided by dampers installed near cable anchorage (Lazar et al 2016;Lu et al 2017) and to improve the dissipation capacity of cable cross-ties (Sun et al 2017a); rotational mass has been proposed to enhance the damping effect by CDOs to high-rise buildings (Liu et al 2018).…”

Nonlinear dynamic P‐delta interaction between TMD and the frame structure under proportional internal resonances

“…[21][22][23][24][24][25][26][27][28][29][30][31] The scopes of some alluded researches have been optimal design and tuning of variant types of TMDs, such as a viscous mass damper (TVMD), 21 nonlinear TMDs, 22 semiactive TMDs, 23 and multiple tuned inerter dampers. 24 The efficiency of the tuned mass damper (TMD) on the torsional balance of nonlinear asymmetric structures has been investigated by Espinoza et al 25,26 However, a less discussed topic in the science of structural dynamics (and in the subset of structural control) is the study of the combined effect of TMD and P-delta on the shear frame in the range of small deformations leading to nonlinear differential equations of motion. The present research focuses on this subject for the first time and applies the method of multiple scales to derive the response of differential equations.…”

“…They consist of a mass mounted on one or more damped springs. In structural control, TMD has been extensively addressed, especially in recent studies 21–24,24–31 . The scopes of some alluded researches have been optimal design and tuning of variant types of TMDs, such as a viscous mass damper (TVMD), 21 nonlinear TMDs, 22 semiactive TMDs, 23 and multiple tuned inerter dampers 24 .…”

A band‐limited reliability‐based robust multimodal optimization of tuned mass dampers

“…Thus, vibration control of structures has become a major issue. In this context, several techniques can be found in the open literature including the passive control using tuned mass dampers (TMDs) 1–4 . Even though the TMDs are reliable and constitute a low‐cost solution, the design of these devices should be done carefully to guarantee optimal performances.…”

“…In this context, several techniques can be found in the open literature including the passive control using tuned mass dampers (TMDs). [1][2][3][4] Even though the TMDs are reliable and constitute a low-cost solution, the design of these devices should be done carefully to guarantee optimal performances. In this regard, a comprehensive optimal design of such devices was first proposed by Den Hartog.…”