Optimal design and performance evaluation of systems with Tuned Mass Damper Inerter (TMDI)

Abstract

Summary The paper concerns the optimal design and performance evaluation of a Tuned Mass Damper Inerter (TMDI) to reduce dynamic vibrations. The system exploits properties of the inerter, a two‐terminal mechanical device able to produce a force proportional to the relative acceleration between terminals, with the ability of generating an apparent mass even two orders of magnitude greater than its own physical mass. A primary single‐degree‐of‐freedom structure is equipped with a classical linear Tuned Mass Damper (TMD), the secondary structure, whose mass is connected to the ground via an inerter. The optimal design of the TMDI is conducted by assuming a white noise process as base input and utilizing three different design methodologies: displacement minimization, acceleration minimization and maximization of the ratio between the energy dissipated in the secondary system and the total input energy. Optimal results obtained with the different methodologies are carried out and compared. Two limit cases are also considered when the inerter is not contemplated: conventional and non‐conventional TMDs, characterized by a low and a large mass ratio, respectively. The TMDI performance is evaluated and compared with conventional and non‐conventional TMDs; moreover, its robustness is assessed with a sensitivity analysis varying the design parameters. Attention is focused not exclusively on the primary structure response but also on the secondary one. Finally, the effectiveness of the optimally designed TMDI is evaluated having considered earthquake base excitation. Results demonstrate the effectiveness of TMDI systems for dynamic response reduction with superior performances and robustness than classical TMDs. Copyright © 2017 John Wiley & Sons, Ltd.

Earthquake Protection of Existing Structures with Limited Seismic Joint: Base Isolation with Supplemental Damping versus Rotational Inertia

“…is implies that the e ectiveness of the TMDI can be jeopardized if the accelerogram has a high impulsive content in the rst instants of motion [15]. Also reported in Figures 15(c) and 15(d) are the displacements of the secondary mass (TMD, TMDI).…”

“…e TMDI is characterized by four parameters in the most general case, namely, μ t , β t , ω t , and ζ t . Among these four parameters, the approach pursued in this paper is to nd the best frequency ratio ] t ω t /ω b and the best TMDI damping ratio ζ t for xed e ective mass ratio μ et μ t + β t , which is similar to other research contributions dealing with inerter-based devices in broad terms [14,15]. Indeed, the e ective mass ratio μ et can be designed according to mechanical considerations, that is, via the selection of a ywheel mass μ t and an inertance ratio β t arising from (2) and Figure 1.…”

“…For the above mentioned characteristics, the TMDI can be viewed as a lower mass and more e ective alternative to the traditional TMD, where the device inertance plays the role of the TMD mass [13][14][15][16]. While very large mass amounts are required for the TMD to achieve an acceptable vibration reduction, e ective vibration control can be attained by the TMDI with reasonably limited physical mass.…”

“…e design graphs also include the limit case of the TMD in place of the TMDI for a zero value of the inertance ratio, that is, β t 0. ree di erent values of the μ t Advances in Civil Engineering ratio are shown, namely μ t 0.01 that is representative of a small-mass ywheel device as shown in Figure 2, μ t 0.1 that is relevant to a conventional TMD system, and μ t 0.4 representing a nonconventional TMD that exploits masses already present in the system [15,38]. By inspection of the OF achieved, the TMDI appears to be very e ective in the displacement reduction of the baseisolated structure.…”

“…is means that high vibration control performance can be achieved by the TMDI without resorting to excessively large secondary mass, as implied in the nonconventional TMD. In other words, the TMDI outperforms the classical TMD as it exploits the light-weight features of the conventional TMD, with the e ectiveness of the nonconventional TMD [15]. e optimal TMDI parameters ] t opt and ζ t opt are signi cantly a ected by the physical mass μ t and by the inertance ratio β t .…”