The tuned mass damper inerter for passive vibration control and energy harvesting in dynamically excited structural systems

A novel passive vibration control configuration, namely the Tuned-Mass-Damper-Inerter (TMDI) is proposed in this work. The TMDI combines the “inerter”, a mechanical two-terminal flywheel device developing resisting forces proportional to the relative acceleration of its terminals, with the well-known and widely used in various passive vibration control applications Tuned-Mass-damper (TMD). Introduced as a generalization of the TMD, the TMDI takes advantage of the “mass amplification effect” of the inerter to achieve enhanced performance compared to the classical TMD. For linear harmonically excited primary systems, analytical closed-form expressions are derived for optimal TMDI design/tuning parameters using the well-established and widely applied for the case of the classical TMD semi-empirical fixed-point theory. It is shown that for the same attached mass the TMDI system is more effective than the classical TMD to suppress vibrations close to the natural frequency of the uncontrolled primary system, while it is more robust to de-tuning effects. Moreover, it is analytically shown that optimally designed TMDI outperforms the classical TMD in minimizing the displacement variance of undamped linear single-degree-of-freedom (SDOF) white-noise excited primary systems. For this particular case, optimal TMDI parameters are derived in closed-form as functions of the additional oscillating mass and the inerter constant.\ud
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Furthermore, pertinent numerical data are furnished, derived by means of a numerical optimization procedure, for classically damped mechanical cascaded chain-like primary systems base excited by stationary colored noise. This exemplifies the effectiveness of the TMDI over the classical TMD to suppress the fundamental mode of vibration for linear MDOF structures. It is concluded that the incorporation of the inerter in the proposed TMDI configuration can either replace part of the TMD vibrating mass to achieve lightweight passive vibration control solutions, or improve the performance of the classical TMD for a given TMD mass.\ud
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The TMDI is further applied for passive vibration control of seismically excited building structures. An input non-stationary stochastic process compatible with the elastic design spectrum of the European aseismic code provisions (EC8) is assumed. The effectiveness of the proposed TMDI configuration over the classical TMD is assessed by performing response history analyses for an ensemble of EC8 spectrum compatible field recorded strong ground motions. The optimally tuned TMDI solution achieves considerable reduction of the peak average top floor displacement and peak average top floor accelerations of the considered primary structures compared to the one achieved by the optimally designed classical TMD, assuming the same additional mass in both cases. Furthermore, the TMDI configuration achieves significant reduction in the maximum displacement of the additional oscillating mass. In this study, the primary structures are assumed to behave linearly in alignment with current trends in performance based requirements for minimally damaged structures protected by passive control devices.\ud
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Furthermore, optimally designed TMDI is applied for vibration suppression and energy harvesting via an electromagnetic device which transforms the mechanical kinetic  energy into electrical energy. Unlike the case of traditional energy harvesting enabled TMD systems, the amount of available energy to be harvested by the herein proposed TMDI-based harvester is leveraged by changing the intensity of the mass amplification effect of the inerter, through mechanical gearing, without changing the weight of the TMDI system. Therefore, the inclusion of the inerter adds a “degree of freedom” or a design parameter to the classical TMD-based harvesters allowing to control the trade-off between vibration suppression and energy harvesting in a more flexible manner.\ud
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Overall, the herein reported numerical data and analytical work provide evidence that the TMDI offers a novel promising solution for passive vibration control and energy harvesting. Most importantly, it opens several new research paths involving numerical/parametric work, as well as, prototyping, experimental testing and field deployment