Inert Devices Research Articles

Design of a Tuned Mass Damper Inerter (TMDI) Based on an Exhaustive Search Optimization for Structural Control of Buildings under Seismic Excitations

A tuned mass damper inerter (TMDI) is a new class of passive control device based on the inclusion of an inerter mechanism into a conventional tuned mass damper (TMD). The inerter device provides inertial resisting forces to the controlled system, through relatively small masses, converting it in a mechanism with the potential to enhance the performance of passive energy dissipating systems. This work presents a study of an optimal TMDI design through an exhaustive search process. TMDI device design using the cited parameter selection methodology consists in the determination of the damper critical damping ratio,ζTMDI, and frequency ratio,υTMDI, which result in the minimum structural response of a multidegree of freedom structural system, considering predefined values for mass ratio (µ) and inertance ratio (β). The used optimization process examines all possible damping device design parameter combinations to select the set of values that results in the best device performance to reduce response parameters in a structure. Four different optimization processes are performed by independently minimizing four performance indices:J1associated to the reduction of the structure’s maximum peak displacement,J2calculates the minimal RMS value for the structure’s peak displacement,J3seeks by the minimal peak interstorey drift, andJPdetermines the lowest value for a linear weighted combination of the abovementioned three indices. A numerical example is developed with the purpose of validating the proposed optimization procedure and to evaluate the benefits of using TMDI as controlling devices for structures under seismic excitation, by carrying out a comparative analysis to contrast the performance of the optimization alternatives developed, running up to 1968192 cases. The obtained results show that devices designed based on exhaustive search optimization produce peak displacement reductions of up to 35% and peak structure displacementRMSreductions of up to 30%.

The missing mem-inerter and extended mem-dashpot found

Anyone who ever gave attention to advances in circuit elements will be familiar with the three elementary two-terminal passive elements: resistor, inductor, capacitor and their memory counterparts: memristor, meminductor and memcapacitor, respectively. Similarly, it is reported that the mem-dashpot and the mem-spring were viewed as the memory counterparts of the damper and the spring in the field of mechanical engineering. However, what is the memory counterpart of the inerter as a new two-terminal element? In 2018, Zhang predicted the existence of such a mechanical element, which he called a mem-inerter. Although he postulated this element, until now no one offered either a useful physical realization or an example of a mem-inerter. Here, a displacement-dependent fluid inerter device is found to be a physical realization of a mem-inerter, though with a parasitic element called the extended mem-dashpot, which is viewed as the mechanical counterpart of an extended memristor. Experimental results confirm this finding and the existence of the mem-inerter and the extended mem-dashpot in the real world. This work is very helpful in finding and designing mem-inerter and extended mem-dashpot devices, and modeling some important nonlinear hysteretic devices and systems, which is a fundamental branch of research in nonlinear dynamics.

Optimal design and seismic performance of Multi‐Tuned Mass Damper Inerter (MTMDI) applied to adjacent high‐rise buildings

SummaryThe tuned mass damper inerter (TMDI) is an enhanced variant of the tuned mass damper (TMD) that benefits from the mass‐amplification effect of the inerter. Here, a multi‐TMDI (MTMDI) system (comprising more than one TMDI) linking two adjacent high‐rise buildings is presented as an unconventional seismic protection strategy. The relative acceleration response of the adjacent structures triggers large reaction forces of the inerter devices in the MTMDI, which in turn efficiently improve the seismic performance of the two buildings. By addressing a real project of two adjacent high‐rise buildings connected by two corridors equipped with the proposed MTMDI system, the displacement‐, interstory drift‐, and acceleration‐based parametric optimizations are separately performed by employing Nondominated Sorting Genetic Algorithm II (NSGA‐II) under 44 ground motions from the FEMA P695 far‐field record set. It is found that the frequency content of the seismic input has strong impact on the MTMDI mitigation performance. Adopting realistic mass ratio constraints, the optimally designed MTMDI outperforms both conventional MTMD and single TMDI in acceleration control, while it is not much effective in mitigating the displacement response due to the highly flexible nature of the high‐rise buildings, in contrast to other literature studies generally focused on low‐to‐medium rise buildings.

Experimental study and numerical modeling of nonlinear dynamic response of SDOF system equipped with tuned mass damper inerter (TMDI) tested on shaking table under harmonic excitation

This paper considers a novel shaking table testing campaign to assess the tuned mass-damper-inerter (TMDI) vibrations suppression attributes in harmonically excited structures under the combined effect of nonlinear structural response and nonlinear inerter device behavior deviating from the ideal linear inerter element developing acceleration-dependent force proportional to the inertance constant. Physical specimens of TMDI-equipped single-degree-of-freedom (SDOF) structure are considered featuring a custom-built rack-and-pinion flywheel inerter device with nonlinear behavior due to friction and backlash effects to connect the TMDI secondary mass to the ground. Damping and elastic properties are endowed to the SDOF structure and to the TMDI via high damping rubber bearings (HDRBs) exhibiting softening nonlinear elastic behaviour. Comprehensive experimental data in time and frequency domains are presented for 9 specimens with different sets of secondary mass and inertance subject to sine-sweep excitations for three different amplitudes. The data demonstrate that the main practical advantage of the TMDI established in the literature for linear structures and ideal inerter elements (i.e., improved vibration suppression through increasing inertance without increasing secondary mass leading to lightweight vibration absorbers) is maintained for nonlinear structures and inerter devices. Moreover, a comparison of experimental data with data derived from two different nonlinear parametric numerical models capturing faithfully the HDRBs response, one using a nonlinear mechanical model to represent the inerter device and the other using an ideal linear inerter element instead, demonstrate that displacement, acceleration and base shear response of the SDOF structure is insignificantly influenced by the nonlinear attributes of the inerter device. This outcome paves the way for developing simplified, thus practically meritorious, optimal TMDI tuning approaches adopting the ideal inerter element assumption to model physical inerter devices.

Smart structures through nontraditional design of Tuned Mass Damper Inerter for higher control of base isolated systems

This paper introduces a smart structure design through the definition of an innovative passive control strategy, referred to as New Tuned Mass Damper Inerter (New TMDI), coupled with a base isolation system (BI), to control displacements in base isolated structures under seismic excitations. The herein proposed New TMDI comprises a recently developed nontraditional Tuned Mass Damper (known as New TMD), in which a secondary mass system is connected to the base plate of the BI system by a spring and to the ground by a dashpot, and of an inerter device placed in parallel with the damper.An optimization procedure which minimizes the base displacement variance of the BI system, considering the case of white noise base excitation, is proposed to determine optimal design parameters of the New TMDI, and pertinent approximate closed-form expression are derived. Note that, this device might be considered for applications in historic buildings, generally built in contiguity with the others. Adopting this nontraditional TMDI, it would be possible to get a smart historic building, offering higher control performance over an ordinary design. Further, the performance of a base-isolated New TMDI-controlled multi-degree-of-freedom structure is examined and compared with that of the simple base-isolated one, using a set of 44 recorded ground motions as base excitation. Results show that the New TMDI is rather effective in reducing the response of base-isolated structures under strong earthquakes.

Performance evaluation of inerter‐based dampers for vortex‐induced vibration control of long‐span bridges: A comparative study

Inerter-based dampers (IBDs) have been proposed to enhance the efficiency of conventional tuned mass dampers (TMDs) in controlling wind-induced vibration of civil structures recently. In this paper, four different IBDs, with each featuring a specific combination of dashpot–spring elements in series or in parallel with the inerter device, are applied to control the vortex-induced vibration (VIV) of long-span bridges. The governing equations of the bridge–IBD system under the effect of VIV are established, and the strategy to optimize the IBD parameters is proposed. The performances of different IBDs in terms of mitigating the VIV response of the deck, the stroke of mass block, the static deformation of spring due to gravity, the reaction force of IBDs on the bridge deck, and the robustness of the system (the control efficiency against the deviation of design parameters from their optimal values) are systematically evaluated and compared. Through this comparative study, the superiorities of IBDs to conventional TMDs in bridge VIV control are illustrated, and two feasible layouts of IBDs that are suitable for bridge VIV control are suggested. On the basis of these results, the guideline for VIV-resistance design of long-span bridges with the help of IBDs is also proposed.

Optimal tuned mass-damper-inerter (TMDI) design in wind-excited tall buildings for occupants’ comfort serviceability performance and energy harvesting

The tuned mass-damper-inerter (TMDI) couples the classical tuned mass-damper (TMD) with an inerter device which develops a resisting force proportional to the relative acceleration of its ends by the “inertance” constant. Previous works demonstrated that the TMDI leads to efficient broadband vibration control for a range of different structures under different dynamic excitations. This paper proposes a novel optimal TMDI design formulation to address occupants’ comfort in wind-excited slender tall buildings susceptible to vortex shedding (VS) effects and to explore optimal TMDI’s potential for transforming part of the wind-induced kinetic energy to usable electricity in tall buildings. Attention is focused on investigating benefits of TMDIs with different inertial properties (i.e., secondary mass/weight and inertance) configured in different topologies defined by the number of floors spanned by the inerter device to connect the secondary mass to the building structure. Optimally designed TMDIs for a wide range of inertial properties and three different topologies are obtained through numerical solution of the underlying optimization problem for a benchmark 305.9 m tall building with more than 6 height-to-width ratio subjected to experimentally calibrated spatially-correlated across-wind force field accounting for VS effects. Fixed performance design graphs on the TMDI inertial (mass-inertance) plane are furnished demonstrating that any fixed structural performance level in terms of occupants’ comfort (i.e., peak top floor acceleration) can be achieved through lightweight TMDIs as long as sufficient inertance is provided. Further, TMDI robustness to host structure properties and to reference wind velocity is shown to increase by increasing inertance or by spanning more floors in connecting the secondary mass with the host structure by the inerter. Lastly, it is found that increased available energy for harvesting in wind excited tall buildings is achieved by incorporating electromagnetic motors in TMDIs with varying damping property, while concurrent reduced floor acceleration and increased available energy for harvesting is accomplished by TMDI topologies with inerters spanning more floors.

Economic Reasoning and Interaction in Socially Extended Market Institutions.

An important part of what it means for agents to be situated in the everyday world of human affairs includes their engagement with economic practices. In this paper, we employ the concept of cognitive institutions in order to provide an enactive and interactive interpretation of market and economic reasoning. We challenge traditional views that understand markets in terms of market structures or as processors of distributed information. The alternative conception builds upon the notion of the market as a “scaffolding institution.” Introducing the concept of market as a “socially extended” cognitive institution we go beyond the notion of scaffolding to provide an enactive view of economic reasoning that understands the market participant in terms of social interactive processes and relational autonomy. Markets are more than inert devices for information processing; they can be viewed as “highly scaffolded,” where strong constraints and incentives predictably direct agents’ behavior. Building on this idea we argue that markets emerge from (a) the economic interaction of both supply and demand sides, in continual and mutual interplay, and (b) more basic social interactions. Consumer behavior in the marketplace is complex, not only contributing to determine the market price, but also extending the consumer’s cognitive processes to reliably attain a correct evaluation of the good. Moreover, this economic reasoning is socially situated and not something done in isolation from other consumers. From a socially situated, interactive point of view buying or not buying a good is something that enacts the market. This shifts the status of markets from external institutions that merely causally affect participants’ cognitive processes to social institutions that constitutively extend these cognitive processes. On this view the constraints imposed by social interactions, as well as the possibilities enabled by such interactions, are such that economic reasoning is never just an individual process carried out by an autonomous individual, classically understood. In this regard, understanding the concept of relational autonomy allows us to see how economic reasoning is always embodied, embedded in, and scaffolded by intersubjective interactions, and how such interactions make the market what it is.

An electromagnetic variable inertance device for seat suspension vibration control

Abstract This paper designs and builds an electromagnetic variable inertance (VI) device for a heavy duty vehicle seat suspension to reduce the vibration transferred to driver bodies. The conventional semi-active vibration control mainly applies the variable damping (VD) and variable stiffness (VS) devices. The VI device is equivalent to an inerter with the capability to vary its inertance, which is a new semi-active system inspired by the VS device design. The VI device consists of a transmission device, a VD device and two flywheels. By varying the damping of the VD device, the equivalent inertance of the VI device is controllable in real time. The VI device prototype is built with an electromagnetic VD device which is controlled by the duty cycle of the pulse width modulation signal. The test results verify the proposed system model and identify the unknown model parameters. Then, a seat suspension applies the VI device prototype for improving the ride comfort. Based on the system model, an implementable controller is proposed and experimentally validated. The proposed seat suspension system shows excellent performance in a random vibration experiment. Compared with a conventional passive seat suspension, the frequency-weighted root mean square acceleration of the proposed one reduces 35.7%. The VI device has expanded the application of the inerter and the area of the semi-active research; it shows great potential in vibration control.

Brain mechanisms of social touch-induced analgesia in females

Supportive touch has remarkable benefits in childbirth and during painful medical procedures. But does social touch influence pain neurophysiology, ie, the brain processes linked to nociception and primary pain experience? What other brain processes beyond primary pain systems mediate their analgesic effects? In this study, women (N = 30) experienced thermal pain while holding their romantic partner's hand or an inert device. Social touch reduced pain and attenuated functional magnetic resonance imaging activity in the Neurologic Pain Signature (NPS)-a multivariate brain pattern sensitive and specific to somatic pain-and increased connectivity between the NPS and both somatosensory and "default mode" regions. Brain correlates of touch-induced analgesia included reduced pain-related activation in (1) regions targeted by primary nociceptive afferents (eg, posterior insula, and anterior cingulate cortex); and (b) regions associated with affective value (orbitofrontal cortex), meaning (ventromedial prefrontal cortex [PFC]), and attentional regulation (dorsolateral PFC). Activation reductions during handholding (vs holding a rubber device) significantly mediated reductions in pain intensity and unpleasantness; greater pain reductions during handholding correlated with greater increases in emotional comfort, which correlated with higher perceived relationship quality and (a trend toward) greater perceived closeness with the romantic partner. The strongest mediators of analgesia were activity reductions in a brain circuit traditionally associated with stress and defensive behavior in mammals, including ventromedial and dorsomedial PFC, rostral anterior cingulate cortex, amygdala/hippocampus, hypothalamus, and periaqueductal gray matter. Social touch affects core brain processes that contribute to pain and pain-related affective distress in females, and should be considered alongside other treatments in medical and caregiving contexts.

Generalisable model development for fluid-inerter integrated damping devices

Vibration absorbers with a combination of stiffness, damping and inertance have been shown to be effective through numerous theoretical studies. One way to realise inertance is by using the fluid-based inerter, with the advantages of durability, structural simplicity and the similarity with existing damper constructions. Previous studies focused on accurate modelling of a specific fluid-based inerter device, while there has been no investigation on whether the dynamic models are still valid when its design parameters change. A model is termed here as being generalisable when it is able to sufficiently accurately characterise the terminal behaviour while allowing its design parameters to vary within their pre-defined ranges. In this paper, a generalisable model is developed for an example fluid-inerter integrated damping (FID) design. The methodology to develop such model uses the hydraulic and the corresponding mechanical networks representing the device, and tailored experimental testing to characterise each network element. Such approach is applicable to other design parameter settings and also other designs of FID devices.

Multi-objective optimal design of inerter-based vibration absorbers for earthquake protection of multi-storey building structures

In recent years different inerter-based vibration absorbers (IVAs) emerged for the earthquake protection of building structures coupling viscous and tuned-mass dampers with an inerter device. In the three most popular IVAs the inerter is functioning either as a motion amplifier [tuned-viscous-mass-damper (TVMD) configuration], mass amplifier [tuned-mass-damper-inerter (TMDI) configuration], or mass substitute [tuned-inerter-damper (TID) configuration]. Previous work has shown that through proper tuning, IVAs achieve enhanced earthquake-induced vibration suppression and/or weight reduction compared to conventional dampers/absorbers, but at the expense of increased control forces exerted from the IVA to the host building structure. These potentially large forces are typically not accounted for by current IVA tuning approaches. In this regard, a multi-objective IVA design approach is herein developed to identify the compromise between the competing objectives of (i) suppressing earthquake-induced vibrations in buildings, and (ii) avoiding development of excessive IVA (control) forces, while, simultaneously, assessing the appropriateness of different modeling assumptions for practical design of IVAs for earthquake engineering applications. The potential of the approach to pinpoint Pareto optimal IVA designs against the above objectives is illustrated for different IVA placements along the height of a benchmark 9-storey steel frame structure. Objective (i) is quantified according to current performance-based seismic design trends using first-passage reliability criteria associated with the probability of exceeding pre-specified thresholds of storey drifts and/or floor accelerations being the engineering demand parameters (EDPs) of interest. A variant, simpler, formulation is also considered using as performance quantification the sum of EDP variances in accordance to traditional tuning methods for dynamic vibration absorbers. Objective (ii) is quantified through the variance of the IVA force. It is found that reduction of IVA control force of up to 3 times can be achieved with insignificant deterioration of building performance compared to the extreme Pareto optimal IVA design targeting maximum vibration suppression, while TID and TMDI achieve practically the same building performance and significantly outperform the TVMD. Moreover, it is shown that the simpler variant formulation may provide significantly suboptimal reliability performance. Lastly, it is verified that the efficacy of optimal IVA designs for stationary conditions is maintained for non-stationary stochastic excitation model capturing typical evolutionary features of earthquake excitations.

Design and testing of a frictionless mechanical inerter device using living-hinges

In this paper a novel type of frictionless mechanical inerter device is presented, where instead of gears, motion of the flywheel is achieved using living-hinges. The design is a type of pivoted flywheel inerter inspired in part by the Dynamic Anti-resonant Vibration Isolator (DAVI) concept, which was first developed in the 1960s. Unlike the DAVI, it will be shown that the pivoted flywheel inerter has the advantage of producing balanced forces. Furthermore the use of living-hinges eliminates the need for gears or other frictional elements in the inerter mechanism. To demonstrate the utility of the new concept, a bench-top experiment was performed using a small-scale living-hinge inerter manufactured using polypropylene hinges. By estimating the experimental system parameters, the transmissibility results from the experiment could be compared to a mathematical model. These results showed that the living-hinge inerter provided an isolation effect of at least three orders of magnitude in terms of the maximum amplitude reduction from the uncontrolled system compared to that with the inerter added. Although friction was eliminated, the living-hinges did introduce additional damping, and this was found to correspond to an increase in the equivalent damping ratio for the uncontrolled system of 1.2%. It is shown that the living-hinge inerter developed in this paper fits all of the essential conditions required to be a practical inerter device. Furthermore, as it operates without mechanical friction, or fluid flow, it represents a new paradigm in experimental inerter technology.

Passive Skyhook Suspension Reduction for Improvement of Ride Comfort in an Off-Road Vehicle

With the use of Routh stability criterion and Pade approximation technique to simplify the passive skyhook damping suspension system, a full-car model involving the reduced-order ISD suspension was established for the analysis of ride comfort. The genetic algorithm of unified objective function was applied for the optimization of structural parameters. Comparative analysis of the system performance was conducted among the conventional passive suspension, the passive skyhook damping suspension and the reduced-order ISD suspension. The results show that the root-mean-square value of body acceleration, tire dynamic load and suspension working space of the reduced-order ISD suspension are close to those of the passive skyhook damping suspension and the main performance can be achieved. It illustrates that the overall performance of the reduced-order ISD suspension can be close to the passive skyhook damping suspension and the research theoretically verified the effectiveness of the reduced-order ISD suspension. Furthermore, a integrated inerter device with inerter and damper connected in series is developed, which is then arranged in the front and rear suspension of an off-road vehicle for road test. As a result of this paper, it was demonstrated that, the reduced-order ISD suspension can suppress the vertical, pitch and roll vibration of vehicle body.

Using tuned mass damper inerter to mitigate vortex-induced vibration of long-span bridges: Analytical study

The undesirable vortex-induced vibration (VIV) may seriously influence the fatigue life and serviceability of bridge structures. It is important to take countermeasures to suppress the adverse VIV of long-span bridges. In the present study, a novel inerter-based system, namely the tuned mass damper inerter (TMDI), is proposed to control the VIV of the main deck of long-span bridges. In this system, an inerter device, which is able to transform the linear motion into the high-speed rotational motion and thus significantly amplifies the physical mass of the system, is incorporated into the conventional tuned mass damper (TMD) system to further improve the performance of TMD. An applicable layout of the TMDI inside the bridge deck is introduced and the governing equations of the structure-TMDI system subjected to VIV are established. The optimization of the TMDI parameters with the consideration of nonlinear aeroelastic effect is derived. The control performance and robustness of the proposed system are investigated through an analytical case study in both the time and frequency domains. It is observed that the TMDI system can obviously reduce the VIV responses of the bridge deck. Moreover, compared to the conventional TMD system, the static stretching of the spring due to gravity and the oscillation amplitude of the mass block in the TMDI system are significantly reduced. These properties make the proposed TMDI system an attractive alternative for the VIV control of long-span bridges.

Novel fluid inerter based tuned mass dampers for optimised structural control of base-isolated buildings

This work studies the advantageous features of the fluid inerter device for optimised structural control of buildings. Experimental data are first presented to characterise the fluid inerter dynamics, and validate the simplified analytical formulations. Building on these observations, the device is modelled as an inerter in parallel with a nonlinear dashpot representing a power law damping term. The latter dissipative effects are mainly induced by the pressure drops occurring in helical channels due to the fluid viscosity and density. Then, novel passive vibration control schemes are implemented for the earthquake protection of base-isolated buildings by combining the fluid inerter with a tuned mass damper system. To account for the uncertain nature of the earthquake input, the base acceleration is modelled as a Kanai–Tajimi filtered stationary random process. The optimal fluid inerter parameters, namely inertance and damping, are identified numerically by minimising stochastic performance indices relevant to displacement, acceleration, and energy-based measures of the structural response. The nonlinear damping behaviour of the fluid inerter is fully incorporated in the optimal design procedure via the statistical linearisation technique. Nonlinear response history analysis under an ensemble of 44 natural earthquake ground motions is carried out to assess the seismic performance of the system. Since inertance and damping are coupled characteristics in a real fluid inerter, design guidelines are finally outlined to determine the actual geometrical and mechanical properties of the device to achieve targeted parameters resulting from the optimisation procedure.

Mitigation of heave response of semi-submersible platform (SSP) using tuned heave plate inerter (THPI)

The undesirable motions resulting from wave loading can lead to the long-term fatigue damage or even catastrophic sinking of offshore semi-submersible platforms (SSP). It is therefore by all means necessary to suppress the excessive vibrations of SSP. Many methods have been proposed to mitigate the heave motion of offshore platforms, such as using a fixed heave plate (FHP) to increase the draft and damping of the system, or adopting a tuned heave plate (THP) to form a tuned mass damper (TMD) system. In this paper, a novel inerter-based control system, namely a tuned heave plate inerter (THPI), is proposed for control of SSP heave vibrations. In this system, an inerter device, which can transform the linear motion into the high-speed rotational motion and thus significantly amplifies the physical mass of the system, is added to the THP to further improve the performance of conventional THP. Analytical studies are performed to investigate the effectiveness of the proposed method. The mean square heave motions of SSP without control device and with FHP, THP and THPI are stochastically formulated, and the optimal design parameters for THP and THPI are derived. Parametric studies are conducted to investigate the influences of the size and original depth of heave plate on the optimal performances of FHP, THP and THPI. Finally, a novel waterwheel inerter is developed to realize the suggested device. The analytical results show that THPI is more effective to mitigate the heave motion of SSP compared to the conventional methods, and the novel waterwheel inerter is capable of generating a large apparent mass by using a small waterwheel.

Improving the dynamic performance of base-isolated structures via tuned mass damper and inerter devices: A comparative study

Improving the dynamic performance of base-isolated structures via tuned mass damper and inerter devices: A comparative study

Fault Current Limiter Placement to Reduce Recloser ‑ Fuse Miscoordination in Electric Distribution Systems with Distributed Generation using Multiobjective Particle Swarm Optimization

This paper presents a method to minimize protective devices in electric distribution systems with Distributed Generation (DG). With the growing penetration of DG in distribution systems, the main practice to maintain protective devices coordination during a fault is to disconnect all DG sources. This practice nullifies the benefits brought by DG in distribution systems, mainly because the majority of faults are proven to be temporary. To solve this problem, this paper proposes the allocation of fault current limiters (FCL), which consist in inert devices on system's normal operation, but insert a high impedance value in series with feeders when a fault occurs, thus, limiting is magnitude. FCL placement is treated as a multiobjective optimization problem, aiming to reduce fault currents difference between situations with DG and without DG penetration. Also, FCL size must be minimized, aiming to reduce costs. The search for the optimal solution is made using multiobjective particle swarm optimization and the method is tested on the Canadian Benchmark Test System, showing great efficiency.

Optimal tuned mass-damper-inerter (TMDI) design for seismically excited MDOF structures with model uncertainties based on reliability criteria

The tuned mass-damper-inerter (TMDI) is a recently proposed linear passive dynamic vibration absorber for the seismic protection of buildings. It couples the classical tuned mass damper (TMD) with an inerter, a two-terminal device resisting the relative acceleration of its terminals, in judicial topologies, achieving mass-amplification and higher-modes-damping effects compared to the TMD. This paper considers an optimum TMDI design framework accommodating the above effects while accounting for parametric uncertainty to the host structure properties, modeled as a linear multi degree of freedom system, and to the seismic excitation, modeled as stationary colored noise. The inerter device constant, acting as a TMD mass amplifier, is treated as a design variable, whereas performance variables sensitive to high-frequency structural response dynamics are used to account for the TMDI influence to the higher structural modes. Reliability criteria are adopted for quantifying the structural performance, expressed through the probability of occurrence of different failure modes related to the trespassing of acceptable thresholds for the adopted performance variables: floor accelerations, interstory drifts, and attached mass displacement. The design objective function is taken as a linear combination of these probabilities following current performance-based seismic design trends. Analytical and simulation-based tools are adopted for the efficient estimation of the underlying stochastic integral defining the structural performance under uncertainty. A 10-story building under stationary Kanai-Tajimi stochastic excitation is considered to illustrate the design framework for various TMDI topologies and attached mass values. It is shown that the TMDI achieves enhanced structural performance and robustness to building and excitation uncertainties compared to same mass/weight TMDs.