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 (T MDI) 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 performanc e-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 EDPs 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 com pared to the extreme Pareto optimal IVA design targeting maximum vibration suppression , while TID and TMDI a chieve 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

The inerter: a retrospective

The paper provides an introduction and overview of the inerter concept and device. Careful attention is given to the distinction between the inerter as an ideal modelling element and devices that approximate the ideal behaviour. The background is given to the formal definition of the inerter as a mechanical one-port with terminal forces proportional to the relative acceleration between them. Four major methods of construction are described and modelled. The discussion focuses particularly on: the notion of terminals; the distinction between a device and an effect; sign reversals; back-driving in geared systems; the conceptual aspects of the modelling step for inerter embodiments; the problem of reverse engineering to discover a purpose. The paper includes an analysis and discussion of the rotational inerter. A brief review of the ideas of passive network synthesis that led to the inerter concept are provided. A discussion and analysis is given on several examples of integrated mechanical devices. The article concludes with an imaginary dialogue between the author and an interlocutor on the understanding and purpose of the inerter

Fluid inerter for optimal vibration control of floating offshore wind turbine towers

This paper proposes the use of a tuned mass damper fluid-inerter (TMDFI) for vibration control of spar-type floating offshore wind turbine towers. The use of an inerter in parallel with the spring and damper of a tuned mass damper (TMD) is a relatively new concept. The ideal inerter has a mass amplification effect on the classical TMD leading to greater vibration control capabilities. Previous work by the authors has shown that inerter based TMDs have great potential in vibration control of floating offshore wind turbines where enhanced vibration mitigation can be achieved using a relatively lighter device than classical TMDs. However, this previous work was based on the assumption of an ideal inerter that assumes the use of a mechanical flywheel type inerter. Mechanical inerters have some inherent disadvantages due to their complexity in design and high cost of maintenance. The use of a fluid inerter can alleviate these disadvantages as its design is rather simple and it comes with very low maintenance. Such devices have been proposed and investigated in the literature, however, their applicability in vibration control of floating wind turbines has not been investigated by researchers. The optimal design of a TMDFI is presented in this paper. It has been shown that optimization of a TMDFI is a six-dimensional non-linear optimization problem whose solution hyperplane contains multiple local minima. A systematic way has been developed in this paper, avoiding the use of metaheuristic search techniques, to optimize the damper while providing greater insight into the damper properties that offers a set of guidance to the designer. Numerical results demonstrate impressive vibration control capabilities of this new device under various stochastic wind-wave loads. It has been shown that the fluid-inerter performs as well as the ideal mechanical inerter. The considerable advantages of a TMDFI over the classical TMD demonstrated in this paper makes it an exciting candidate for vibration control

Design of a fluid inerter for the control of rotor vibrations

Nel 2008, due articoli della rivista sportiva “Autosport” rivelarano dettagli di una nuova sospensione meccanica nota con il nome di "J-damper" che era entrata in Formula 1 e che aveva offerto in termini di prestazioni significativi aumenti di maneggevolezza e aderenza. Si trattava di un "inerter", la cui origine sta nel lavoro accademico su circuiti meccanici ed elettrici realizzati dal prof. M. C. Smith. Gli Inerter sono particolari dispositivi meccanici con la proprietà che la forza applicata ai punti fissi, detti terminali, è direttamente proporzionale all'accelerazione. Tale dispositivo ha offerto nuove possibilità per il “controllo meccanico passivo” in una varietà di applicazioni ed è tutt’ora impiegato in F1 e in altre parti del settore automotive ma potenzialmente potrebbe avere molte altre applicazioni. Nel caso dei rotori non vi sono al momento applicazioni, per cui risulta molto interessante capirne le potenzialità. Pertanto l'obiettivo di questa tesi, in parte svolta all'estero presso ISVR della University of Southampton, è stato studiare le performance e la stabilità, tramite modelli matematici e simulazioni numeriche, di un sistema con diverse configurazioni di “inerter”. In particolare, nella prima parte di questa tesi, sono state sviluppate le equazioni della dinamica dei rotori e nella seconda sono stati analizzati sistemi a diversi gradi di libertà e ricavate le frequenze naturali in funzione dell'inertanza. Infine si è realizzato un banco prova per testare il fluid inerter. In questa tesi si è dimostrata la validità delle equazioni della dinamica dei rotori ricavate nella prima parte del lavoro; si è inoltre dimostrato che anche nel caso dei rotori l'inerter abbassa le frequenze naturali del sistema. Infine i risultati sperimentali del Fluid Inerter, ottenuti a diversi valori di ampiezza e frequenza, hanno dimostrato che l'oggetto costruito si comporta effettivamente come un inerter

Tuned inerter dampers with linear hysteretic damping

This paper explores the influence of linear hysteretic damping on the performance of passive tunedinerter devices. An inerter is a device that produces a force proportional to the relative acceleration across its two terminals; devices incorporating inerters have received widespread attention in the earthquake engineering community, because they offer the ability to improve the seismic response of structures. However, the majority of this research has assumed that the damping components within the tuned-inerter device exhibit viscous, rather than hysteretic, damping. This restriction imposes an essential question on how the hysteretic damping model will change the performance of the device compared to the viscous damping model. It is shown that the response of viscous and hysteretic inerter systems have significant differences in displacement amplitude due to the frequency-dependency of the damping. Therefore, a new formulation for obtaining the optimum loss factor of the hysteretic damping in the inerter system is proposed. Next, the challenges associated with accurately predicting the time-response of a hysteretically damped system are discussed. A numerical time-integration method is extended to address these challenges, using a new formulation that has the benefit of being broadly applicable to multi-degree-of-freedom hysteretic linear systems and nonstationary random signals. The results show that the earthquake responses from the hysteretic damping model can differ significantly from the ones obtained via the viscous model