Reliability-based design of tuned mass-damper-inerter (TMDI) equipped multi-storey frame buildings under seismic excitation

The reliability based optimal design is considered of tuned mass-damper-inerter (TMDI) equipped linear building frames subject to seismic excitations modeled as stationary colored random processes. The TMDI is a recently introduced generalization of the classical linear tuned mass-damper (TMD) benefitting from the mass amplification property, the so-called inertance, of the inerter device to enhance the vibration suppression capabilities of the TMD. The frequency, damping ratio, and inertance TMDI properties are treated as design variables to minimize out-crossing rates of prespecified thresholds for building floor accelerations, inter-storey drifts, and TMDI mass displacement. Numerical data pertaining to a 10-storey frame structure equipped with a TMDI arranged in 12 different topologies are furnished indicating the enhanced performance of the TMDI over the classical TMD especially for relatively small additional attached mass

Use of inerter devices for weight reduction of tuned mass-dampers for seismic protection of multi-storey buildings: the tuned mass-damper-interter (TMDI)

This paper explores the practical benefits of the recently proposed by the authors tuned mass-damper-inerter (TMDI) visà- vis the classical tuned mass-damper (TMD) for the passive vibration control of seismically excited linearly building structures assumed to respond linearly. Special attention is focused on showcasing that the TMDI requires considerably reduced attached mass/weight to achieve the same vibration suppression level as the classical TMD by exploiting the mass amplification effect of the ideal inerter device. The latter allows for increasing the inertial property of the TMDI without a significant increase to its physical weight. To this end, novel numerical results pertaining to a seismically excited 3-storey frame building equipped with optimally designed TMDIs for various values of attached mass and inertance (i.e., constant of proportionality of the inerter resisting force in mass units) are furnished. The seismic action is modelled by a non-stationary stochastic process compatible with the elastic acceleration response spectrum of the European seismic code (Eurocode 8), while the TMDIs are tuned to minimize the mean square top floor displacement. It is shown that the TMDI achieves the same level of performance as an unconventional “large mass” TMD for seismic protection (i.e., more than 10% of attached mass of the total building mass), by incorporating attached masses similar to the ones used for controlling wind-induced vibrations via TMDs (i.e., 1%-5% of the total building mass). Moreover, numerical data from response history analyses for a suite of Eurocode 8 compatible recorded ground motions further demonstrate that optimally tuned TMDIs for top floor displacement minimization achieve considerable reductions in terms of top floor acceleration and attached mass displacement (stroke) compared to the classical TMD with the same attached mass

Control of across-wind vortex shedding induced vibrations in tall buildings using the tuned mass-damper-inerter (TMDI)

In this paper, the effectiveness of the tuned mass-damper-inerter (TMDI) vis-à-vis the classical tuned mass-damper (TMD) is assessed to suppress vortex shedding induced vibrations to tall building structures in the across-wind direction. The TMDI, previously proposed in the literature to mitigate earthquake-induced vibrations in multi-storey buildings, benefits from the mass amplification effect of the inerter (i.e., a two-terminal device developing a resisting force proportional to the relative acceleration of its terminals by the inertance constant) to achieve improved vibration suppression performance from the classical TMD for the same attached mass. Herein, a linear reduced-order structural system is developed, defined by a diagonal mass matrix and full damping and stiffness matrices, which captures faithfully the dynamic properties of a detailed finite element model corresponding to a benchmark 74-storey building with square floor plan. A TMDI is added to the structural system by elementary operations to the mass, damping, and stiffness matrices under the assumption of an ideal linear inerter. The wind action is represented by an analytical spectral density matrix modelling correlated across-wind induced forces accounting for vortex shedding and the structural analysis step is undertaken in the frequency domain for efficiency. A comprehensive parametric analysis is undertaken demonstrating that the TMDI achieves better performance in terms of peak top floor acceleration reduction with increasing inertance than a classical TMD with the same attached mass. This is also true for relatively small attached masses of practical interest to tall buildings (less than 0.5% the total buildings mass) for the case of peak top floor displacements. Further, it is shown that the TMDI reduces significantly the peak attached mass displacement, while the peak developing forces at the inerter are not excessive and can be locally accommodated by the building

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

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

Robust reliability-based design of seismically excited tuned mass-damper-inerter (TMDI) equipped MDOF structures with uncertain properties

This paper considers a reliability-based approach for the optimal design of the tuned mass-damper-inerter (TMDI) in linear building frames with uncertain structural properties subject to seismic excitations defined as stationary colored random processes with uncertain parameters. The TMDI is a recently introduced generalization of the classical linear passive tuned mass-damper (TMD) comprising an additional mass attached to the primary structure whose oscillations are to be suppressed via a linear spring and dashpot in parallel. The TMDI benefits from the mass amplification property, the so-called inertance, of an inerter device that links the additional mass to a different floor from the one it is attached to which improves the vibration suppression capabilities of the TMD. Herein, the structural seismic performance is quantified through the probability of occurrence of different failure modes, related to the floor acceleration, the inter-storey drifts, and the attached mass displacement exceeding acceptable thresholds. The overall design objective is taken as a linear combination of these probabilities whereas the TMDI linear spring constant , viscous damping constant , and inertance properties are taken as the design variables. The parametric structural and excitation uncertainty is efficiently addressed through a two-stage approach combining a Taylor series approximation and Monte Carlo simulation. Numerical data for a 10-storey shear frame structure equipped with a TMDI with different values of attached mass and arranged in 8 different topologies are furnished indicating the enhanced performance of the TMDI over the classical TMD for relatively small attached masses. The reported numerical results evidence that the performance of optimally designed TMDIs is less affected by the parametric uncertainties as the total inertia TMDI properties (attached mass and inertance) increases, indicating that the inclusion of the inerter leads to more robust passive vibration control