Inerter based dampers have shown great promise in structural vibration control, particularly for enhancing the seismic resilience of buildings. Among various implementation strategies, their use as vibrating barriers (ViBa) stands out due to the unique advantage of providing external and non-invasive vibration mitigation. When installed adjacent to the primary structure, an inerter based vibrating barrier (IViBa) engages through soil structure interaction, enabling effective energy dissipation without interfering with the structural integrity or architectural design of the main building. This makes the IViBa especially well suited for retrofitting existing buildings and for application in densely populated urban environments. In its conventional form, the IViBa has an inerter attached to its mass, forming a configuration known as a tuned mass damper inerter (TMDI). While effective, the IViBa with a TMDI configuration still requires a substantial physical mass to achieve satisfactory performance, which can limit its practicality. To address this challenge, this study explores the use of a tuned inerter damper (TID) configuration, where the inerter replaces the conventional IViBa mass entirely. The results demonstrate that the IViBa with a TID configuration can significantly reduce the required physical mass while maintaining the vibration mitigation performance of the system. Additionally, the internal motion of the IViBa is markedly reduced, resulting in lower stroke and reduced space demand, which further improves the feasibility, durability, and ease of implementation of the device in real world applications.

Inerter-based dampers have received significant attention in the structural engineering community. Among these, the tuned viscous mass damper (TVMD) is the only variant that has been implemented in real-world buildings. The conventional TVMD model comprises an inerter connected in parallel with a dashpot and in series with a spring. However, this simplified model overlooks the influence of the physical mass of the device itself, which includes the moving components between the inerter and spring. In this paper, the device's physical mass, whether explicitly accounted for or intentionally added to enhance its performance, is referred to as an auxiliary mass. The device configuration of the TVMD with an auxiliary mass is the same as that of a novel tuned mass damper inerter (NTMDI) reported in the literature. However, optimal design formulae that minimise the HPo norms of the transfer function from ground displacement to floor displacement relative to the ground are lacking. These shortcomings are addressed in this study. Furthermore, shake table tests were conducted on a scaled single-storey steel specimen containing an NTMDI. The device features a flywheel with permanent magnets and is connected to the structural mass via leaf springs. The experimental results demonstrate that the auxiliary mass significantly improves the dynamic performance of the TVMD.

Abstract Over the past two decades, inerters have attracted significant attention in structural control. Numerous applications in engineering fields have proposed employing inerter-based control devices to mitigate structural vibrations. While theoretical studies have demonstrated performance enhancements, practical implementation and experimental validation have remained limited primarily due to cost and technical challenges. Studies conducted with the physically built inerters have showed discrepancies between theoretical model of the inerter and its actual performance because of factors such as nonlinearities and damping effects. Computational Fluid Dynamics (CFD) can provide a more accurate model of the inerter without the need for costly experimental setups. This paper presents a CFD analysis aimed at evaluating the actual performance of a fluid inerter-based control device for vibration mitigation of single degree of freedom (SDOF) structure. The accurate modeling of the inerter obtained through CFD is used to evaluate the performance of the inerter-based control device. The results reveal an important difference between vibration mitigation performance when comparing the ideal theoretical model and the CFD model.

Inerter-based-dampers have received substantial interest from the earthquake engineering community in the last two decades. These typically consist of an inerter, a linear spring and a viscous damper arranged into various possible configurations. In this paper, for the first time, experimental results are presented from shake table tests on a scaled three-storey structure with an inerter-based damper included, in order to suppress vibration amplitudes at the resonant frequencies. In particular two types of device are used to demonstrate the differences between using viscous and hysteretic damping in the inerter-based device. The two different types of experimental dampers were manufactured using eddy current dampers and gel damping material. The inerter was manufactured based on a flywheel design. The experimental results were compared with four analytical models tuned to suppress vibrations in the first resonance; namely the tuned-inerter-damper, the tuned-inerter-hysteretic-damper, the tuned-mass-damper-inerter, and the tuned-mass-hysteretic-damper-inerter. These experimental results confirm the observations made from the models that the suppression of higher resonance peaks is significantly different between the viscous and hysteretic damped inerter-based-dampers. Consequently, it is recommended that future studies exploring the performance of inerter-based seismic mitigation systems pay close attention to the damping mechanisms that are prevalent within the structure.

This paper explores the use of a novel tuned-inerto-viscous-hysteretic-damper (TIVhD) for reducing the seismic response of multi-storey building structures. The TIVhD is an inerter-based damper device consisting of a linear hysteretic damper connected in series with an inerto-viscous damper. The layout of TIVhD is similar to that of tuned-inerter-hysteretic-damper (TIhD) with an additional viscous damping element in parallel with an inerter. The design is motivated by the fact that most inerter designs cannot completely remove the parasitic damping due to friction, fluid compression, etc. Moreover, the use of linear hysteretic damping is considered to be a more realistic approach when material damping is present. In this paper, the TIVhD is installed between the ground and the first-storey and is tuned by firstly assumed the viscous damping coefficient to be zero. Then the other three parameters are optimised following the tuning procedure of the TIhD that is based on the fixed-point theory with additional fine-tuning procedure by targeting the first vibration mode of the multi-storey structure. The optimum TIVhD parameters are finally obtained using two scenarios: (1) amplifying its viscous damping coefficient and stiffness while keeping the inertance constant; (2) amplifying its inertance and stiffness while keeping the viscous damping constant. Both scenarios are aiming at the same reduction level of that given by the TIhD. Finally, the effectiveness of the TIVhD on reducing the structural response is demonstrated for both harmonic and seismic base excitation cases in the time domain. This has been made possible by a newly developed time domain response of linear hysteretic damping via the Hilbert transform and a time reversal technique.

This paper explores the influence of linear hysteretic damping on the performance of passive tuned-inerter 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 with 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 multidegree-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.

. This paper discusses optimum design approaches for a novel tuned-inerter-hysteretic-damper (TIhD) which is a passive vibration suppression device for building structures subject to earthquake base excitations. The TIhD has a linear hysteretic damping element connected in series with an inerter. This device exploits the advantage of linear hysteretic damping which can reduce the structural response amplification at frequencies above resonance, due to the frequency dependent damping. In the present study, the effectiveness of this device in reducing seismic response of building structures is assessed and the optimum tuning of the device parameters is explored. In particular, eight different earthquakes are selected for a case study. The optimum parameters of the TIhD are obtained numerically by using the Self-Adaptive Differential Evolution (SADE) algorithm. The optimisation criterion is the minimum root-mean-square (RMS) value of the top-storey displacement response of the structure. The performance of this tuning configuration is then compared to that of a classically tuned device. The also compared across a of simulated giving new insight into the of optimising inerter designs that involve hysteretic damping.

The use of viscous damping terms to simplify the damping of a vibrating system has been well established for decades. For solid materials whose energy dissipated per cycle is frequency-independent, an equivalent viscous damping has often been used. However, this may give inaccurate results, especially at higher excitation frequencies. Alternatively, a complex stiffness term can be used. In this case, a challenge arises for the time domain analysis due to the unstable poles in the resulting model. Several methods have been proposed to deal with this issue. The use of an analytic signal along with Hilbert transform and a time reversal technique is one of the first introduced methods. In this paper, we extend the method so that it can be used for solving the system equations of motion using the numerical integration algorithm solvers that are available in MATLAB. We also present the application of this extended method to simulate a multi-degree-of-freedom (MDOF) structure with supplemental passive vibration suppression systems using linear hysteretic damping in the time domain.

Many lightly damped flexible structures suffer from unwanted vibrations. Typically a tuned-mass-damper (TMD) can be used to reduce unwanted vibrations of a specific mode of vibration. The inerter is a novel passive vibration control device offering a wide range of potential applications in engineering practice. It has been analytically proven to be an effective device for controlling unwanted vibrations in structural systems. One of the most effective control strategies employing an inerter is the tuned inerter damper (TID) whose inerter element is connected in series with parallel connected spring-damper. When the inerter element is in parallel with the damper element, it is then called Parallel Viscous Damper Inerter (PVID). In this paper, we will introduce a new passive modal vibration control strategy for the PVID based on a fluid inerter combined with a linear spring connected in parallel. The fluid inerter produces inertance by the acceleration of the fluid inside a helical pipe coiled around the outside of the main fluid chamber. The fluid inerter has both inertance and damping in one device and these properties are coupled to each other. Hence, it is a particular challenge to tune both parameters to fit with optimized values resulting from a design analysis. In this paper, a new analysis will be presented for this device that demonstrates how the PVID with a fluid inerter can be modelled to achieve the targeted parameters.

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.

An inerter is a mechanical analogue to a capacitor, where the force across the device is proportional to relative, rather than absolute, acceleration. This concept can offer attractive performance in a wide variety of engineering vibration problems, because the engineer can tune the device without dramatically increasing the physical mass of the structure. Consequently, there have been many studies over the last two decades that have explored their application to bridge vibrations, seismic isolation of tall buildings, vehicle suspensions, and other engineering problems. Several configurations of inerter systems have been proposed, typically involving the inerter in a vibration absorber, or by using the inerter as part of an isolation system. However, to date there have been limited studies that have explored the combination of inerters with semi-active devices such as magnetorheological fluid dampers. Furthermore, because one manifestation of inerters involves the use of hydraulic fluid, it is possible for magnetorheological effects to be integrated into the inerter itself. The present study investigates the feasibility of this approach for practical scenarios. A quasi-static model is developed, combining an existing model of a fluid inerter with simplified models for magnetorheological fluids. The trade-off between damping performance and inerter performance is explored. The model is then used in a case study, where its potential use in a control strategy known as a parallel-layout inerter damper is investigated.