Tuned Mass Damper Inerter Research Articles

H2 Optimization of a New Type of Tuned Lever Inerter-like Mass Damper (TLIMD) for Attenuating Structure Vibrations

The lever or the lever-type mechanism can achieve an inertia amplification effect by appropriately calibrating its structural configuration, and it is also proven to be one of the most cost-effective solution for the inerter realization compared with other mechanical devices. Benefitting from this property, the present paper adopted a new type of tuned lever inerter-like mass damper (TLIMD) for attenuating stochastic load-induced structure dynamic responses. A set of closed-form formulae for the TLIMD optimal parameters are developed by the use of H2 norm optimization criterion, wherein the structure’s inherent damping is explicitly accounted for. It is theoretically demonstrated that the TLIMD optimal parameters are mainly dominated by three critical parameters, i.e., the damper mass ratio, the lever length ratio (known as the inertia amplification ratio) and also the host structural damping. The proposed formulae for the TLIMD optimization are validated through the seismic analysis, where two classic inerter-based dampers (i.e., the tuned mass damper inerter (TMDI) and the tuned inerter damper (TID)) optimized by the numerical technique are included in the discussion. It is found that the TLIMD has a superior advantage in reducing the structure responses and also exhibits stronger robustness for the detuning condition than the classic inerter-based dampers. Furthermore, the increase in the damper mass ratio and the lever length ratio can be beneficial for enhancing its performance.

Multi-objective optimal design of Tuned Mass Damper Inerter for base isolated structures

The BIS-TMDI is a hybrid control strategy that significantly reduces the seismic response of structures compared to conventional BIS through proper tuning, albeit with the trade-off of increased control forces exerted by the TMDI on the host building structure. However, these potentially significant forces are generally not considered in current TMDI tuning approaches. In this paper, a multi-objective optimization design method is herein developed to determine the compromise between the competing objectives of suppressing earthquake-induced vibrations in buildings and avoiding the generation of excessive control forces of TMDI. The study shows that under non-stationary excitations, the average control force of the TMDI system can be reduced by 16% compared to single optimization constraint, with a maximum reduction of up to 25%. Finally, the optimization design methods of this paper are applied to an 8-story frame as a validation case.

Closed‐form optimal solution of two‐degree‐of‐freedom system with Inerter based on equal modal damping with potential application in non‐structural elevator for seismic control

AbstractTargeting the great demand for adding non‐structural elevators to old residential buildings, this article proposes an updated configuration of tuned mass damper inerter (U‐TMDI) applied in external non‐structural elevators. An analog 2‐DOF system is established to describe the residential building controlled by an inerter elevator. Then, three closed‐form optimal solutions for designing the U‐TMDI are derived via the fixed‐point method, equal modal damping criterion, and the infinity damping assumption. Subsequently, these optimal solutions are compared and discussed involving the expressions of tuning frequency ratio and the optimal damping parameters, root locus diagram and supplemental damping ratios, transfer function, and robustness to frequency variation, respectively. Finally, a residential building example is adopted to validate the feasibility of the proposed retrofitting strategy and the closed‐form optimal design solutions. It is demonstrated that the optimal tuning frequency ratios derived by the fixed‐point method and equal modal damping criterion are different for U‐TMDI due to the influence of elevator stiffness ratio , while its degradation forms for tuned mass damper (TMD) are identical, recognizing the importance of the elevator stiffness. Moreover, the proposed retrofitting strategy of using an inerter elevator can significantly mitigate the main structure displacement by about 18%∼23% for both far‐field and near‐fault earthquakes.

Protección sísmica de estructuras civiles mediante dispositivo INERTER en la provincia de Huancayo

This research work proposes the use of a Tuned-Mass-Damper-Inerter (TMDI), which combines a new configuration of passive vibration control using an “Inerter”. This two-terminal mechanical flywheel device, based on the well-known Tuned-Mass-Damper (TMD), generates resistance forces proportional to the relative acceleration of its terminals. TMDI takes advantage of the “mass amplification effect” of Inerter to improve performance compared to TMD. For harmonically excited primary linear systems, closed-form analytical software is modeled to obtain optimal design and tuning parameters of the TMDI, using established methods. It is observed that, with proper distribution of the dampers, the TMDI system is more effective in suppressing vibrations close to the natural frequency of the uncontrolled primary system and is more resistant to the effects of detuning and misdistribution. Furthermore, the results of the modeled structures show the effectiveness of the TMDI, modeled as a classical damper, in suppressing the fundamental mode of vibration for linear MDOF structures. The incorporation of the Inerter in the proposed TMDI configuration can replace part of the vibrating mass, achieving lightweight passive vibration control solutions or improving structural performance. The solution proposed and modeled with traditional dampers behaves linearly, in line with current performance trends for minimally damaged structures protected by passive control devices. Additionally, optimized TMDI is applied for vibration suppression and displacement control, offering optimal seismic protection.

H∞ optimum design and nonlinear seismic performance assessment of tuned-mass-damper-inerter (TMDI) supported by an auxiliary structure

Tuned Mass Damper Inerter (TMDI) and its simplified form, Tuned Inerter Damper (TID), are highly effective in mitigating seismic responses in buildings, particularly when rigidly connected to the ground. However, practical constraints often limit the feasibility of this ideal setup. This study introduces a novel configuration: the AS-type TMDI, which connects the TMDI to an auxiliary structure (AS) adjacent to the main building to simulate a ground connection. To design the AS-type TMDI, this research builds upon insights from studies on TMDIs in adjacent buildings and develops an analogous 3-DOF model representing the TMDI-linked adjacent-building system. This model incorporates two buildings of different heights, allowing the TMDI to be connected at any floor level. Utilizing fixed-point theory, the study derives an analytical solution for the optimal design of TMDI systems within this novel configuration. Additionally, a method is introduced to determine the optimal stiffness and design procedure for the AS itself. The performance of the proposed AS-type TMDI is evaluated through comprehensive nonlinear seismic analysis of a benchmark nine-story steel frame structure, accounting for material and geometric nonlinearities. Results demonstrate that the AS-type TMDI performs comparably to a virtually grounded TMDI in effectively reducing the seismic responses. Furthermore, this innovative configuration outperforms both a conventional retrofitting technique, where the building is rigidly connected to the AS, and a system where a viscous damper alone connects the main building to the AS. This highlights the AS-type TMDI's potential to significantly improve the building’s seismic performance.

Assessing Vibration Control Performance of Optimized Tuned Mass Damper Inerter (TMDI) Configurations

Assessing Vibration Control Performance of Optimized Tuned Mass Damper Inerter (TMDI) Configurations

Optimal design of inerter-based absorbers with amplified inertance: from the improved tuned liquid column damper inerter (ITLCDI) to the improved tuned mass damper inerter (ITMDI) and improved tuned inerter damper (ITID)

Optimal design of inerter-based absorbers with amplified inertance: from the improved tuned liquid column damper inerter (ITLCDI) to the improved tuned mass damper inerter (ITMDI) and improved tuned inerter damper (ITID)

Bidirectional pendulum-type tuned mass damper inerter for synchronously controlling the alongwind and crosswind responses of super-tall buildings

In the context of slender super-tall buildings, which have a high height-to-width ratio and low damping, significant bidirectional vibrations can occur under strong winds. Traditional TMDI device is mainly focused on controlling unidirectional wind-induced vibration responses. To address this issue, the present study introduces a bidirectional pendulum-type tuned mass damper inerter (BPTMDI) designed to synchronously mitigate alongwind and crosswind responses. The study derives nonlinear equations of motion for a multiple degrees of freedom (MDOF) structure integrated with the BPTMDI, using the Euler-Lagrange method. These equations capture the three-dimensional motion characteristics of the BPTMDI. Additionally, linear equations of motion are derived for a simplified planar model. The time-domain responses of the MDOF structure coupled with the BPTMDI are calculated by dividing the system into linear and nonlinear subsystems and applying the state space method and Runge-Kutta method, respectively. The effectiveness of the BPTMDI is evaluated through time history response analysis of a 400 m tall case-study building subjected to bidirectional wind loadings. Results show that the BPTMDI can significantly reduce both alongwind and crosswind responses, with reductions of at least 29.75 % in displacement and 48.64 % in acceleration, regardless of wind direction. Furthermore, the BPTMDI demonstrates improved control efficacy compared to BPTMD systems. Lastly, the simplified planar model of the BPTMDI shows basic similarity to the nonlinear planar-spherical model.

Optimal tuning and assessment of non-grounded regenerative tuned mass damper inerter (RE-TMDI) configurations for concurrent motion control and energy harvesting

Optimal tuning and assessment of non-grounded regenerative tuned mass damper inerter (RE-TMDI) configurations for concurrent motion control and energy harvesting

Robust damping improvement against the vortex-induced vibration in flexible bridges using multiple tuned mass damper inerters

The tuned mass damper inerter (TMDI) is considered as one of countermeasures to mitigate the very-low-frequency vertical bending vortex-induced vibration (VIV) in flexible bridges. However, the control robustness of the TMDI against the system uncertainty is a serious concern due to the limited inerter span capacity. In this paper, the multiple tuned mass damper inerter (MTMDI) is used instead of identical TMDIs to provide a robust equivalent damping ratio against the uncertain VIV within the entire lock-in wind speed range. A design framework of the MTMDI considering the inerter span length is proposed based on a universal VIV model suitable for the fully closed, centrally slotted, and semi-closed box decks. In the framework, the fluctuation of VIV characteristics with the wind speed, the probability of occurrence of the VIV, and the uncertainties in VIV characteristics and deck dynamics are considered, simultaneously. Two objection functions are defined to focus on the maximizing the equivalent damper ratio and reducing the VIV mitigation failure, respectively. Finally, numerical analysis of a flexible bridge-MTMDI system subjected to the VIV is performed. The results show that the wind speed probability distribution plays a role of weighting coefficient in the MTMDI optimization. The choice of the objective function depends on the mass ratio of the MTMDI and the level of the system uncertainty. The well-optimized MTMDI achieved a more robust control result than the TMDI within the entire lock-in wind speed range.

Analytical design of non-grounded tuned mass-damper-inerter for base-excited structures

This research contributes new analytical formulae for H∞ optimal tuning of non-grounded tuned mass-damper-inerter (TMDI) for minimizing free-end displacement of base-excited cantilevered structures. The derivation relies on the fixed-point theory, making use of single-mode modelling of the cantilevered structure while accommodating arbitrary TMDI placement along the structural height. Optimal TMDI tuning parameters are derived for given dominant mode shape of structure and TMDI inertial properties (i.e., secondary mass and inertance) under two different types of harmonic excitations with frequency-independent displacement and acceleration amplitudes. The applicability of the derived TMDI tuning formulae for response mitigation of lightly damped cantilevered structures under stationary broadband support excitation is established through comparisons with numerically optimal TMDI properties for a wide range of TMDI inertial properties. Moreover, the analytical TMDI tuning formulae derived in this study achieve enhanced structural performance for base-excited structures compared to those from the literature, derived under various modelling assumptions and optimality criteria. Lastly, the potential of the proposed TMDI tuning for structural response mitigation is numerically evaluated by examining displacement, acceleration, and energy dissipation response history data of an experimentally identified reinforced concrete bridge pier model subjected to 100 earthquake ground motion (GM) records. Overall, reported results demonstrate that the derived analytical formulae can significantly extend the practical application of TMDI as a bona fide dynamic vibration absorber for base-excited structures by circumventing the need for computationally demanding numerical TMDI tuning optimization.

Inerter-based tuned mass dampers for response control of multi-degree-of-freedom structures subjected to wind and earthquake excitations

The present work explores the utilization of the tuned mass damper-inerter (TMDI) in controlling the structural response subjected to wind and earthquake excitations. An example of a 25-storey reinforced concrete building is taken up. The equations of motion of the structure-TMDI combined system are established by assuming the building behaves as a shear-building with multiple degrees of freedom. These equations are solved using Newmark’s time integration method. The objective functions are the wind- and earthquake-induced structural response quantities, such as the maximum inter-storey drift ratio (MIDR) and peak floor acceleration (PFA). The prime contribution of this study is the inclusion of statistical measures such as the mean, 85th, and 95th percentiles for these quantities. A genetic algorithm-based multi-objective optimization is performed to estimate the optimum TMDI parameters. Based on the outcomes of this study, it can be recommended that the TMDI be optimized to perform well under the 95th percentile for MIDR and PFA in effectively reducing the peak structural responses. Frequency domain analysis results demonstrate TMDI’s multiple-mode controlling capability. The energy comparison plots of the uncontrolled and controlled structures prove the effectiveness of the optimum TMDI in providing enough damping and ensuring structural stability.

Wave-induced vibration control of Floating production storage and offloading systems by tuned mass damper inerter

Wave-induced vibration control of Floating production storage and offloading systems by tuned mass damper inerter

Pendulum-type tuned tandem mass dampers-inerters for crosswind response control of super-tall buildings

In the present study, the pendulum-type tuned tandem mass dampers-inerters (PTTMDI) is proposed to control the crosswind-induced dynamic responses in super-tall buildings. This innovative configuration allows for the placement of both terminals of inerters at the same floor, thereby overcoming the challenge issue of installation associated with the tuned tandem mass dampers-inerters (TTMDI). The equations of motion for a PTTMDI equipped multiple-degree-of-freedom (MDOF) structure is derived using the Euler-Lagrange method. To optimize the primary tuning parameters of the PTTMDI for a 400 m super-tall building, the pattern search algorithm is employed. The control effectiveness and robustness of the PTTMDI device are studied and compared with those of the pendulum-type tuned mass damper (PTMD), pendulum-type tuned tandem mass dampers (PTTMD), and pendulum-type tuned mass damper-inerter (PTMDI). Likewise, the design framework for the PTTMDI equipped super-tall building is established. The results indicate that the PTTMDI has superior acceleration control performance and the stronger robustness compared to the PTMD, PTTMD, and PTMDI. Furthermore, the PTTMDI can significantly reduce the necessary damping coefficients with respect to the PTMDI with the maximum reduction rate reaching about 70%, making it easier to implement in engineering practice.

On the optimization of Tuned Mass Damper Inerter (TMDI) systems for buildings subjected to real ground motions using slime mould algorithm

This paper proposes a novel optimization framework for the optimal design of Tuned Mass Damper Inerter (TMDI) devices to mitigate the excess vibration of multi degree of freedom (MDOF) buildings under earthquake ground motions. Minimizing the H∞- norm of the top floor displacement transfer functions is considered as the objective function for the optimization process. A Tuned Mass Damper Inerter (TMDI) is employed in which a TMD is placed at the top floor of a building connected via inerter. The top floor displacement of the building under eighteen (18) real earthquake ground motions classified in terms of low, intermediate and high frequency contents, is minimized using three optimization algorithms, particle swarm optimization (PSO), slime mould algorithm (SMA) and Harris Hawks optimization (HHO). The effectiveness of different algorithms is assessed using the RMS (root mean square) based values and the reduction ratio. The optimised parameters of the TMDI (mass ratio, frequency ratio, damping ratio and inertance ratio) obtained using the slime mould algorithm (SMA) are found to be better than the other optimization algorithms for the numerical example carried out in this paper. The results show that, the optimised TMDI has significant effect on the suppression of top floor displacement, acceleration with a lightweight TMD. The optimal parameters of TMDI shows a remarkable potential in suppressing maximum displacement reduction ratios of 0.83, 0.85 and 0.86 in response to low, intermediate and high frequency content earthquake ground motion, respectively. Based on the numerical results, the passive TMDI unveils a promising vibration calming system for damped elastic structure.

Optimum tuned mass damper inerter under near-fault pulse-like ground motions of buildings including soil-structure interaction

This study investigates the effectiveness of the tuned mass damper inerter (TMDI) in mitigating building response, considering the soil structure interaction (SSI). Three types of models are examined: single degree of freedom (SDOF), low-rise multi-degree of freedom (MDOF), and high-rise MDOF. Additionally, the natural period of the SDOF model is varied to explore the TMDI's efficacy across different ranges. Frequency and time domain analysis are conducted under pulse-like ground motions. The H2 and genetic algorithm (GA) are used to optimize the parameters of the TMDI. In this optimization method the transfer function for displacement response is minimized. In time domain analysis we used Newmark's integration method to solve the equation of motion for all the cases considered. It is found that the optimized TMDI proves highly effective in mitigating the displacement response of the buildings, accounting for SSI. Notably, its efficiency is more pronounced when pulse period aligns closely with the buildings' natural period. In addition, a notable pattern emerges, wherein the TMDI excels in mitigating response for buildings experiencing large motion, thereby enhancing safety under severe conditions. These findings offer valuable insights into the application and optimization of the TMDI to enhance seismic performance in various buildings, while considering complex interaction with the soil.

The Role of a Simple Inerter in Seismic Base Isolation

The present study investigates the role of a simple inerter in supplemental devices for possible implementation in the mature seismic base isolation technique. Firstly, the response of the base-isolated structure with an optimally tuned mass damper inerter (TMDI) is investigated to see the tuning effects. The time required to tune the TMDI was found to be significantly longer than the duration of a strong-motion earthquake. There was still a reduction in the response of the isolated structure, which is primarily due to the added damping and stiffness (ADAS) of TMDI and not because of the tuning effects. Hence, it is proposed that the corresponding ADAS of the TMDI be directly added to the isolation device. Secondly, the response of the base-isolated structures to the fluid inerter damper (FID) is studied. It was observed that the inerter of the FID does not influence the displacement variance of an isolated structure under broadband earthquake excitation. It implies that the response of the isolated structure to FID is primarily controlled by its counterpart fluid damper (FD). The performance of optimal TMDI, ADAS, FID, and FD to mitigate the seismic response of the flexible multi-story base-isolated structure under real earthquake excitations is also investigated. In terms of suppressing the displacement and acceleration responses of the isolated structure, it has been found that TMDI and ADAS perform similarly. Comparing the response of the isolated structure with FID and FD demonstrated that the inerter in the FID has detrimental effects on the isolated structures, in which the top floor’s acceleration and base shear are substantially increased.

The impact of the frequency content of far-field earthquakes on the optimum parameters and performance of tuned mass damper inerter

Tuned mass damper inerter is a passive control device that is proven to be effective in mitigating structural responses under earthquake excitations, however, its efficiency highly depends on its design parameters. This paper aims to investigate how the optimum parameters of TMDI change with the frequency content of far-field earthquakes to minimize the need for repeatedly optimizing these parameters for varying far-field earthquakes and structural characteristics. To achieve this objective, the ratio of the earthquake's frequency to the structure's frequency is defined as an index to simultaneously represent the structure and the earthquake. Case studies of 5, 10, 15, and 20-story building structures are analyzed under twenty-three far-field earthquakes which are categorized into three main groups based on their frequency (PGA/PGV) including “Low”, “Intermediate”, and “High”. Particle Swarm Optimization (PSO) is employed to obtain the optimum parameters of TMDI including the damping and the frequency ratio to minimize two distinct objective functions: (1) the peak displacement and (2) the peak acceleration of the top story in a time domain analysis. To validate the applicability of the proposed method in determining the optimal parameters of TMDI regardless of the earthquake and structure frequency, a 10-story benchmark building is employed. Moreover, this study demonstrates the effectiveness of TMDI in minimizing the objective functions concerning the frequency content of the earthquake. It also illustrates the trend of the PSO optimization process. The results show that the index provides a discernible pattern for the variation of the optimum parameters of TMDI. Furthermore, it is demonstrated that the difference in the structural response between tuning the TMDI with the PSO algorithm and the suggested method is less than 3 % when the index is greater than 1. As the ratio of earthquake frequency to the frequency of structure increases, the objective functions will correspondingly increase. The results also indicate that, an increment in the inertance ratio leads to an increase in the value of optimum parameters of TMDI. Furthermore, among all structures analyzed, those subjected to intermediate frequency earthquakes exhibit the most significant reduction in both objective functions.

Application of a new two dimensional nonlinear tuned mass damper in bi-directional vibration mitigation of wind turbine blades

A new two-dimensional non-linear tuned mass damper inerter (2d-NTMDI) is proposed in the present paper with the aim of suppressing bi-directional vibrations. The proposed 2d-NTMDI includes a single mass and two sets of springs, dashpots and inerters configured in two axes. With respect to the displacements in two axes, the resulting restoring forces have nonlinear characteristics. While the proposed novel 2d-NTMDI has the capability of mitigating bi-directional vibrations simultaneously, the nonlinearity of the system makes the optimization a challenging task. The particle swarm optimization (PSO) algorithm is adopted to obtain the optimum design parameters of the 2d-NTMDI. To evaluate the effectiveness, the proposed 2d-NTMDI is deployed in a 5MW-wind turbine blade suffering from bi-directional vibrations in the edgewise and flapwise directions. Therefore, an analytic model of a wind turbine blade with a 2d-NTMDI is derived. The aerodynamic loading is computed using blade element momentum theory. The effectiveness of the 2d-NTMDI is tested under different loading conditions. Also, the fatigue damage of the wind turbine blades is calculated according to the rain-flow cycle counting approach and Miner’s law. It is concluded that the optimized design 2d-NTMDI can prolong the blade fatigue life by 24.6%.

A Review of the Tuned Mass Damper Inerter (TMDI) in Energy Harvesting and Vibration Control: Designs, Analysis and Applications

A Review of the Tuned Mass Damper Inerter (TMDI) in Energy Harvesting and Vibration Control: Designs, Analysis and Applications