Tuned Mass Damper Inerter Research Articles

Hybrid seismic isolation of vertical pressure vessels in CO2 capture plant

This study investigates the hybrid seismic isolation of vertical pressure vessels in the CO2 capture plant using high-damping viscoelastic isolators and a grounded tuned mass damper inerter (TMDI), to improve the resilience of the CO2 capture plant against earthquakes. The vessel with the hybrid isolation is modeled as a cantilever beam connected in series with a linear oscillator and a TMDI. A parameter design framework of the hybrid isolation is developed based on a simplified two-degree-of-freedom model and the Pareto front. Numerical simulations of a vertical pressure vessel with the conventional base isolation, the high-damping base isolation, and the hybrid base isolation subjected to historical earthquakes are performed. The results show that the hybrid base isolation has the best control result in reducing the displacement, stress, and isolator deformation among the three base isolations. The role of the TMDI in the hybrid base isolation is equivalent to further increasing the damping of the high-damping base isolation. The larger of the inertance in the TMDI, the better the control result of the hybrid base isolation. The hydrodynamics induced by the solvent has little influence on seismic responses of the vessel, but greatly weakens the control result of base isolations when the solvent height is high. The hybrid base isolation is more recommended for the vessel considering the hydrodynamics than the conventional base isolation and high-damping base isolation.

Optimization and performance assessment of tuned mass damper inerter systems for control of buildings subjected to pulse-like ground motions

Optimal tuned mass damper inerter (TMDI) systems in controlling displacement demands on structures affected by pulse-like near fault ground motions is presented. Simplified mathematical models of three buildings and many recorded near-fault ground motions, all containing a dominant velocity pulse, are used to make this investigation valid for a wide range of structural vibration periods and ground motion frequency content. For each of these ground motions, optimal parameters of TMDIs are estimated by minimizing structural displacement demand. Time history analysis is used for structural response simulation and Genetic Algorithm is used for minimizing the structural displacement demands. The performance or lack of it of the TMDIs are investigated and explained in relation to important properties of ground motions such as the frequency and oscillatory nature of the dominant pulse contained in the ground motion. The results indicate that properly optimized TMDIs can effectively control structural response under certain circumstances. When the structure resonates with the ground motion pulse, the less impulsive the ground motion, the more effective is the control scheme. An interesting finding is that TMDIs can be very effective in controlling response of structures which are not resonating with the pulse but nevertheless experience high demands due to other frequency components of near-fault ground motions. It is found that TMDI solutions obtained by minimizing the H2 norm of the elastic transfer function are not optimal when the fundamental period of vibration of the structure is lower than the period of the dominant pulse carried by the ground motion. Such solutions also result in unnecessarily high damping in the TMDI dashpot, without any benefit in controlling structural response.

Inerter-Connected Double Tuned Mass Damper for Passive Control of Buildings under Seismic Excitation

In current work the Inerter-Connected Double Tuned Mass Damper (ICDTMD) is employed for structural control of a well-recognized benchmark 10-story linear shear building. The ICDTMD is introduced to overcome the practical limitations of the roof-top tuned mass damper inerter (TMDI), in which the second terminal of the inerter is connected to the lower floors of the building. To this end, a modification of the double tuned mass damper (DTMD) with a linking inerter is proposed to not only exploit the promising features of inerter but also surmount the architectural interference of the effective TMDI configurations. The TMDs free parameters are optimized using particle swarm optimization algorithm (PSO) for two different single objective functions, i.e., the H∞ norms of roof displacement and story drifts were minimized for robust tuning. To evaluate the robustness of the optimal damper, its performance was compared to a traditional roof-top single tuned mass damper (STMD) and DTMD in both frequency and time domains (time history analysis for four far- and near-field records) for different preselected mass and inertance ratios. The performance indices in the time domain were selected as the maximum story drifts, story acceleration and shear. Results show that the rooftop ICDTMD, unlike the rooftop TMDI, provides a similar level of response reduction as STMD, while being more reliable due to redundancy. In addition, the ICDTMD exhibits a similar level of response reduction as the DTMD with significantly smaller optimized spring stiffness.

Clutching inerters enhanced tuned mass dampers for structural response mitigation under impulsive and seismic excitations

Inerters, a type of two-terminal inertial elements, have significantly enhanced the performance of conventional control devices. The clutching inerters are especially appealing since they take energy away from the structural system without transferring back. In this study, a clutching inerter enhanced tuned mass damper (TMDCI) is proposed. First, the formation of the TMDCI is described based on a tuned mass damper inerter and two clutching flywheels. Then, the equations of motion are derived for the TMDCI on a single-degree-of-freedom (SDOF) primary structure. Subsequently, the modal properties of the TMDCI system are revealed by examining the steady-state responses under harmonic ground excitations. Afterward, performance analyses are conducted for the TMDCI on SDOF and three-DOF steel structures when subjected to initial velocities. The frequency robustness and parametric sensitivity of the TMDCI are evaluated on the SDOF structure, whereas practical concerns regarding the hosting location and stiffness demand of the TMDCI are addressed on the three-DOF structure. Finally, the seismic performance of the TMDCI is investigated on the three-DOF structure under a suite of earthquakes. The results show that the TMDCI exhibits a large damping effect which can reduce responses in both the structure and device and maintain strong robustness against frequency uncertainties. This study demonstrates the great potential of TMDCIs as an effective and affordable control strategy for the seismic protection of structures.

Filter-based inerter location dependence analysis approach of Tuned mass damper inerter (TMDI) and optimal design

Tuned Mass Damper Inerter (TMDI) is a novel type of dynamic vibration absorber for achieving lightweight design while maintaining excellent control performance. Compared to traditional Tuned Mass Damper (TMD), the complex dependence characteristics of inerter bring difficulties to evaluate the control performance and design the inerter. In order to address this problem, this paper investigates the vibration control of TMDI subjected to wind and seismic loads. The closed-form solutions of the control performance of TMDI are obtained via a filter approach. By using the filter approach, the computation cost is largely reduced in calculating structural responses and control performance. Subsequently, the empirical formulas for determining optimal design parameters (frequency ratio νopt and damping ratio ζdopt) based on mass ratio μ, inertance ratio β and inerter location parameter φ is proposed. By comparing the optimal control performance of TMDI with TMD, the inerter dependence analysis is conducted to investigate the enhancement effect. An index β·(1–φ)2/μ is proposed as a criterion, where β·(1–φ)2/μ ≥ 1 indicates that the control performance of TMDI is enhanced by inerter. In addition, TMDI results in similar performance to TMD with an equivalent mass ratio μe = μ + β·(1–φ)2. Based on the investigation of an actual high-rise chimney, the proposed formulations and criterion are validated. The wind- and seismic-induced responses are reduced up to 60% and 55% respectively. The proposed method provides guidance for determining the optimal parameters of TMDIs.

Tuned-mass-damper-inerter optimal design and performance assessment for multi-storey hysteretic buildings under seismic excitation

Inerter-based vibration absorbers (IVAs), such as the tuned-mass-damper-inerter (TMDI), have become popular in recent years for the earthquake protection of building structures. Previous studies using linear structural models have shown that IVAs can achieve enhanced vibration suppression, but at the expense of increased control forces exerted from the IVA to the host building structure. The authors recently developed a bi-objective IVA design framework for linearly behaving buildings to balance between structural performance (drift/acceleration suppression) and IVA forces. This paper extends the framework to multi-storey hysteretic/yielding structures under seismic excitation. Though the proposed design framework can accommodate any type of IVA, the focus is herein on TMDI applications, with tuned-mass-damper (TMD) and tuned-inerter-damper (TID) treated as special cases of the TMDI. Earthquake hazard is modeled through representative, design-level acceleration time-histories and response of the IVA-equipped structure is evaluated through nonlinear response-history analysis. A high-fidelity finite element model (FEM) is established to accurately describe hysteretic structural behavior. To reduce the computational burden, a reduced order model (ROM) is based on the original FEM, using the framework proposed recently by the first and second authors. The ROM maintains the accuracy of the original FEM while enabling for a computationally efficient solution to the optimization problem. As an illustrative example, the bi-objective design for different IVA placements along the height of a non-linear benchmark 9-storey steel frame structure is examined. The accuracy of the ROM-based design is evaluated by comparing performance to the FEM-based response predictions across the entire Pareto front resulting from the bi-objective optimization. Then, the designs and associated performance predicted by using a linear or a nonlinear structural model are compared to evaluate how the explicit consideration of nonlinearities, as well as the degree of nonlinear behavior, impact the IVA design and efficiency.

Use of Kane’s Method for Multi-Body Dynamic Modelling and Control of Spar-Type Floating Offshore Wind Turbines

This paper demonstrates the use of Kane’s method to derive equations of motion for a spar-type floating offshore wind turbine taking into account the flexibility of the members. The recently emerged Kane’s method reduces the effort required to derive equations of motion for complex multi-body systems, making them simpler to model and more readily solved by computers. Further, the installation procedure of external vibration control devices on the wind turbine using Kane’s method is described, and the ease of using this method has been demonstrated. A tuned mass damper inerter (TMDI) is installed in the tower for illustration. The excellent vibration mitigation properties of the TMDI are also presented in this paper.

Seismic response control of adjacent buildings using optimal backward-shared tuned mass damper inerter and optimal backward-shared tuned inerter damper

Seismic response control of adjacent buildings using optimal backward-shared tuned mass damper inerter and optimal backward-shared tuned inerter damper

Optimal design and performance evaluation of tuned mass damper inerter in building structures

This paper concerns the numerical performance evaluation of multi-degree-of-freedom systems equipped with Tuned Mass Dampers-Inerter (TMDIs); a passive control device used for the mitigation of mechanical vibrations induced by dynamic loads. The inerter device is commonly used to increase the apparent mass of classics tuned mass dampers (TMDs), improving its seismic performance. To evaluate the TMDI action, three case studies are employed, determined from three real buildings of Medellin city from low, medium to high rise (30 meters, 97 meters, and 144 meters, respectively). Optimum design parameters are found using a metaheuristic optimization based on the differential evolution method, first, for the minimization of the horizontal peak displacements, and then, for the minimization of the root mean square (RMS) response of displacements. Besides, the case studies are assessed using eight seismic accelerations records representative of the literature. Finally, the seismic performance is evaluated on each case study considering different levels of inertance induced by the inerter device: 5%, 20%, and 50% with respect to the total mass of the building, for which it is observed a better dynamic behavior when TMDIs with lower values of inertance are implemented.

Optimum Double Mass Tuned Damper Inerter for Control of Structure Subjected to ground motions

Tuned mass damper inerter (TMDI) is commonly reported to be a lightweight tunable device that can significantly reduce buildings' seismic response. However, the backward action produced by the inerter and returned to the building in conventional TMDIs may either reduce the device performance or limit the inerter potential. This study proposes and investigates a novel control scheme using large physical mass ratios generated by lightweight inerters. Hence, a double mass tuned damper inerter (DMTDI) is formulated. The proposed control scheme consists of two TMDs placed at the roof of the building and connected via an inerter. Thus, the inerter backward action is transmitted to the secondary mass instead of the building. Both TMDI and DMTDI parameters are optimized using a genetic algorithm (GA). The top floor displacement transfer function's H2- norm is considered as the objective function for minimization. The optimally tuned devices are then tested under one hundred (100) near and far-field ground motions. The results obtained show a significant response improvement in peak displacement, acceleration, and base shear. The structure energy is also investigated; the lowest energy response in the studied structure is observed while using the proposed DMTDI scheme.

Symmetric and asymmetric periodic motions of a nonlinear oscillator with a tuned mass damper inerter

Symmetric and asymmetric periodic motions of a nonlinear oscillator with a tuned mass damper inerter

Experimental seismic performance assessment and numerical modelling of nonlinear inerter vibration absorber (IVA)‐equipped base isolated structures tested on shaking table

AbstractIn recent years, inerter vibration absorbers (IVAs), such as the tuned mass damper inerter (TMDI), attracted much attention in the literature for reducing seismic displacement demands of base isolated structures (BISs). Several theoretical studies reported reduced BIS seismic demands with increasing inertance endowed by a grounded inerter element, but adopted mostly idealized linear dynamical models. Herein, the potential of TMDI‐configured IVAs for seismic response reduction of BISs modelled as single‐mass structures is assessed under the combined effects of nonlinear inerter and structural behavior. To this aim, experimental data from a shaking table testing campaign are considered utilizing a custom‐built flywheel rack‐and‐pinion grounded inerter prototype with variable inertance, along with high damping rubber bearings in the isolation layer and in the BIS‐to‐absorber link. White noise excitation and an ensemble of six ground motions (GMs) with different frequency content are used in the tests for which bearings exhibit softening nonlinear behavior. Experimental results demonstrate improvement of BIS nonlinear seismic response in terms of displacement and base shear with increasing inertance for nonlinear and nonoptimally tuned IVAs. It is found though that the considered IVAs may be detrimental to BIS acceleration response depending on the GMs time‐varying frequency content signatures as captured by the continuous wavelet transform spectrogram. Finally, it is concluded that representing the inerter device by a simplified linear dissipative model as opposed to a nonlinear model with friction and gear backlash suffices to trace the BIS response with acceptable accuracy and, thus, can be used for optimal seismic TMDI design.

Optimal design of the ideal grounded tuned mass damper inerter for comfort performances improvement in footbridges with practical implementation considerations

Optimal design of the ideal grounded tuned mass damper inerter for comfort performances improvement in footbridges with practical implementation considerations

Enhanced motion control performance of the tuned mass damper inerter through primary structure shaping

The tuned mass-damper-inerter (TMDI) is a linear passive dynamic vibration absorber widely considered in the literature to mitigate the motion of dynamically excited primary structures. Previous studies focused on optimal TMDI tuning approaches and connectivity arrangements to improve motion control efficiency for some given primary structure. This paper investigates the influence of the elastic and mass properties of the primary structure to the TMDI motion control performance. This is pursued through an innovative parametric study involving a wide range of tapered beam-like cantilevered primary structures with different continuously varying flexural rigidity and mass distributions equipped with TMDIs optimally tuned for resonant harmonic and for white noise excitations. Optimal TMDI tuning and performance assessment are expedited through a novel simplified two-degree-of-freedom dynamic model which accounts for the properties of the primary structure. It is found that reduced free-end displacement and TMDI stroke are achieved for primary structures in which the ratio of flexural rigidity over mass decreases faster with height resulting in vibration modal shapes with higher convexity. The latter is quantified though the average modal curvature shown to be well-correlated with TMDI motion control improvement. It is concluded that judicial shaping of the primary structure extends the applicability of the TMDI to structures where connecting the inerter away from the free-end is practically challenging while contains the magnitude of the inerter and damping forces exerted to the primary structure. Therefore, this study paves the way towards combining optimal TMDI tuning with primary structure design for improved performance to dynamic loads.

Simultaneous vibration reduction and energy harvesting of a nonlinear oscillator using a nonlinear electromagnetic vibration absorber-inerter

Recently, considerable attention has been given to electromagnetic resonant shunt tuned mass damper-inerters (ERS-TMDI) for simultaneous vibration mitigation and energy harvesting. The application of this design is already well-established for linear structures, however, it is not extensively explored for nonlinear structures. This work, for the first time, aims to achieve both vibration mitigation and energy harvesting for nonlinear oscillating structures using a single device. For this, a novel nonlinear electromagnetic resonant shunt tuned mass damper-inerter (NERS-TMDI) is proposed with two different configurations. The proposed NERS-TMDI is coupled to a nonlinear oscillator via linear and nonlinear springs. For the first configuration, the electromagnetic and the inerter devices are grounded on one side and connected to the nonlinear vibration absorber on the other side. In the second configuration, the electromagnetic device is placed between the nonlinear vibration absorber and the primary structure. The nonlinear governing equations of motion are solved analytically using the method of harmonic balance in conjunction with the fixed arc-length continuation method. The analytical approach is validated using numerical simulations. A detailed parametric analysis for both configurations is conducted to identify the key design parameters that render the best performance of the NERS-TMDI. The results show that the proposed NERS-TMDI configurations perform better than the existing approaches, including the nonlinear tuned mass damper (NTMD), and the ERS-TMDI, in terms of vibration control. The results also show that the first configuration of NERS-TMDI always performs better for simultaneous vibration mitigation and energy harvesting than the second configuration of NERS-TMDI. This implies that grounding the electromagnetic transducer extends the range of effectiveness of the NERS-TMDI. Further, a sensitivity analysis on the optimal Configuration-1 showed that the NERS-TMDI is robust to variations in nonlinear stiffness, but its performance degrades for variations in inertance, resistance, inductance, and capacitance. Additionally, a parametric study demonstrates that higher values of nonlinear stiffness, inertance, and resistance, and lower values of inductance and capacitance render an optimal design of the Configuration-1 of the NERS-TMDI for energy harvesting. The findings are very promising and open a horizon of future opportunities to optimize the design of the NERS-TMDI for superior performance.

A shape memory alloy-tuned mass damper inerter system for passive control of linked-SDOF structural systems under seismic excitation

This work introduces a passive control device, shape memory alloy tuned mass damper inerter (SMA-TMDI), for the control of linked-single degree of freedom (SDOF) systems subjected to base excitation. The adjacent SDOF systems are connected through a device called inerter with force proportional to the relative acceleration of the individual SDOF oscillators of the linked-SDOF systems. The SMA element of SMA-TMDI dissipates the energy of primary oscillator through the hysteretic phase transformation, while, the mass-amplification effect of the inerter is utilized to reduce displacement of the secondary oscillator of the linked-SDOF systems. The mean square displacement responses of both the oscillators of the linked-SDOF systems subjected to white noise base excitation are derived based on stochastic equivalent linear parameters of the SMA spring through an iterative process. Parametric studies under white noise excitation are conducted and based on the results obtained, a multi-objective optimization is performed considering displacement variances of both the SDOF oscillators as the objective function. Under white noise excitation, the optimal performances of SMA-TMDI and TMDI systems are analyzed in terms of displacement mean square responses and the root mean square control forces transferred to the linked-SDOF systems are also examined. Further, the performance comparison of the SMA-TMDI and TMDI passive control devices are carried out under non-stationary Kanai-Tajimi excitation based on an Ito-Taylor formulation of the mean square stochastic differential equations. Based on the results obtained for both white noise and ground motion base excitation cases, it can be observed that the SMA-TMDI system performs better in comparison to the TMDI system with significantly lesser requirement on total damper mass and inertance.

Assessment of the tuned mass damper inerter for seismic response control of base‐isolated structures

Assessment of the tuned mass damper inerter for seismic response control of base‐isolated structures

Top-Story Softening for Enhanced Mitigation of Vortex Shedding-Induced Vibrations in Wind-Excited Tuned Mass Damper Inerter-Equipped Tall Buildings

An innovative structural modification, top-story softening, is herein proposed in conjunction with an optimally tuned top-floor tuned mass damper inerter (TMDI) for improved serviceability performance in typical core-frame slender buildings with rectangular floor plan susceptible to wind-induced vortex shedding (VS) effects causing occupant discomfort. This is supported through formulating a novel optimal TMDI tuning problem in which TMDI inertial properties, i.e., attached mass and inertance, as well as the lateral top-story stiffness are design parameters aiming to minimize peak acceleration of the highest occupied floor. The optimal TMDI tuning problem is numerically solved for a wide range of design parameters for a 34-story composite core-frame building subject to stochastic spatially-correlated wind-force field accounting for VS effects. A low-order dynamical model capturing faithfully modal properties of the case-study building is developed to facilitate computational work and parametric investigation. It is found that top-story softening reduces attached TMDI mass/weight requirements and inerter force for fixed performance and inertance. It further reduces TMDI stroke and achieves increased robustness to TMDI stiffness and damping properties as well as to the assumed inherent structural damping. It is concluded that by leveraging inertance and top-story stiffness, the proposed solution can efficiently control VS-induced floor acceleration with small additional gravitational (added weight) and horizontal (inerter and damping) forces.

Input energy reduction principle of structures with generic tuned mass damper inerter

The incorporation of the inerter with tuned mass damper yields the inerter-based tuned mass damper that has been verified as effective lightweight or performance-enhanced control devices. This study theoretically proved an intrinsic effect, namely, the input energy reduction, that the inerter reduces the input energy transmitted into the controlled structures from ground motion. A generic tuned mass damper inerter (GTMDI) including two separating inerters (the total inertance keeps constant) is analyzed to facilitate a universal analysis of typical inerter-based tuned mass dampers. Closed-form displacement and power equations are derived for the GTMDI to reveal and clarify the working mechanisms, especially the functionality of inerters. Correspondingly, an energy-based design framework is established for the design of a new GTMDI and the retrofitting of an existing tuned mass, in which the inertances distributed on the two separating inerters are optimized to make GTMDI outperform the conventional TMDI. Finally, a series of examples verified the discovered effect and derived power equation of GTMDI. In this study, two derived equations confirm that the GTMDI possesses dual benefits, referring to the input energy reduction and the enhanced dissipation power effects. The required physical mass of the GTMDI is relieved due to the reduced input energy, which essentially lays the foundation for lightweight control. The developed energy-based design framework is suitable for utilizing the dual benefits of GTMDI with a clear physical basis, where the introduced two separating inerters are designed with optimized inertances to guarantee the displacement control demand with a minimized total energy cost.

Study on wind-induced vibration control of linked high-rise buildings by using TMDI

Due to the aerodynamic interference of two closely-spaced linked high-rise buildings, large out-of-phase vibrations of two buildings may be induced at across-wind direction. Tuned mass-damper-inerter (TMDI) is employed to mitigate wind-induced responses of the linked buildings. The linked buildings with TMDI takes advantage of the large relative motion between the two terminals of the inerter to reduce wind-induced responses of the individual building. Firstly, the motion equation of the linked buildings with TMDI under wind loads is presented. Secondly, synchronous multi-point pressure measurement wind tunnel tests for two linked buildings with 268 ​m (the building-1) and 210.2 ​m heights (the building-2), respectively, are carried out to obtain their wind loads. Finally, wind-induced responses of the linked buildings with TMDI are analyzed and are compared with the responses of the buildings with tuned mass damper (TMD) and without any control device to demonstrate the advantages of the TMDI. The analysis of the case indicates that TMDI has better mitigation effects than TMD, even if the mass of TMDI is one third of the TMD. TMDI can effectively reduce the acceleration responses of both the buildings for all wind directions, and yet fail to mitigate displacement responses of the building-2 at few wind directions.