Classical Tuned Mass Damper Research Articles

Performance of TMDI for Tall Building Damping

This study investigates the vibration reduction of tall wind-excited buildings using a tuned mass damper (TMD) with an inerter (TMDI). The performance of the TMDI is computed as a function of the floor to which the inerter is grounded as this parameter strongly influences the vibration reduction of the building and for the case when the inerter is grounded to the earth whereby the absolute acceleration of the corresponding inerter terminal is zero. Simulations are made for broadband and harmonic excitations of the first three bending modes, and the conventional TMD is used as a benchmark. It is found that the inerter performs best when grounded to the earth because, then, the inerter force is in proportion to the absolute acceleration of only the pendulum mass, but not to the relative acceleration of the two inerter terminals, which is demonstrated by the mass matrix. However, if the inerter is grounded to a floor below the pendulum mass, the TMDI only outperforms the TMD if the inerter is grounded to a floor within approximately the first third of the building’s height. For the most realistic case, where the inerter is grounded to a floor in the vicinity of the pendulum mass, the TMDI performs far worse than the classical TMD.

A generalized 2-DOF model for optimal design of MDOF structures controlled by Tuned Mass Damper Inerter (TMDI)

The paper illustrates a methodology to perform the optimal design of a Tuned Mass Damper Inerter (TMDI) equipped on a multi degree of freedom (MDOF) structure through a generalized model. The TMDI is considered in both configurations grounded and ungrounded. A generalized 2-DOF model is obtained: the primary oscillator, representing the original MDOF structure and the secondary oscillator, representing the control system. A Gaussian zero mean white noise random process is adopted for the excitation. The TMDI design is carried out adopting an energy objective function, maximized over the space of the design parameters which are: the mass and inertance ratios, the frequency ratio, the damping factor and a parameter that accounts for the TMDI location on the MDOF structure. Synthetic performance-based design maps of the TMDI parameters are carried out. It is shown that is possible to have different design configurations to achieve a target performance level. The maps furnish, as limit cases, the design of a Tuned Inerter Damper (TID) and a Tuned Mass Damper (TMD), when the mass or the inertance ratios are respectively assumed null. It is shown straightforwardly the regions of the design parameters where the inerter enhances the performances achievable by classical TMD. Furthermore, an analytical expression which links the optimal design variables necessary to obtain a desired target performance is proposed. Frequency response functions and modal parameters of certain 2-DOF models with optimally designed control system are reported and considerations on how the design parameters influence the system dynamics and the damping capabilities are highlighted. Comparisons of the TMDI optimally designed with cases of no control and same mass TMD are evidenced throughout the paper. Finally, the main responses of the primary structure and the TMDI are estimated in the space of variation of the design parameters in order to assess the effectiveness of the control system.

Seismic effectiveness of hysteretic tuned mass dampers for inelastic structures

The problem of reducing the damage due to seismic loads in engineering structures by means of tuned mass dampers (TMDs) is addressed. Differently from previous studies focused on linear or geometrically nonlinear TMDs, the present work is concerned with a device that exhibits a hysteretic restoring force with pinching. A numerical TMD optimization is carried out so as to ensure optimal energy transfer from the main structure to the TMD for various seismic ground motion severities. The effectiveness of the vibration protection strategy is discussed for two different structural systems, i.e. a multi-story steel building with a purely elastoplastic behavior and a masonry building that exhibits stiffness and strength degradation.Numerical simulations demonstrate that the hysteretic TMD can achieve a meaningful average reduction of the root mean square (RMS) displacement of the steel structure between 40% (for 1% mass ratio) and 60% (for 5% mass ratio). Various seismic records related to soil types and seismic intensity levels different from those considered at the design stage, or unpredictable variations of the main system stiffness up to 10%, are shown to have rather limited influence on the TMD performance. It is shown that a classical linear TMD can attain a protection level comparable to that of the hysteretic TMD only at the expense of much higher mass ratios. Compared to the multi-story structure, the performance of the hysteretic TMD in a masonry building is still satisfactory although degraded, i.e. by about 15% in terms of RMS displacement. The performance is better than that of a classical linear absorber for very small mass ratios, especially for mid- or high-intensity seismic ground motions. The greater robustness of the hysteretic TMD performance for a wide range of seismic ground motions is due to its softening-type backbone, which can be optimized to accommodate the frequency changes that engineering structures typically undergo under seismic excitation. The role of the pinching in the performance of the hysteretic TMD is clarified.

Enhanced tuned mass damper using an inertial amplification mechanism

This paper proposes a novel inertial-amplification-mechanism (IAM) to enhance the vibration mitigation performance of the classical tuned mass damper (TMD). To this aim, the IAM is coupled to a standard TMD to form a so-called IAM-TMD. Analytical derivations are developed to extend the theory of the classical TMD to the IAM-TMD. Next, H∞ and H2 optimizations are performed and closed-form solutions for the optimal parameters of the IAM-TMD are obtained. Parametric studies are conducted to evaluate the influence of the geometrical configuration of the IAM system on the performance of the IAM-TMD. Finally, numerical simulations are performed to validate the efficiency of the IAM-TMD. In details, time history analyses of a structure without TMD, with TMD, and with IAM-TMD under harmonic and earthquake ground motions are computed and compared. Results show that when using the classical TMD, dynamic responses of the primary structure are suppressed, but the responses of the absorber are relatively large. Conversely, when using the IAM-TMD, dynamic responses of both the primary structure and the absorber are mitigated at the same time.

A comparative study on optimization of multiple essentially nonlinear isolators attached to a pipe conveying fluid

In recent years, nonlinear energy sinks (NES) have been recognized as a promising method for passive vibration control of pipes conveying fluid due to their advantages over the classic tuned mass damper (TMD). Nevertheless, it has been shown that their performance is highly sensitive to uncertainties, and they are only effective in a narrow range of flow velocities and external excitations. Therefore, uncertainties in both design and aleatory parameters must be considered in their optimal design. For the first time, this article investigates stochastic optimization of multiple NESs configured in parallel and series configurations attached to a simply supported pipe conveying fluid. The main goal of this optimization approach is to overcome the inherent sensitivity of NES performance and increase the efficiency range of that. The optimization problem is based on a multi-objective model, with the aim of maximizing the expected value of the NES efficiency estimated from the monte-carlo (MC) simulations, as well as minimizing the corresponding standard deviation. Stiffness property, damping, mass ratio, and location of NES are considered as random design parameters. The distributions of NESs efficiency for stochastic based optimizations are compared to deterministic optima. The results demonstrate that the stochastic optima are much more robust than the deterministic one, and is able to deal with various sources of uncertainties particularly in initial excitation and flow velocity. It is observed that there is an optimal number for NESs in both configurations, above which the performance would not be improved and maybe reduced by increasing the number of them. Also, comparing the present work to other similar works, yields a satisfying result.

Simplified analytical solution for the optimal design of Tuned Mass Damper Inerter for base isolated structures

Abstract In this paper the use of the Tuned Mass Damper Inerter (TMDI) to control the response of base isolated structures under stochastic horizontal base acceleration is examined. Notably, the TMDI, recently introduced as a generalization of the classical Tuned Mass Damper, allows to achieve enhanced performance compared to the other passive vibration control devices. Thus, it represents an ideal alternative for reducing displacements of base isolated structures. To this aim, firstly a straightforward numerical approach is developed for the optimal design of this device considering a white noise base excitation. Further, a simplified analytical solution for the optimal design of TMDI parameters for base isolated structures is proposed minimizing the displacement variance of the corresponding undamped base isolated system. A thorough numerical analysis is performed and related results, in terms of optimal parameters and control performance, are compared with pertinent data obtained by a more computationally demanding iterative optimization procedure on the original damped system, considering both white noise and coloured noise stationary base excitation. Analytical and numerical results are found in good agreement, especially in terms of control performance, thus establishing the reliability and efficiency of the proposed approach. Finally, numerical analyses on a five-story benchmark base isolated structure controlled with an optimally designed TMDI are performed considering real recorded ground motions as base excitation. It is concluded that the TMDI, properly optimized with the proposed procedure, can effectively reduce the response of base isolated structures even under strong earthquakes.

Optimal design and seismic performance of tuned mass damper inerter (TMDI) for structures with nonlinear base isolation systems

SummaryThe tuned mass damper inerter (TMDI) couples the classical tuned mass damper (TMD) with an inerter, a mechanical device whose generated force is proportional to the relative acceleration between its terminals, thus providing beneficial mass‐amplification effects. This paper deals with a dynamic layout in which the TMDI is installed below the isolation floor of base‐isolated structures in order to enhance the earthquake resilience and reduce the displacement demand. Unlike most of the literature studies that assumed a linearized behavior of the isolators, the aim of this paper is to investigate the effectiveness of the TMDI while accounting for the nonlinearity of the isolators. Two nonlinear constitutive behaviors are considered, a Coulomb friction model and a Bouc‐Wen hysteretic model, representative of friction pendulum and of lead‐rubber‐bearing isolators, respectively. Optimal design is based on the stochastic dynamic analysis of the system, by modeling the base acceleration as a Kanai‐Tajimi filtered stationary random process and resorting to the stochastic linearization technique to handle the nonlinear terms. Different tuning criteria based on displacement, acceleration, and energy‐based performance indices are defined, and their implications in a design process are discussed. It is proven that the improved robustness of the TMDI reduces its performance sensitivity to the tuning frequency and to the earthquake frequency content, which are well‐known shortcomings of TMD‐like systems. This important feature makes the TMDI particularly suitable for nonlinear base‐isolated structures that are affected by unavoidable uncertainties in the isolators' properties and that may experience changes of isolators effective stiffness depending on the excitation level.

Optimal tuned mass-damper-inerter (TMDI) design for seismically excited MDOF structures with model uncertainties based on reliability criteria

The tuned mass-damper-inerter (TMDI) is a recently proposed linear passive dynamic vibration absorber for the seismic protection of buildings. It couples the classical tuned mass damper (TMD) with an inerter, a two-terminal device resisting the relative acceleration of its terminals, in judicial topologies, achieving mass-amplification and higher-modes-damping effects compared to the TMD. This paper considers an optimum TMDI design framework accommodating the above effects while accounting for parametric uncertainty to the host structure properties, modeled as a linear multi degree of freedom system, and to the seismic excitation, modeled as stationary colored noise. The inerter device constant, acting as a TMD mass amplifier, is treated as a design variable, whereas performance variables sensitive to high-frequency structural response dynamics are used to account for the TMDI influence to the higher structural modes. Reliability criteria are adopted for quantifying the structural performance, expressed through the probability of occurrence of different failure modes related to the trespassing of acceptable thresholds for the adopted performance variables: floor accelerations, interstory drifts, and attached mass displacement. The design objective function is taken as a linear combination of these probabilities following current performance-based seismic design trends. Analytical and simulation-based tools are adopted for the efficient estimation of the underlying stochastic integral defining the structural performance under uncertainty. A 10-story building under stationary Kanai-Tajimi stochastic excitation is considered to illustrate the design framework for various TMDI topologies and attached mass values. It is shown that the TMDI achieves enhanced structural performance and robustness to building and excitation uncertainties compared to same mass/weight TMDs.

Seismic control of a SDOF structure through electromagnetic resonant shunt tuned mass-damper-inerter and the exact H2 optimal solutions

This paper proposes a novel inerter-based component dynamic vibration absorber, namely, electromagnetic resonant shunt tuned mass-damper-inerter (ERS-TMDI). To analyze the performances of the ERS-TMDI, the combined ERS-TMDI and a single degree of freedom system are developed. The H2 norm performances of the ERS-TMDI, whose aim is to minimize the root mean square (RMS) value of structure damage under random ground acceleration excitation, are introduced in comparison with the energy-harvesting series electromagnetic tuned mass dampers (ERS-TMDs), tuned mass-damper-inerter (TMDI) and the classical tuned mass damper (TMD). The closed-form solutions, including the optimal mechanical tuning ratio, the optimal electrical damping ratio, the optimal electrical tuning ratio and the optimal electromagnetic mechanical coupling coefficient, are obtained. It is shown that the ERS-TMDI is superior to both the classical TMD and the ERS-TMD systems for protection from structure damage. Specifically, from the frequency-domain analyses, a case study is performed to illustrate the effectiveness, robustness of the ERS-TMDI and the sensitivity to the parameter changes. From the time-domain analyses, four types of earthquakes are studied to demonstrate the performances of vibration suppression.

Combining TMD and TLCD: analytical and experimental studies

In these years several research efforts have been focused on developing efficient and reliable control devices for mitigating the structural response of tall and lightly damped buildings in case of strong dynamic excitations, such as wind and earthquake ones. In this context, Tuned Mass Dampers (TMDs) represent probably the most common control device due to their high control performances. On the other hand, Tuned Liquid Column Dampers (TLCDs) are increasingly becoming more popular because of some of their attractive features, cost-effectiveness among the others, even though they yield slightly less control performance compared to the classical TMDs. Aiming at combining the beneficial effects of the TMD and the attractive characteristics of the TLCD, in this paper a novel control device is introduced which is realized joining this two systems. The pertinent equations of motion are derived, and the analytical study is developed to analyze the control performance of this device. Finally, theoretical results are validated via vast experimental campaign undertaken in the Laboratory of Experimental Dynamics of the University of Palermo, Italy.

Optimal design and performance evaluation of systems with Tuned Mass Damper Inerter (TMDI)

SummaryThe paper concerns the optimal design and performance evaluation of a Tuned Mass Damper Inerter (TMDI) to reduce dynamic vibrations. The system exploits properties of the inerter, a two‐terminal mechanical device able to produce a force proportional to the relative acceleration between terminals, with the ability of generating an apparent mass even two orders of magnitude greater than its own physical mass. A primary single‐degree‐of‐freedom structure is equipped with a classical linear Tuned Mass Damper (TMD), the secondary structure, whose mass is connected to the ground via an inerter. The optimal design of the TMDI is conducted by assuming a white noise process as base input and utilizing three different design methodologies: displacement minimization, acceleration minimization and maximization of the ratio between the energy dissipated in the secondary system and the total input energy. Optimal results obtained with the different methodologies are carried out and compared. Two limit cases are also considered when the inerter is not contemplated: conventional and non‐conventional TMDs, characterized by a low and a large mass ratio, respectively. The TMDI performance is evaluated and compared with conventional and non‐conventional TMDs; moreover, its robustness is assessed with a sensitivity analysis varying the design parameters. Attention is focused not exclusively on the primary structure response but also on the secondary one. Finally, the effectiveness of the optimally designed TMDI is evaluated having considered earthquake base excitation. Results demonstrate the effectiveness of TMDI systems for dynamic response reduction with superior performances and robustness than classical TMDs. Copyright © 2017 John Wiley & Sons, Ltd.

Wind Induced Vibration Control and Energy Harvesting of Electromagnetic Resonant Shunt Tuned Mass-Damper-Inerter for Building Structures

This paper proposes a novel inerter-based dynamic vibration absorber, namely, electromagnetic resonant shunt tuned mass-damper-inerter (ERS-TMDI). To obtain the performances of the ERS-TMDI, the combined ERS-TMDI and a single degree of freedom system are introduced. H2 criteria performances of the ERS-TMDI are introduced in comparison with the classical tuned mass-damper (TMD), the electromagnetic resonant shunt series TMDs (ERS-TMDs), and series-type double-mass TMDs with the aim to minimize structure damage and simultaneously harvest energy under random wind excitation. The closed form solutions, including the mechanical tuning ratio, the electrical damping ratio, the electrical tuning ratio, and the electromagnetic mechanical coupling coefficient, are obtained. It is shown that the ERS-TMDI is superior to the classical TMD, ERS-TMDs, and series-type double-mass TMDs systems for protection from structure damage. Meanwhile, in the time domain, a case study of Taipei 101 tower is presented to demonstrate the dual functions of vibration suppression and energy harvesting based on the simulation fluctuating wind series, which is generated by the inverse fast Fourier transform method. The effectiveness and robustness of ERS-TMDI in the frequency and time domain are illustrated.

Exact H2 Optimal Tuning and Experimental Verification of Energy-Harvesting Series Electromagnetic Tuned-Mass Dampers

Energy-harvesting series electromagnetic-tuned mass dampers (EMTMDs) have been recently proposed for dual-functional energy harvesting and robust vibration control by integrating the tuned mass damper (TMD) and electromagnetic shunted resonant damping. In this paper, we derive ready-to-use analytical tuning laws for the energy-harvesting series EMTMD system when the primary structure is subjected to force or ground excitations. Both vibration mitigation and energy-harvesting performances are optimized using H2 criteria to minimize root-mean-square (RMS) values of the deformation of the primary structure or maximize the average harvestable power. These analytical tuning laws can easily guide the design of series EMTMDs under various external excitations. Later, extensive numerical analysis is presented to show the effectiveness of the series EMTMDs. The numerical analysis shows that the series EMTMD more effectively mitigates the vibration of the primary structure nearly across the whole frequency spectrum, compared to that of classic TMDs. Simultaneously, the series EMTMD can better harvest energy due to its broader bandwidth effect. Beyond simulations, this paper also experimentally verifies the effectiveness of the series EMTMDs in both vibration mitigation and energy harvesting.

On the efficiency and robustness of damping by branching

This paper investigates the mechanism referred to as damping by branching (DBB), and its ability to attenuate the response of an oscillating structure, in the range of large amplitudes. More specifically, we give an experimental proof of this mechanism and we show that it is very robust against variations of the physical parameters and constituents: nature of the damping mechanism, geometrical structure. These results motivated the design of the Tuned Mass Branched Damper (TMBD) which is shown to be a little more efficient than the classical Tuned Mass Damper (TMD) in some domains of the parameter space.

Optimal design of a novel tuned mass-damper–inerter (TMDI) passive vibration control configuration for stochastically support-excited structural systems

This paper proposes a novel passive vibration control configuration, namely the tuned mass-damper–inerter (TMDI), introduced as a generalization of the classical tuned mass-damper (TMD), to suppress the oscillatory motion of stochastically support excited mechanical cascaded (chain-like) systems. The TMDI takes advantage of the “mass amplification effect” of the inerter, a two-terminal flywheel device developing resisting forces proportional to the relative acceleration of its terminals, to achieve enhanced performance compared to the classical TMD. Specifically, it is analytically shown that optimally designed TMDI outperforms the classical TMD in minimizing the displacement variance of undamped single-degree-of-freedom (SDOF) white-noise excited primary structures. For this particular case, optimal TMDI parameters are derived in closed-form as functions of the TMD mass and the inerter constant. Furthermore, pertinent numerical data are furnished, derived by means of a numerical optimization procedure, for a 3-DOF classically damped primary structure base excited by stationary colored noise, which exemplify the effectiveness of the TMDI over the classical TMD to suppress the fundamental mode of vibration for MDOF structures. It is concluded that the incorporation of the inerter in the proposed TMDI configuration can either replace part of the TMD vibrating mass to achieve lightweight passive vibration control solutions, or improve the performance of the classical TMD for a given TMD mass.

Experimental validation of a novel smart electromechanical tuned mass damper beam device

This paper validates the novel concept of utilising piezoelectric vibration energy harvesting (PVEH) beams as a tuned mass damper (TMD)—which suppresses a particular vibration mode of a generic host structure over a broad band of excitation frequencies. The proposed device comprises a pair of bimorphs shunted by a resistor, capacitor and inductor connected in various alternative circuit configurations. A benchmark for the performance is established through Den Hartog's theory for the optimal damping of a classical TMD. Experimental results demonstrate that such optimal damping is equivalently generated by the PVEH effect for appropriately tuned circuitry. These results correlate reasonably well with the results of a theoretical analysis introduced in a previous paper. The proposed TMD beam device combines the relative advantages of the classical (‘mechanical’) TMD and the shunted piezoelectric patch (‘electrical’ vibration absorber), presenting the prospect of a functionally more readily-adaptable class of ‘electromechanical’ tuned vibration absorbers. Moreover, with further development, this dual PVEH/TMD beam device holds the potential of simultaneous energy storage.

A theoretical study of a smart electromechanical tuned mass damper beam device

Research into piezoelectric vibration energy harvesting (PVEH) beams has so far largely overlooked the fact that these are, in many practical applications, mechanical absorbers of the vibration of the structure to which they are attached. This paper introduces the novel concept of utilizing a PVEH beam as a tuned mass damper (TMD)—which suppresses a particular vibration mode of a generic host structure over a broad band of excitation frequencies. This device comprises a pair of bimorphs shunted by resistor–capacitor–inductor circuitry. The optimal damping required by this TMD is generated by the PVEH effect of the bimorphs. The theoretical basis of this dual PVEH/TMD beam device is presented and verified by alternative analytical methods. The simulation results demonstrate that the ideal degree of vibration attenuation can be achieved through appropriate tuning of the circuitry for a device whose effective mass is less than 2% of the equivalent modal mass of the host structure. The proposed dual PVEH/TMD beam device combines the relative advantages of the classical (mechanical) TMD and the shunted piezoelectric patch (electrical vibration absorber), presenting the prospect of a functionally more readily adaptable class of ‘electromechanical’ tuned vibration absorbers.

Vibration suppression of a cantilever beam using magnetically tuned-mass-damper

Eddy currents are induced by the movement of a conductor through a stationary magnetic field or a time varying magnetic field through a stationary conductor. These currents circulate in the conductive material and are dissipated, causing a repulsive force between the magnet and the conductor. These electromagnetic forces can be used to suppress the vibrations of a flexible structure. A tuned mass damper is a device mounted in structures to reduce the amplitude of mechanical vibrations and is one of the effective vibration suppression methods. In the present study, an improved concept of this tuned mass damper for the vibration suppression of structures is introduced. This concept consists of the classical tuned mass damper and an eddy current damping. The important advantages of this magnetically tuned mass damper are that it is relatively simple to apply, it does not require any electronic devices and external power, and it is effective on the vibration suppression. The proposed concept is designed for a cantilever beam and the analytical studies on the eddy current damping and its effects on the vibration suppression. To show the effectiveness of the proposed concept and verify the eddy current damping model, experiments on a cantilever beam are performed. It is found that the proposed concept could significantly increase the damping effect of the tuned mass damper even if not adequately tuned.

Closed-form formulas for the optimal pole-based design of tuned mass dampers

This paper deals with the analysis and optimization of tuned mass dampers (TMDs). It provides design formulas for maximizing the exponential time-decay rate (ETDR) of the system transient response. A detailed analysis is presented for the classical TMD configuration, involving an auxiliary mass attached to the main structure by means of a spring and a dashpot. Analytic expressions of the optimal ETDR are obtained for any mass ratio and tuning condition. Then, a further optimization with respect to the latter is performed. The proposed method is applied also to other TMD configurations involving an auxiliary mass connected to both the main structure and the ground, as well as to a piezoelectric damping device. A justification to the well-known heuristic optimality condition based on the enforcement of coincident couples of complex conjugate poles is presented. That condition is shown, however, to fail in providing optimal solutions for some mass ratio values and/or TMD configurations, and the optimality conditions prevailing in those cases are derived. The present analysis, besides its theoretical interest, may be useful in practical applications, e.g., to assess the sensitivity of the optimal ETDR with respect to the design parameters or to promptly adjust some of those parameters during service, after any variation of the operative conditions.

Passive vibration control of plan-asymmetric buildings using tuned liquid column gas dampers

The sealed, tuned liquid column gas damper (TLCGD) with gas-spring effect extends the frequency range of application up to about 5 Hz and efficiently increases the modal structural damping. In this paper the influence of several TLCGDs to reduce coupled translational and rotational vibrations of plan-asymmetric buildings under wind or seismic loads is investigated. The locations of the modal centers of velocity of rigidly assumed floors are crucial to select the design and the optimal position of the liquid absorbers. TLCGD`s dynamics can be derived in detail using the extended non-stationary Bernoulli`s equation for moving reference systems. Modal tuning of the TLCGD renders the optimal parameters by means of a geometrical transformation and in analogy to the classical tuned mass damper (TMD). Subsequently, fine-tuning is conveniently performed in the state space domain. Numerical simulations illustrate a significant reduction of the vibrations of plan-asymmetric buildings by the proposed TLCGDs.