Optimal Tuned Mass Damper Research Articles

Optimization of tuned mass dampers parameters using Artificial Neural Networks

Control systems are usually employed to minimize the dynamic effects on structures. These controllers must be designed according to the physical and geometric characteristics of the system and the environmental loads to which the structure will be subjected. Passive control is the most suitable for extreme events because it does not depend on an external power source to function properly. The use of a linear attenuator, such as the tuned mass damper (TMD), allows for dynamic analysis in the frequency domain, which provides a reduction in the computational cost of the analysis. Among the several methods used to determine the optimal parameters of the damper, analytical methods in their closed form can be applied to simpler structures. In structures with several degrees of freedom or complex geometry, the optimal TMD parameters, as well as its optimal position, can be acquired by methods based on stochastic optimization. This kind of problem is commonly solved in the state-of-the-art by Metaheuristic algorithms. However, in general, these procedures require high computational costs, which makes Artificial Neural Networks (ANN) a viable alternative to minimize the processing time. Thus, this paper proposed a methodology based on ANN in comparison with the Circle-Inspired Optimization Algorithm (CIOA) to determine the optimal parameter of tuned mass dampers, i.e., the damper period. Training of the neural networks was performed with a dataset of optimal TMD values, which were obtained in the frequency domain. The model developed from these results was subsequently tested on different shear-building models, including the influence of seismic excitation. The response of the structures in displacements was evaluated with the optimal values obtained through ANN and compared with the structures without the control device. In addition, the optimal parameters obtained by ANN were also compared with the closed analytical formulations. The results obtained by the neural networks were as effective as the CIOA metaheuristic algorithm but required up to 0.02% of its processing time.

Optimization-Based Vibration Control Analysis of Dampers in High-Rise Building

Tuned mass dampers (TMDs) are a useful control of vibrations for tall buildings and can be considered equal to burdens such as breezes and earthquakes. The better limits for TMD are to reduce the earthquake vibrations of tall buildings including soil–structure interaction (SSI) influences. This study proposes the multi-objective Black Widow Optimization (BWO) with Elman neural network (ENN) computation that is brought on to find the optimal limits of TMD. Considering that this proposed model analyzed the mass, stiffness, and damping ratio of TMD to get the maximum accelerations and displacement of 40 story building model, from the execution results, starting from this proposed BWO–Elman model to the expected methodology, the most outrageous TMD limits are better, likewise, the reduction of acceleration and displacement are 25% and 19.86% in the proposed study. This study assists the researchers with a better understanding of earthquake vibration and leads the fashioners to achieve superior TMD for tall designs. The impact of vibration control on the displacements and accelerations of both controlled and uncontrolled buildings is investigated in this work. It uses a MATLAB software technique to analyze their modal replies, moreover, this proposed optimal TMD model is compared with conventional techniques by acceleration and stiffness parameters.

Performance of differently arranged double-tuned mass dampers for structural seismic response control including soil-structure interaction

Reducing vibrations occurring in structures under environmental loads makes a significant contribution to the development of structural safety. Tuned mass dampers (TMD) are one of the systems commonly used to control structural vibrations. Since TMD is adjusted according to the dominant frequency of the structure, factors that may cause changes in the frequency of the structure can significantly reduce the effectiveness of TMD. One of the main factors that can cause changes in the frequency values of the structure is the interaction between the structure and the soil. To overcome this situation, it is recommended to apply control systems consisting of multiple TMDs (MTMD) to the main structure instead of a single TMD. MTMD systems are arranged in two different types, serial and parallel. In this paper, a methodology that considers the structure-soil interaction (SSI) is presented for the optimum design of control systems with different configurations placed on a main structure under the influence of ground motion. To research the SSI effects, the TMDs-structure coupled system is supported by rocking and swaying springs and the corresponding dashpots, and then the equations of motions of the structural system are derived. In the optimization process based on particle swarm optimization in the frequency domain, different soil types, configuration types, and mass ratios are considered. The efficiency of optimum TMDs arranged in series and parallel is also evaluated using near and far fault ground motions in the time domain. Numerical results show that if structures are constructed on soils with low shear wave velocities, ignoring SSI can significantly change the design parameters and effectiveness of the control system.

Optimization of tuned mass dampers – minimization of potential energy of elastic deformation

A tuned mass damper (TMD) optimization can be performed under various assumptions and objectives. All the variables of the optimization, such as structural model, performance index and load type affect the optimal parameters of the TMD. This paper presents a new optimization method that implements straightforward performance index and allows taking load spectral characteristics into account. Thanks to the usage of modal coordinates, the method allows fast numerical optimization of TMD attached to large or complicated structures with numerous degrees of freedom. One of the complicated tasks while optimizing TMD is the choice of a performance index. In this paper, the mean value of potential energy stored in the elastic deformation of a structure under periodic load serves as a performance index, which leads to a low numerical complexity task if the optimization is performed in the frequency domain. The new method also allows a simple inclusion of load spectral characteristics and permits TMD optimization for any loading spectral range. When applied to a structure with a single degree of freedom, this method leads to H2 optimization in the case of white noise excitation. However, it is applicable to multiple degrees of freedom structures with single or multiple TMDs and any given load. The paper also presents several examples of numerical optimization of the TMD attached to both single and multiple degrees of freedom structures under various loads, including white noise excitation, pedestrian load, and earthquake strong motion.

Development of Fragility Curves for Tall Buildings with Tuned Liquid Dampers for Vibration Control Under Wind Loading

In this study, fragility curves of a tall building subjected to along-wind loads are developed to evaluate the enhancement in reliability when a Tuned Liquid Damper (TLD) system is employed. For the analysis, a mathematical model of a tall building is designed and subjected to along-wind loads simulated with an autoregressive and moving-average (ARMA) model that includes spatial and temporal variations in the turbulent wind component. For comparison purposes, fragility curves of the tall buildings fitted with a Tuned Mass Damper (TMD) system are also developed. To develop the fragility curves, predefined wind-induced acceleration thresholds are employed as damage states. The numerical results indicate that the use of optimal TLD or TMD systems is effective at reducing the wind-induced acceleration for different mean wind speeds. In addition, the auxiliary damping systems are more effective at reducing the probability of exceedance as the percentage of individuals who perceive acceleration increases from 10 to 50%. Finally, the highest reliability enhancement with the use of both damping systems is achieved for mean wind speed values ranging from 41 to 62 m/s for the damage states considered.

Optimal Design of Formulas for a Single Degree of Freedom Tuned Mass Damper Parameter Using a Genetic Algorithm and H2 Norm.

One of the researchers' concerns in structural engineering is to control the dynamic behavior of structures efficiently. The TMD (tuned mass damper) is one of the effective methods of controlling the vibration of structures, and various numerical techniques have been proposed to find the optimal parameters of the TMD. This paper develops a new explicit formula to derive the optimal parameters of the TMD of a single degree of freedom (SDOF) structure under seismic load using a genetic algorithm (GA). In addition, the state-space model and the H2 norm function are used to identify the optimal frequency ratio and damping ratio of the TMD that minimize the overall vibration energy of the structure. The MATLAB curve fitting toolbox is used for the explicit formula proposal, and the validity of the proposed formula is verified through multidimensional performance verification technique. Finally, the TMD parameters of the SDOF structure are applied to the multi-degrees of freedom (MDOF) structure to compare and analyze with the existing research results, and the results of the explicit formula proposed in this paper are confirmed to be excellent. This paper can suggest a new direction for determining the optimal TMD parameters using a GA and can be effectively applied to vibration control problems of various structures.

Probabilistic assessment of optimum tuned mass damper in offshore platforms considering fluid–structure interaction

Probabilistic assessment of optimum tuned mass damper in offshore platforms considering fluid–structure interaction

Vibration Suppression of Two Adjacent Cables Using an Interconnected Tuned Mass Damper/Nonlinear Energy Sink

Due to their high flexibility, low damping, and small mass, stay cables are prone to large-amplitude vibrations. Various mechanical measures, typically installed near the cable anchorage to the deck, have been developed to suppress cable vibration. These dampers, however, may not be effective for ultralong cables since the damper is close to the cable anchorage, the cable node. In this paper, a tuned mass damper (TMD)/nonlinear energy sink (NES) are considered for installation between two adjacent stay cables for vibration mitigation. Firstly, the static equilibrium equation of the stay cable–damper system is established, and the influence of the self-weight of the damper on cable shape is investigated. The governing equations describing the motion of the two adjacent cables with a damper are then established using the Hamilton principle, which are then solved by the method of separation of variables. For cases of swept-sine excitation and harmonic excitation, the optimal designs of TMD and NES are achieved with the purpose of suppressing the first- and third-mode-dominated vibrations, respectively. Both optimal TMD and NES may substantially suppress cable vibrations, with each having advantages under certain situations. Finally, the dynamic response characteristics of two adjacent cables with an optimal damper are analyzed. Interesting dynamic behaviors, such as energy input suppression, phase shift, cable frequency shift, and phase diagram boundary rotation, are identified, and their mechanisms are explained.

Optimized design of multiple tuned mass dampers for vibration control of offshore wind turbines

Offshore wind turbines (OWTs) are dynamically sensitive structures to low-frequency wind-wave loadings due to their low damping and high flexibility. This makes them vulnerable to unwanted vibrations in ocean environments. Therefore, there is a need to implement innovative vibration control devices to suppress undesired vibration and ensure their structural safety. A tuned mass damper (TMD) has been a promising solution to control excessive vibrations recently in OWTs due to higher efficiency and low installation cost. However, TMD performance in vibration mitigation of OWTs when placed at a nacelle is still challenging to investigate because the generator torque and pitch control may affect the dynamics of the overall system. In this paper, an optimal multiple TMD system is designed by placing TMDs at optimal locations along the tower, which are defined using the maximum amplitude of the displacements for the first three natural frequencies of the tower. In addition, extensive simulations are carried out with integrated OWT-TMD systems to find the optimal mass ratio values and quantity of the TMDs. The TMD system is also tuned for several scenarios, including operating, parked, and idling conditions under the combined wind-wave loadings. A numerical model of the 5 MW NREL OWT developed in OpenFAST is considered as the baseline in this study. The results show a root mean square (RMS) response reduction of 10.2% and 42% in fore-aft (FA) and side-side (SS) tower displacement with optimally designed multiple TMDs. Moreover, improved mitigation effects on tower base moment of RMS 43.6% and 20.8% are observed in orthogonal directions, respectively. The findings of this paper may have the potential for designing passive TMD systems for vibration reductions in OWT.

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.

Integrated design and real-world application of a tuned mass damper (TMD) with displacement constraints for large offshore monopile wind turbines

Passive tuned mass dampers (TMDs) have been increasingly investigated for vibration control of wind turbines. However, TMD designs based on individual or a few operating conditions may result in insufficient consideration of the TMD's impact on wind turbines. For instance, the influence of end-stop collision forces on the main structural damage may be significantly underestimated, thereby affecting the overall lifecycle evaluation. In this study, focusing on large offshore fixed-bottom monopile wind turbines, we propose an integrated TMD design methodology taking the damper displacement constraints into full account. A comprehensive optimization of the passive omnidirectional pendulum-type TMD is conducted considering large number of operating conditions in the offshore environment. Next, a real-world application of the optimally designed TMD is performed for a 6450 kW monopile offshore wind on the Yellow Sea, China. We develop an on-site testing methodology and evaluation criteria for assessing the effectiveness of the TMD offshore. The results of resonance, emergency stop, operatingand reliability test conditions demonstrate the following: under the optimized TMD design taking into account all operating conditions, the TMD with a mass ratio of 1.56% can offer added damping in the fore-aft and side-side directions of the turbine, and provides the desired damping ratio of 1%; within a 4% frequency range around the design frequency, the TMD achieves effective vibration control; at rated power, the TMD achieves a reduction of more than 50% in the amplitude of the tower base side-side bending moment (Mx). The integrated TMD design with displacement constraints allows for the optimal TMD design across all operating conditions, thereby achieving superior overall vibration control and reduction in fatigue loads. The successful real-world application of the TMD based on integrated design methodology is of high value to the research community.

Site-Specific Aseismic Design of Multi-Storeyed Buildings Using Optimum Tuned Mass Damper Inerter

ABSTRACT The effectiveness of the tuned mass damper inerter (TMDI) in reducing the vibration of building structures under site-specific earthquake excitation is investigated. The site is Guwahati, Assam, which lies in the most severe seismic intensity zone in India. In this paper, the optimization of the TMDI design parameters is carried out for the site-specific input derived for the building site by a modulated Clough-Penzien (C-P) spectrum fitted to the power spectral density function obtained from a strong motion model of the site. All possible topologies of the TMDI, with one terminal of the inerter being connected to the damper mass attached to the top storey of the example buildings, and the other terminal being connected to any other floor, are investigated. The structure-TMDI system is analyzed both in the frequency-domain and in the time-domain. A numerical study is conducted with two example building structures. Optimization of design parameters of the TMDI is carried out using the technique of simulated annealing in the frequency-domain using the site-specific modulated Clough-Penzien spectrum as input. The performance of the optimal TMDI cases is evaluated by subjecting the example structures to 10 site-specific synthetically generated accelerograms. Results indicate that the TMDI is superior to the TMD for all topologies of the TMDI in case of the 3-storieed structure; and for topologies of the TMDI in which the inerter spans more than 4 floors for the 8-storied structure, with improved reductions in top-floor displacement, acceleration, and stroke length.

Torsional vibration attenuation of a closed-loop engine crankshaft system via the tuned mass damper and nonlinear energy sink under multiple operating conditions

In recent years, nonlinear energy sink (NES), as a nonlinear dynamic vibration absorber (NDVA), has been widely studied due to its high robustness and broadband vibration attenuation effectiveness, compared with the traditional linear dynamic vibration absorber (LDVA). In the area of crankshaft torsional vibration reduction, the external excitation of a closed-loop crankshaft model changes with the variation of speed, which puts forward higher requirements for wide-band torsional vibration attenuation. This study attempts to explore the feasibility of NES replacing the traditional linear tuned mass damper (TMD) for engine crankshafts in possible practical engineering application by studying a four-cylinders diesel engine crankshaft. Firstly, a multi-inertias nonlinear closed-loop self-excited coupled oscillation model (M-NCSCO) of crankshaft is established, and the correctness of the model is verified through comparison with those from experiments. Based on this, the crankshaft is coupled with optimal TMD (O-TMD), general NES (G-NES), and optimal NES (O-NES), respectively. An improved Newmark–β method is proposed to solve the nonlinear dynamic model numerically. The effects of NES and TMD on the vibration attenuation behavior of the crankshaft are studied under different engine operating conditions (including power, injection timing, single cylinder flameout, and load). The results show that the vibration attenuation efficiency and robustness of G-NES are 7.90% and 3.47% higher than that of O-TMD when considering the above four typical working conditions comprehensively. After further optimization of G-NES, the vibration reduction efficiency of O-NES is improved by 3.1% compared with G-NES.

A novel passive nonlinear two-DOF internal resonance-based tuned mass damper

This paper presents a novel passive nonlinear two-degree-of-freedom (DOF) tuned mass damper (TMD) for harmonic vibration suppression. Proposed TMD has two translational modes of vibration. Both of the modes can be active during the vibration because of existing the nonlinear terms in the motion equations and internal resonance phenomenon. The vibration modes of the TMD can become active due to 1:2 internal resonance occurrence. Activation of the both modes during the vibration, helps the nonlinear TMD to have a better performance. Proposed TMD can be designed even by using low damping ratios. Three plans are considered for the design and optimization of the novel TMD. In the first plan, the damping ratios of the TMD are relatively high. Moreover, the jump phenomenon does not take place. In two other plans, the nonlinear TMD system is capable of the jump phenomenon. The performance of the two-DOF nonlinear TMD depends on the excitation amplitude. In the higher excitation amplitudes, proposed TMD can outperform the optimal linear TMD. Finally, a novel mechanical design is presented for the proposed two-DOF TMD which allows it to experience large displacements without any problem. The novel design solves the problems of frequency mistuning in the proposed TMD, and the natural frequency of the TMD can be retuned.

Bi-directional semi-active tuned mass damper for torsional asymmetric structural seismic response control

Tuned mass damper (TMD) is a popular vibration absorber. To improve the seismic protection performance of a bi-directional passive TMD, a bi-directional semi-active TMD (BSTMD) with adaptive stiffness, variable mass and semi-active damping is proposed in this study. The BSTMD can adapt to structural X- and Y-directional instantaneous frequencies at the same time under bi-directional ground motions, which are identified through wavelet transform (WT), and the instantaneous angle of a diamond spring device is adjusted according to the instantaneous frequency ratio of two directions, which means that the stiffness ratio of two directions is retuned first. Then, the mass is retuned to match the exact instantaneous frequency. At last, the semi-active damping is realized according to an extended output signals-based control algorithm. A two-directional asymmetric torsional benchmark model is proposed as a case study. For comparison, two optimal passive TMDs implemented in X and Y directions separately and two unidirectional STMDs with variable stiffness and damping implemented in X and Y directions separately are investigated as well. Numerical results show that under bi-directional earthquake excitations in the benchmark problem, the two optimal passive TMDs have a good control effect. Two unidirectional STMDs have the best aseismic mitigation effect generally, in both lateral and torsional dynamic responses; while the BSTMD has a comparable control effect with less electromechanical devices, and can reduce the stroke of unidirectional STMD to a great degree. Though the BSTMD is aimed at X- and Y- directional dynamic responses, it can control torsional responses effectively as well, and when the eccentricity is enlarged to double, it remains effective for seismic mitigation.

TMD Design by an Entropy Index for Seismic Control of Tall Shear-Bending Buildings.

This study proposes a new arrangement-tuning method to maximize the potential of tuned mass dampers (TMDs) in decreasing the seismic responses of tall buildings. The method relies on a Grammian-based entropy index with the physical meaning of covariance responses to white noise without the involvement of external inputs. A twelve-story RC frame-shear wall building was used as an example to illustrate the method. Indices were computed for the building with TMDs placed on different stories and tuning to different modes and were compared with responses to white noise (colored) time histories. Results showed that greater index reduction cases agree well with greater story-drift reductions cases, despite the differences in the time step of the white noises and structural model types (pure shear vs. shear-bending), and the optimal TMD is not necessarily the traditional "roof-1st mode tuning" case. Comparisons were also made for the shear-bending building under seven earthquake excitations. It is found that, though TMDs are not full-band effective controllers, the index-selected TMDs still perform the best in three out of seven earthquakes. So, the proposed internal-property-based entropy index provides a good controller design for large-scale structures under unpredictable none-stationary excitations.

Passive-Tuned Mass Dampers for the Pointing Accuracy Mitigation of VLBI Earth-Based Antennae Subject to Aerodynamic Gust

This paper proposes an optimization procedure to achieve the best configuration of multiple degrees of freedom Tuned Mass Dampers (TMDs) to mitigate the pointing error of Very-Long-Baseline Interferometry (VLBI) Earth-based radio antennae operating under aerodynamic gust conditions. In order to determine the optimum sets of TMDs, a Multi-Objective design optimization employing a genetic algorithm is implemented. A case study is presented where fourteen operational scenarios of wind gust are considered, employing two models of atmospheric disturbances, namely the Power Spectral Density (PSD) function with a statistical profile presented by the Davenport Spectrum (DS) and a Tuned Discrete Gust (TDG) modeled as a one-minus cosine signal. It is found that the optimal configurations of TMDs are capable of reducing the pointing error of the antenna by an average of 66% and 50% for the PSD and TDG gust excitation scenarios, respectively, with a mass inclusion of 1% of the total mass of the antenna structure. The optimal TMD parameters determined herein can be utilized for design and field implementation in antenna systems, such that their structural efficiency can be enhanced for radio astronomy applications.

Design of Optimal Passive Tuned Mass Damper with Static Output Feedback and Updating Iterative Procedure

In this study, the optimal design issue of a passive tuned mass damper (TMD) was transformed into the nonsparse control gain matrix optimization problem, and a general passive TMD optimization design method to minimize structural mean square responses or impulse response is therefore proposed. The proposed optimization procedure combines the static output feedback (also known as direct output feedback) algorithm and the updating iterative procedure. The proposed method can be applied to variant design scenario, whether the main structure is single-degree-of-freedom (SDOF) or multidegree-of-freedom (MDOF) structures, undamped or damped structures, subjected to wind disturbances or earthquake excitations. In addition, the proposed method is capable to consider the excitation shaping filter, so the design results are more suitable for practical application. The design procedure of the proposed method is presented, and all the required weighting matrices are introduced and derived in detail. Firstly, the SDOF structures are used as the main structure to demonstrate the correctness of the proposed method. The numerical simulation results verify that the obtained optimal design parameters of TMD were found identical to some cases which contain the analytic solution. The accuracy and feasibility of the proposed design method are confirmed. Finally, a passive TMD is optimally designed for a 5-story MDOF structure subjected to Kanai–Tajimi spectrum comparable earthquakes and a 60-story high-rise MDOF structure subjected to Davenport spectrum comparable wind loads for demonstration.

Tuned Mass Damper Design for Vortex-Induced Vibration Control of a Bridge: Influence of Vortex-Induced Force Model

Existing studies optimized the tuned mass damper (TMD) for vortex-induced vibration (VIV) control of bridges based on an empirical linear model or Scanlan’s nonlinear model, which cannot accurately simulate the effect of the vortex-induced force and hence results in a TMD design that lacks effectiveness or robustness. Four vortex-induced force models are considered to systematically analyze the influence of force models on TMD design for VIV control. The design results based on various vortex-induced force models, as well as three design formulas, are compared in terms of effectiveness and robustness. Numerical results suggest that the empirical linear model and Scanlan’s nonlinear model significantly underestimate the TMD mass ratio required to suppress the VIV amplitude to be lower than a threshold. The empirical linear model may overestimate the robustness of the TMD to changing the frequency ratio, while Scanlan’s nonlinear model may overestimate or underestimate the robustness depending on the threshold VIV amplitude. The TMD design based on the polynomial model is considered more accurate since it can accurately predict VIV responses at various effective damping levels. The aerodynamic envelope model can be used as a convenient model for TMD optimization. The results generated using the free vibration formula are the closest to that of the polynomial model. An appropriate safety factor should be considered to convert the TMD design based on sectional model experiments to real bridges.

Effect of foundation embedment ratio in suppressing seismic-induced vibrations using optimum tuned mass damper

Tuned mass damper (TMD), which is used in structures to mitigate the dynamic responses caused by environmental loads, is tuned according to the dominant frequency of the structures. The dominant frequency of structure built on soil with low stiffness is significantly affected by the soil-structure interaction (SSI). In previous studies, only the surface foundation case is considered to investigate the design parameters of TMD considering SSI effects and the embedment depth of the foundation is neglected in these studies. Thus, this paper investigates the optimization of TMD for mitigation of responses of a high-rise building considering various depths of embedment and soil properties. The optimum parameters of TMD are investigated using five different optimization algorithms (i.e., simulated annealing, sequential quadratic programming, genetic algorithm, pattern search, and particle swarm optimization). The objective function minimizes the peak acceleration amplitude at the top of the structure. The effectiveness of optimum TMD is verified to use 20 near-fault pulse-like ground motions. The comparisons show that the embedment ratio of the foundation and the soil properties significantly affect the optimization of TMD.