Optimal TMD Research Articles

Tuned two-mass dampers for vibration control of offshore platforms

A Tuned Two-Mass Damper (TTMD) for minimizing vibrations of an offshore platform is developed in this study. TTMD is a passive vibration absorber, and it consists of two parallel undamped tuned mass dampers connected by a dashpot. The influences of its parameters on the vibration absorption capacity are studied through numerical examples. Next, the optimum parameters of TTMD are found, and the performance and robustness of TTMD are determined. The results from this study show that, for absorbing the structural vibration, an optimum TTMD is more effective than a conventional TMD with the same weight as TTMD. In other words, using TTMD significantly reduces the added weight to the main structure compared with using TMD based on the same condition and obtained effectiveness. Moreover, while maintaining the same performance and weight, an optimum TTMD is much more robust than an optimum TMD for resisting the change in structural stiffness.

Pole-Placement-Based Calibration of an Electromagnetically Realizable Inerter-Based Vibration Absorber (IDVA) for Rotating Wind Turbine Blades

This paper deals with edgewise vibration mitigation of rotating wind turbine blades by means of inerter-based vibration absorber (IDVA), which can be realized both mechanically and electromagnetically. Introducing the electromagnetically-realizable IDVA to the blade forms a 3-degree-of-freedom (3-DOF) blade-IDVA system consisting of the rotating blade, an absorber, and a series inerter-dashpot-spring subsystem. Analytical optimal design formulas of the rotating blade-installed IDVA are then derived using a pole-placement method where the equal-modal-damping-ratio principle and the triple-root-bifurcation condition are applied. The analytical formulas show that the optimal parameters for the blade-IDVA system merely depend on the spinning speed of the rotor given the IDVA location and the absorber mass. Numerical results of the NREL 5 MW wind turbine with optimal IDVA show that optimal IDVA leads to superior performance than optimal TMD in mitigating the blade edgewise vibration and behaves nearly as same as optimal RIDTMD, along with slightly optimal damper parameters variation. This means that the inerter-dashpot-spring system can be deployed flexibly for damping edgewise vibrations of rotating blades.

A piezoelectric tuned mass damper for simultaneous vibration control and energy harvesting

This work proposes a novel piezoelectric tuned mass damper (PE-TMD) with dual function of energy harvesting and vibration control. The dual function is achieved by introducing several piezoelectric transducers into the conventional TMD. Unlike the conventional TMDs, the stiffness and damping of the PE-TMD can be adjusted by changing the circuit resistance. Moreover, the vibration energy absorbed from the primary structure, which is dissipated by the conventional TMD in the form of thermal energy, can be efficiently converted into electrical energy by the piezoelectric transducers for reuse. A railway bridge is selected as the research object to investigate the performance of the PE-TMD. The electromechanical coupling equations between the bridge and the PE-TMD are given first and then verified by a scaled model experiment. The results show the feasibility of the PE-TMD to achieve the two functions of vibration control and energy harvesting simultaneously. Subsequently, the parameters optimized results show that when the damper is completely replaced by the piezoelectric transducers, the two functions can be optimized simultaneously. The expressions for the optimal parameters to optimize the two functions are derived separately, and they are consistent. Finally, the performance comparison with the optimal conventional TMD shows that the optimal PE-TMD exhibits a slightly better performance in vibration control, and its output electrical power is almost identical to the dissipated power by the conventional TMD.

Damage-based design of multiple tuned mass dampers to improve the seismic performance of steel frame structures

Tuned mass dampers are robust tools that can control the undesired vibrations induced by wind and earthquakes. Although vibration control systems such as tuned mass dampers have been used many times by researchers to reduce roof displacement, story drift ratio, and roof acceleration, no research has been reported regarding the reduction of damage's value in the structure. Therefore, in this paper, a three-bay ten-story steel frame building is modeled using the OpenSees software. The building is excited by an earthquake. The Park-Ang damage index is utilized here as an objective function to determine the optimum TMD numbers and parameters. The optimal numbers and properties of TMD systems are calculated by a hybrid binary and real-coded particle swarm optimization (PSO) algorithm. The results indicate the ability of multiple tuned mass dampers to reduce the overall damage and damage stories' values. The results show that this objective function also decreases the maximum drift ratio, residual displacements, and roof displacements. It will lead to improving the seismic performance of the structure. Also, the results show that the damage values are distributed uniformly along with the structure's height by selecting the appropriate domain for the value of the story's damage. A comparison between the proposed method and the Den-Hartog method shows that the proposed method's ability to improve the structure's seismic performance is greater than the classical methods. It can also be concluded from the results that by optimally adjusting the parameters of the control system, the residual displacement of the roof and the displacement of the roof have been reduced by 68.91% and 66.01%, respectively.

Vibration suppression of multi-component floating structures via passive TMDs and Bayesian ascent

This paper aims to achieve vibration suppression for multi-component floating structures under ocean waves. To this end, a multiple-passive-TMD (tuned mass damper) structure is employed, and a numerical model is developed incorporating both the dynamics of a hinged floating foundation and passive TMDs. A data-driven parameter optimization method is developed to search for optimal TMD parameters. This method is built upon Bayesian Ascent (BA) – an advanced sequential searching strategy for optimizing black-box functions, combining the merits of both the Bayesian Optimization method and the gradient-free trust-region algorithm. Simulation results under different wave conditions verify the effectiveness of the BA-based parameter selection method, showing that the resulting passive TMDs can significantly reduce the vibration of the whole floating structure.

Optimal TMD design for torsional balance of asymmetrical 3D structures considering soil–structure interaction

Optimal TMD design for torsional balance of asymmetrical 3D structures considering soil–structure interaction

The effect of soil-structure interaction on longitudinal seismic responses of suspension bridges controlled by optimal TMD

Suspension bridges contain high towers due to having long span. Large height makes them to experience remarkable displacement responses against dynamic loading, like seismic excitation which disturbs their performance. In order to overcome this problem, control strategies, like tuned mass damper or in brief TMD as a passive system can be used. The performance of these systems can be addressed by the indices defined according to structural responses. On the other hand, its parameters should be adjusted to their optimum values to providing the best performance accessible by the meta heuristic algorithm. Here, the seismic displacement and energy responses of the Golden gate bridge considering soil-structure interaction were investigated using the optimum TMD optimized by observer teacher learner algorithm, and the performance of it was addressed by the energy indices. The results indicated that by increasing the softness of the bed soil the first mode plays the dominant role in the final response. Also, TMD was a successful system to control the vibration of the tower-pier system according to the defined energy indices for all the conditions of the bed soil considered. Suspension bridges contain high towers due to having long span. Large height makes them to experience remarkable displacement responses against dynamic loading, like seismic excitation which disturbs their performance. In order to overcome this problem, control strategies, like tuned mass damper or in brief TMD as a passive system can be used. The performance of these systems can be addressed by the indices defined according to structural responses.

Optimal dynamic control for a maglev vehicle moving on multi-span guideway girders

Abstract An optimal control algorithm using a virtual tuned mass damper called virtual TMD to control the levitation force of a magnetic system is developed for resonance suppression of a maglev vehicle moving on multi-span guideway girders. Since the optimal dynamic parameters of a TMD in vibration control are well developed, the optimal tuning gains required to control the magnetic oscillations of the maglev bogie can be directly used and fed back to the maglev control system. To address the dynamic interaction analysis from the maglev vehicle to the guideway girders and vice versa, the entire coupling system is decomposed into two subsystems, one is the moving vehicle subsystem and another the stationary guideway subsystem. Then, an incremental–iterative procedure associated with the Newmark method is presented to solve the two sets of subsystem equations. Finally, the control effectiveness and parametric studies of the optimal virtual TMD scheme on resonance reduction of the moving maglev vehicle are demonstrated.

Inerter-enhanced tuned mass damper for vibration damping of floating offshore wind turbines

This paper investigates the use of an inerter-enhanced vibration absorber, the rotational inertia double tuned mass damper (RIDTMD), for damping in-plane vibrations of a floating offshore wind turbine (FOWT). First, a 17-degree-of-freedom (17-DOF) aero-hydro-servo-elastic model for the FOWT is developed and verified, based on which the damper performance can be evaluated in the time domain (TD) with realisitc load conditions. Next, a reduced-order 6-DOF model is established for the RIDTMD-controlled FOWT in-plane vibrations including rotor mass moment of inertia, hydrodynamic added mass, as well as stiffness contributions from mooring lines and buoyancy. This model enables revealing the dynamics of the coupled spar-tower-RIDTMD system, and provides an efficient yet robust procedure for optimal tuning of the FOWT-mounted RIDTMD in the frequency domain (FD). Comparison of the optimal RIDTMD and the optimal TMD is performed in both FD and TD. It is seen that both TMD and RIDTMD effectively suppress tower side-side vibrations when mounted at the tower top. RIDTMD consistently outperforms TMD due to the extra DOF (extra resonance) introduced into the device, at the cost of slightly larger damper stroke. Both dampers positively influence spar roll motion and blade edgewise vibration as well.

Optimal calibration of the rotational inertia double tuned mass damper (RIDTMD) for rotating wind turbine blades

This paper presents the closed-form formulas for optimal calibration (tuning) of the rotational inertia double tuned mass damper (RIDTMD) for damping edgewise vibrations in rotating wind turbine blades. A 3-DOF model is first established for the rotating blade-RIDTMD system, based on which the optimal calibration formulas are derived by means of pole-placement method. Equal modal damping criterion is applied together with the utilization of the triple-root bifurcation point. It is seen from the derived closed-form formulas that the optimal damper parameters depend explicitly on the rotor rotational speed. Comparison of the optimal RIDTMD and the optimal TMD is performed using the NREL 5 MW wind turbine as the numerical example. Results indicate superior performance of the RIDTMD in damping blade vibrations comparing with the TMD, at the cost of slightly increased damper stroke.

A low-cost and efficient d33-mode piezoelectric tuned mass damper with simultaneously optimized electrical and mechanical tuning

This paper proposes a low-cost and efficient piezoelectric tuned mass damper (Piezo-TMD) for structural vibration reduction and energy harvesting. The Piezo-TMD consists of not only a proof mass, piezoelectric materials deforming in the d33 mode, and an electrical resistance, but also a spring and an inductor which enable the mechanical frequency and electrical frequency of the Piezo-TMD to be tuned to the structural resonance frequency. The equations of motion of a structure with the Piezo-TMD are derived, and an optimal design procedure for the Piezo-TMD is proposed to achieve a simultaneous maximum vibration reduction and energy harvesting. The performance of the Piezo-TMD is compared with that of a conventional optimal TMD installed in a footbridge under a pedestrian loading. The simulation results show that the Piezo-TMD performs better than the optimal conventional TMD in terms of vibration reduction while efficiently converting the absorbed mechanical energy to electricity with a high energy harvesting ratio. The innovative development of simultaneously tuning the mechanical and electrical systems leads to a much lower number of PZT stacks (saving 88% of piezoelectric materials in an illustrated case). The parametric study shows that the Piezo-TMD achieves the best performance when the optimal values for the spring stiffness, resistance, inductance, and the number of piezoelectric stacks are adopted from the proposed optimal design. If the selected spring stiffness and inductance are uncertain in a range between 0.94-1.07 times the optimal values, the vibration reduction performance of the Piezo-TMD remains similar, and the energy harvesting performance reduces less than 5%, as compared to the optimal performance. The effect of the number of piezoelectric stacks was also investigated. An insufficient number of piezoelectric stacks reduces the Piezo-TMD performance, and an excessive stack number does not improve the Piezo-TMD performance but increases the Piezo-TMD cost. Finally, the proposed Piezo-TMD employs inductance to significantly reduce the PZT stack number, thereby significantly reducing the cost of Piezo-TMDs.

Seismic design of passive tuned mass damper parameters using active control algorithm

Tuned mass dampers are a widely-accepted control method to effectively reduce the vibrations of tall buildings. A tuned mass damper employs a damped harmonic oscillator with specific dynamic characteristics, thus the response of structures can be regulated by the additive dynamics. The additive dynamics are, however, similar to the feedback control system in active control. Therefore, the objective of this study is to develop a new tuned mass damper design procedure based on the active control algorithm, i.e., the H2/LQG control. This design facilitates the similarity of feedback control in the active control algorithm to determine the spring and damper in a tuned mass damper. Given a mass ratio between the damper and structure, the stiffness and damping coefficient of the tuned mass damper are derived by minimizing the response objective function of the primary structure, where the structural properties are known. Varying a single weighting in this objective function yields the optimal TMD design when the minimum peak in the displacement transfer function of the structure with the TMD is met. This study examines various objective functions as well as derives the associated equations to compute the stiffness and damping coefficient. The relationship between the primary structure and optimal tuned mass damper is parametrically studied. Performance is evaluated by exploring the h2-and h∞-norms of displacements and accelerations of the primary structure. In time-domain analysis, the damping effectiveness of the tune mass damper controlled structures is investigated under impulse excitation. Structures with the optimal tuned mass dampers are also assessed under seismic excitation. As a result, the proposed design procedure produces an effective tuned mass damper to be employed in a structure against earthquakes.

Optimum earthquake-tuned TMDs: Seismic performance and new design concept of balance of split effective modal masses

The present paper, concerning the performance of optimum TMDs in seismic engineering, is composed of two parts. First, Part I deals with a comprehensive investigation on the effectiveness of an optimum seismic-tuned TMD towards reducing the earthquake response of linear frame structures, which is set up by a dedicated optimisation algorithm, allowing to achieve the best control device for a specific structural system and earthquake event. First, a representative set of 16 primary structures and 18 selected earthquakes has been considered, for a total of 288 cases. Second, additional trials based on a benchmark 10-storey frame and on a codified set of far-field earthquakes (FEMA P695 database), composed of 2×22=44 records, have been developed, for a further assessment. The presented outcomes provide extensive information about the TMD performance in the seismic engineering scenario, for a-priori known seismic input. Then, Part II reports a comprehensive post-processing and interpretation analysis of the results above. Specifically, connections between seismic TMD performance and modal structural properties are envisaged. Cross-comparisons, presented here through typical sample cases, analyse the changes of the structural characteristics after TMD insertion and monitor the associated effects on the seismic response reduction. The crucial role of achieving a balanced split of effective modal masses on the tuned mode is investigated, and highlighted as an essential ingredient to rely on a high TMD effectiveness in the seismic context. This criterion may be implemented within the tuning process, as a basic true structure-based concept for TMD design in Earthquake Engineering applications, thus for a-priori unknown seismic input.

LQR-based optimization of multiple tuned resonators for plate sound radiation reduction

A linear quadratic regulator based optimization problem is formulated in order to minimize the broad-band low-frequency domain vibration and acoustic response of a baffled simply supported plate by means of multiple optimally tuned mass–spring–damper systems. To this end, we propose a robust method to obtain a (stable) state–space model describing the far-field radiated sound power, also known as the radiation filter. The Kirchhoff plate equation, which describes the plate vibrations, is discretized based on the Rayleigh–Ritz method. The resulting state–space models of the plate and the mass–springdamper systems are coupled to the radiation filter. Finally, the optimal spring stiffness and damping values of each mass–spring–damper system are successfully obtained by minimizing the kinetic energy or the far-field radiated sound power of the plate for low computational cost. In general, the results indicate that tuned mass-spring-damper systems have great potential to reduce the broadband low frequency vibration and acoustic response of vibro-acoustic systems. From the results, it can be concluded that there are fundamental differences between the optimal TMD systems if one minimizes the kinetic energy or the far-field radiated sound power.

Response of discussion “Estimating optimum parameters of tuned mass dampers using harmony search”

In the discussion of Saberi et al., the optimum TMD parameters obtained by using Harmony Search (HS) algorithm were investigated for two different method. These methods are mode superposition method and expressing governing equations in state space format. In original paper, modal superposition method was used as defined. In this response, the optimization process was repeated for the same numerical examples by directly solving coupled equations of motion.

Study on semi-active tuned mass damper with variable damping and stiffness under seismic excitations

SUMMARY In the present study, a semi-active tuned mass damper (STMD) with variable damping coefficient and stiffness is evaluated under seismic excitations. Variation of the damping ratio of the STMD is implemented through tracking the displacement of the STMD.If the tracked amplitude of the STMD is increasing, damping ratio of the STMD is set to zero, or else it is set to an appropriate nonzero value. Stiffness of the STMD is tuned through tracking the displacement of the primary structure, which is analyzed using a short-time Fourier transform-based control algorithm. Both far-field and near-fault ground motions are used to examine the effectiveness of the STMD and the control algorithm. Displacement time history and response (displacement and acceleration) spectra are obtained for the cases of an optimal passive TMD and an STMD. It is found that the STMD with variable damping ratio and frequency can effectively attenuate the seismic responses and outperform the optimal passive TMD. In addition, results are obtained for the case that damage occurs to the primary structure during an earthquake. The study indicates that the STMD controlled by the proposed algorithm can rapidly capture the variation of the structure and remains tuned with the primary structure, whereas the optimal TMD becomes off-tuned when damage occurs. Copyright © 2013 John Wiley & Sons, Ltd.

The Applied Research on TMD Control in Structures for Seismic Protection

Based on the theoretical analysis of the dynamic parameters of multi-DOF complex structures, it is shown that the optimum TMD parameters under the harmonic base excitation are not the exact optimization for seismic protection, whose main reason is that the optimum damping ratio of TMD for seismic protection is obviously lower than that under the harmonic base excitation. In this paper, an effective TMD design method is developed to control the seismic responses of many-degree-of-freedom complex structures. The EI-Centro seismic wave is introduced as the excitations and the approach to determining the optimum TMD parameters for seismic protection is effectively solved. Then with the case to design the TMD of a series reactor, the optimum TMD parameters for seismic protection are obtained. Its result proves that the designed TMD is able to reduce the seismic responses of the series reactor significantly, and this approach can provide a reference for the TMD design for seismic protection of other multi-DOF structures.

A comparison between different optimization criteria for tuned mass dampers design

Tuned mass sampers (TMDs) are widely used strategies for vibration control in many engineering applications, so that many TMD optimization criteria have been proposed till now. However, they normally consider only TMD stiffness and damping as design variables and assume that the tuned mass is a pre-selected value. In this work a more complete approach is proposed and then also TMD mass ratio is optimized. A standard single degree of freedom system is investigated to evaluate TMD protection efficiency in case of excitation at the support. More precisely, this model is used to develop two different optimizations criteria which minimize the main system displacement or the inertial acceleration. Different environmental conditions described by various characterizations of the input, here modelled by a stationary filtered stochastic process, are considered. Results show that all solutions obtained considering also the mass of the TMD as design variable are more efficient if compared with those obtained without it. However, in many cases these solutions are inappropriate because the optimal TMD mass is greater than real admissible values in practical technical applications for civil and mechanical engineering. Anyway, one can deduce that there are some interesting indications for applications in some actual contexts. In fact, the results show that there are some ranges of environmental parameters ranges where results attained by the displacement criterion are compatible with real applications requiring some percent of main system mass. Finally, the present research gives promising indications for complete TMD optimization application in emerging technical contexts, as micromechanical devices and nano resonant beams.

Using upper storeys as semi-active tuned mass damper building systems

This paper presents an exploratory case study based analysis of the seismic performance of multi-storey passive and semi-active tuned mass damper (PTMD and SATMD) building systems are investigated for 12-storey moment resisting frames modelled as ‘10+2’ storey and ‘8+4’ storey. Segmented upper stories of the structure are isolated as a tuned mass, and a passive viscous damper or semi-active resetable device is adopted for energy dissipation. Optimum TMD control parameters and appropriate matching SATMD configurations are adopted from a companion study on a simplified two degree of freedom (2-DOF) system. Log-normal statistical performance results are presented for 30 probabilistically scaled earthquake records. The time history analysis and normalised reduction factor results show the response reductions for all seismic hazards. Thus, large SATMD systems can effectively manage seismic response for multi degree of freedom (MDOF) systems across a broad range of ground motions in comparison to passive solutions. This research demonstrates the validity of the TMD building systems for consideration in future design and construction. It also provides a template for the design and analysis of passive or semi-active TMD buildings utilising large masses, or more efficiently, added storys, for improving seismic response performance.

Optimum properties of multiple tuned mass dampers for reduction of translational and torsional response of structures subject to ground acceleration

The application of multiple tuned mass dampers (MTMD) with identical stiffness and damping coefficient but different mass for suppressing translational and torsional responses is discussed for a simplified two-degree-of-freedom (2DOF) structure, able to represent the dynamic characteristics of general asymmetric structures subject to ground motions. This 2DOF structure is a generalized 2DOF system of an asymmetric structure with predominant translational and torsional responses under earthquake excitations using the mode reduced-order method. Depending on the ratio of the torsional to the translational eigenfrequency, i.e. the torsional to translational frequency ratio (TTFR), of asymmetric structures, the following cases can be distinguished: (1) torsionally flexible structures (TTFR<1.0), (2) torsionally intermediate stiff structures (TTFR=1.0), and (3) torsionally stiff structures (TTFR>1.0). Taking into account the even placement of the MTMD within the width of the asymmetric structure, a careful examination of the effects of the normalized eccentricity ratio (NER) on the performance of the MTMD are carried out with resort to the provided analytical expressions for the dynamic magnification factors (DMF) of both the translational and torsional responses of the asymmetric structure. Extensive numerical simulations have been performed to accurately estimate the dynamic characteristics of the MTMD for asymmetric structures subject to ground acceleration. In the simulations, the dimensionless DMF parameters, bounded between zero and unity, are used as the formal indexes estimating the effectiveness of the MTMD in reducing both the translational and torsional responses of the asymmetric structure. A new basic result is that the NER affects significantly the performance of the MTMD for both torsionally flexible and torsionally intermediate stiff structures; while the influence of the NER is rather negligible on the performance of the MTMD for torsionally stiff structures, thus implying that in such a case the MTMD may be designed by ignoring the effects of torsional coupling. Likewise, the effectiveness and robustness of the MTMD strategies with different layouts are also investigated and demonstrated for the case of mitigating the torsional response of asymmetric structures, thus providing valuable guidance for the MTMD design. Furthermore, the frequency response curves of asymmetric structures without and with both the optimum MTMD and TMD are plotted for the three cases of TTFR as well, consequently obtaining some very useful results.