Variable Stiffness Tuned Mass Damper Research Articles

Experimental study on adaptive-passive tuned mass damper with variable stiffness for vertical human-induced vibration control

Serviceability problem and human-induced vibration control of slender footbridges are of increasing interest to structural engineers. Passive tuned mass dampers (TMDs) have a wide range of applications in human-induced vibration control. However, a passive TMD is sensitive to the frequency deviation and, as a result a mistuned TMD will lose its control effect. An adaptive TMD can solve the mistuning problem of a passive TMD. However, there is few adaptive TMDs with variable stiffness in this issue. To fill this gap, an adaptive-passive variable stiffness TMD (APVS-TMD) is proposed in this study. The stiffness and frequency of APVS-TMD can be retuned through changing the length of free end of cantilever beam, while the damping can be retuned by adjusting the air gap between the conductor plate and magnets. As for the target natural frequency to be adjusted, the first two modal frequencies of the TMD-structure coupled system are identified under ambient excitation first, and then, the decoupled structural natural frequency is obtained according to the developed method based on the undamped 2-degree of freedom (DOF) modal analysis. By means of numerical simulation, the identification strategy is verified using a SDOF lumped mass main structure and an ideal simply supported beam model. Then, the identification and stiffness retuning operations of the APVS-TMD are further verified through a footbridge model experiment. Here, control effects of the APVS-TMD to walking- and running-induced vibrations are highlighted and compared with those of a mistuned TMD. Experimental results show that the APVS-TMD can identify the decoupled structural natural frequency from the coupled system accurately, and control human-induced vibrations effectively.

Dynamics Analysis of a Variable Stiffness Tuned Mass Damper Enhanced by an Inerter

A tuned mass damper with variable stiffness can achieve vibration reduction without changing the resonant frequency, but the large mass limits its engineering applications. To overcome this drawback, a novel tuned mass damper is proposed with the stiffness adjusted by a PI controller and the mass block replaced by an inerter. The tuned mass damper is attached to a two-degrees-of-freedom primary structure, and the dynamic equations are established. The frequency responses are obtained from a harmonic balance method and verified by numerical simulations. With the mass block of the tuned mass damper replaced by an inerter, the additional weight is reduced by 99%, and the vibration reduction performances are improved, especially in large excitation conditions. The vibration reduction rate increases with larger negative stiffness ratio and larger inertance ratio, while unstable responses appear with the parameters exceeding the thresholds. The optimum negative stiffness ratio and inertance ratio are searched by a frequency change indicator, and the maximum vibration reduction rate can reach 87.09%. The impulse response analysis shows that the proposed tuned mass damper improves the energy absorption rate. The primary structure and the vibration absorber engage in 1:1, 1:2, and 1:3 internal resonance with different impulse amplitudes. This paper aims to promote and broaden the engineering applications of the variable stiffness system and the inerter.

Vibration control of offshore wind turbine under multiple hazards using single variable-stiffness tuned mass damper

With high flexibility and low damping, offshore wind turbines (OWTs) are prone to external vibrations such as wind, wave and earthquake, either attacked individually or as combined loading cases. This study proposes a semi-active variable-stiffness tuned mass damper (VSTMD) with magnetorheological elastomer (MRE) materials to mitigate undesired dynamic responses of OWT. A jacket supported OWT with MRE-TMD installed at the top of the tower is adopted as an example to demonstrate the effectiveness of the proposed design under multiple hazards. A semi-active frequency tracing algorithm is proposed through which the current-dependent stiffness of MRE-TMD is controlled by tracking the acceleration of OWT tower. The numerical results demonstrate that the semi-active MRE-TMD can effectively attenuate the dynamic responses of OWT under multi-hazard loadings, and it outperforms the passive TMD in reducing the peak and RMS displacements of tower structure. Robustness analysis of semi-active MRE-TMD is also validated by considering OWT sudden loss of partial stiffness under multiple-loadings.

Identification and semi-active control of structures with abrupt stiffness degradations

This paper presents for variable stiffness tuned mass dampers (VS-TMDs) a vibration control algorithm combined with a nonlinear system identification method. The objective of the proposed approach is the control of multistory shear frame structures, which exhibit abrupt stiffness degradations. A stiffness variable control (SVC) algorithm is developed to control the stiffness of the VS-TMD, which is based on the mitigation of the potential energy of the structure. For the identification of the system parameters, an adaptive unscented Kalman filter (A-UKF) scheme is utilized. The paper describes the theoretical background of the proposed approach with its governing equations and conducts performance studies on a semi-actively controlled 2-story shear frame structure. Harmonic, white noise and earthquake excitation scenarios including seismic aftershock effects are investigated. Sensitivity studies are conducted. With the proposed approach, the abrupt stiffness changes of the structure are detected and the damper stiffness is adapted successfully. The results show that the SVC together with the A-UKF clearly outperforms the passive TMD control.

Study on the fluctuating wind responses of constructing bridge towers with magnetorheological elastomer variable stiffness tuned mass damper

Constructing bridge towers are high-rise and flexible structures subjected to significant wind induced vibrations. Tuned Mass Dampers (TMDs) have been widely used to reduce dynamic responses of high-rise structures under fluctuating wind loadings. By resonance with main structure, TMD can effectively suppress structural vibrations. However, the natural frequencies of bridge tower usually decrease continuously during its construction progress. The frequency shift characteristic will cause the detune of TMD, leading to a great control efficiency loss. As a novel stiffness tunable device made of magnetorheological elastomer (MRE), MRE-TMD can adjust its natural frequency in real-time to track the main structure, avoid detuning and achieve better control performance. To study the wind induced vibration control performance of MRE-TMD, this paper explores the fluctuating wind responses of constructing bridge towers in along wind and cross wind directions. The fluctuating wind loads are generated by harmonic superposition method with the along wind fluctuating wind speed spectrum and the empirical power spectrum of fluctuating lift force. By comparing among the uncontrolled, TMD controlled and MRE-TMD controlled constructing bridge towers, the simulation results show that the MRE-TMD system can effectively maintain the tuning state, and significantly reduce the wind induced vibrations during whole construction process.

Wind-induced vibration control of a constructing bridge tower with MRE variable stiffness tuned mass damper

With the rapidly increasing number of long span bridges being built all over the world, the wind-induced vibrations of their constructing high bridge towers are becoming a serious issue. These vibrations will discomfort workers, affect construction accuracy, lead to construction period delay, and sometimes even cause accidents. Tuned mass dampers (TMDs) are well accepted to have a good performance in wind-induced vibration control under the condition that their natural frequencies are tuned to the natural frequencies of the main structures. However, as the natural frequencies of the bridge towers keep varying during its construction, their wind-induced vibrations can hardly be controlled by conventional TMDs. To improve the control efficiency, a novel magnetorheological elastomer variable stiffness tuned mass damper (MRE VSTMD) was proposed to retune the system. To verify the efficiency of the proposed system, a constructing bridge tower was modeled analytically and the corresponding MRE VSTMD was designed. Simulations were carried out and evaluations were made among the uncontrolled, passive controlled and semi-active controlled structures. It is proved that the proposed MRE VSTMD can improve the performance of passive TMDs by up to 40%. It is also observed that the softening behavior can double the stiffness variable range of MRE layers, indicating MRE VSTMD’s potential to further improve its performance with time varying excitation powers.

Study on an improved variable stiffness tuned mass damper based on conical magnetorheological elastomer isolators

Use of a variable stiffness tuned mass damper (VSTMD) is an effective approach to reduce the dynamic responses of a structure with shifting natural frequencies. Magnetorheological elastomer (MRE) isolators can be used to build VSTMD due to their tunable stiffness by applying a magnetic field. However, conventional MRE isolators show deformation limits, huge energy consumption and uneconomic production. Focused on developing a MRE VSTMD system to improve this situation, a conical MRE isolator has been proposed and tested. Compared to conventional MRE isolators, the conical isolator shows much higher efficiency, better overall stability, greater deformability and a larger tunable range. The experimental results indicate that the prototype can provide a 46.29% increase in frequency and a 75 N control force range with a 25 W power source. The quick responding MRE VSTMD system has the potential to accurately provide the desired stiffness in two directions to achieve a better structure control.

Invited Review: Recent developments in vibration control of building and bridge structures

This paper presents a state-of-the-art review of recent articles published on active, passive, semi-active and hybrid vibration control systems for structures under dynamic loadings primarily since 2013. Active control systems include active mass dampers, active tuned mass dampers, distributed mass dampers, and active tendon control. Passive systems include tuned mass dampers (TMD), particle TMD, tuned liquid particle damper, tuned liquid column damper (TLCD), eddy-current TMD, tuned mass generator, tuned-inerter dampers, magnetic negative stiffness device, resetting passive stiffness damper, re-entering shape memory alloy damper, viscous wall dampers, viscoelastic dampers, and friction dampers. Semi-active systems include tuned liquid damper with floating roof, resettable variable stiffness TMD, variable friction dampers, semi-active TMD, magnetorheological dampers, leverage-type stiffness controllable mass damper, semi-active friction tendon. Hybrid systems include shape memory alloys-liquid column damper, shape memory alloy-based damper, and TMD-high damping rubber.

Semiactive Control of Earthquake/Wind Excited Buildings Using Output Feedback

Output feedback control using Magnetorheological dampers and Variable Stiffness Tuned Mass Dampers is considered. Firstly, seismic response control of a building with MR dampers is considered. Optimal Static Output Feedback (OSOF) control yields the desired control force. Two laws are proposed to obtain voltage that achieves the desired force. OSOF yields a reduction in responses and CPU time vis-a-vis LQG and Passive-on controllers. Instantaneous Optimal Control is also considered. Next, a stiff and a flexible building are connected by a MR damper. Input voltage is predicted by a Recurrent Neural Network using desired control force from LQG/OSOF. Both output feedback controllers yield significant reduction in response and base shear and require much less control effort compared to passive-on control. Lateral-torsional seismic response control of plan asymmetric buildings connected by MR dampers is also studied. Finally, control of a wind excited benchmark building using a Variable Stiffness TMD is considered. The nominal stiffness corresponds to the fundamental frequency, resulting in an LTI system for which the desired control force is computed using OSOF/LQG control. A simple control law yields the device configuration. The present control is comparable with active-TMD and better than Short-time-Fourier-Transform control. A variable length pendulum TMD is proposed.

Design of self-tuneable mass damper for modular fixturing systems

Enhancing dynamic characteristics of fixtures for large workpieces is essential to assure chatter free machining of heavy-duty milling operations. Variable stiffness tuned mass dampers (VSTMD) can effectively improve the dynamic stiffness of modular fixtures by changing their dynamic characteristics. The theory of a new VSTMD concept is presented. Their realisable optimal tuning is determined and the results are compared to the standard constant stiffness TMDs. By means of the developed automatic tuning procedure, stiffness is varied via a rotary spring, while damping is provided by eddy currents. The prototype and the effectiveness of the concept are experimentally validated by heavy-duty milling tests on a modular fixture.

Vibration control performance of tuned mass dampers with resettable variable stiffness

Vibration control of civil engineering structures using tuned mass dampers (TMDs) is a widely acknowledged control strategy based on numerous analytical and experimental verifications. Although the design and application of traditional linear TMD systems are well established, nonlinear TMD systems that may have better control performance remain in the developmental stage. The TMD systems have two main problems, i.e. detuning effect and excessive TMD’s stroke. To improve the overall performance of TMD systems, a novel semi-active TMD named resettable variable stiffness TMD (RVS-TMD), is proposed. The RVS-TMD consists of an undamped TMD and a resettable variable stiffness device (RVSD). This RVSD is composed of a resettable element and a controllable stiffness element. By varying the stiffness of controllable stiffness element in the RVSD, force produced by the RVSD can be controlled smoothly through a semi-active control law. By operating the resettable element, the hysteretic loops of the RVSD can cover all four quadrants in the force–deformation diagram and, thus, increases energy dissipation. In other words, both stiffness and damping of the RVS-TMD are adjustable via only the RVSD device. The harmonic and seismic responses of a building equipped with the RVS-TMD were investigated. Numerical results show that the proposed RVS-TMD system can avoid detuning effect automatically and assure the optimal control performance as desired when the frequency of primary structure is changed.

LQR Control of Wind Excited Benchmark Building Using Variable Stiffness Tuned Mass Damper

LQR control of wind induced motion of a benchmark building is considered. The building is fitted with a semiactive variable stiffness tuned mass damper adapted from the literature. The nominal stiffness of the device corresponds to the fundamental frequency of the building and is included in the system matrix. This results in a linear time-invariant system, for which the desired control force is computed using LQR control. The control force thus computed is then realized by varying the device stiffness around its nominal value by using a simple control law. A nonlinear static analysis is performed in order to establish the range of linearity, in terms of the device (configuration) angle, for which the control law is valid. Results are obtained for the cases of zero and nonzero structural stiffness variation. The performance criteria evaluated show that the present method provides displacement control that is comparable with that of two existing controllers. The acceleration control, while not as good as that obtained with the existing active controller, is comparable or better than that obtained with the existing semiactive controller. By using substantially less power as well as control force, the present control yields comparable displacement control and reasonable acceleration control.

1A23 Vibration Control of Variable Stiffness Tuned Mass Damper with Consideration of Time Delay(The 12th International Conference on Motion and Vibration Control)

This study employed a resettable variable stiffness TMD (RVS-TMD) to alleviate detuning effect. The RVS-TMD is composed of a TMD and a resettable variable stiffness device (RVSD), which consists of a resettable element and a controllable stiffness element. By varying the stiffness element of RVSD, the detuning effect can be mitigated. While, by actuating the resettable element, the hysteresis loop of the RVSD can cover all four quadrants in the force-deformation diagram and thus result in more energy dissipation. However, to adjust the stiffness of the TMD system, the problem of time-delay is inevitable. For an active control system, time is consumed in data acquisition, data processing, on-line calculation, and control force execution. There is always a delay between the time at which the control force is assumed to be applied and actually applied, which may cause degradation in control efficiency. Therefore, the control design of a RVS-TMD system should take into account the effect of time delay. This study applied delayed control gains to alleviate the time delay effect based on the LQR optimal output feedback control algorithm. A parametric study was conducted to demonstrate the relationships of delayed gains with intentionally-added delay time. The results of numerical simulation show the application of optimally-delayed gains significantly alleviates the time delay effect and assure the desired control efficacy.

Bang-Bang and Semiactive Control with Variable Stiffness TMDs

A semiactive control strategy for the vibration control of structures using a stiffness varying tuned mass damper (TMD) with application of bang-bang control force to TMD is proposed. The control strategy involves a combination of controlling the response of structure using bang-bang control with a control force applied to the TMD, and the use of the principle of minimizing the maximum value of the frequency response function (FRF) for the coupled structure-variable stiffness TMD system. The optimal tuning parameter and damping ratio for the TMD are obtained based on this principle. When the control force is applied to the TMD, the TMD is simultaneously retuned (by varying the stiffness) in real time to achieve the minimax principle for the desired level of response reduction. When the active control is ineffective or is turned off, the damper system acts as a passive TMD. The performance of the control strategy is examined under harmonic excitations and is compared to previous results on bang-bang control and minimax shaping of the FRF when the TMD is not retuned in real time. In order to examine the robustness of the controller, a wind excitation obtained from the Davenport spectrum is applied to a structure with low natural frequency. The control strategy is shown to achieve substantial response reduction with relatively low control force requirements.

Effect of Geometrical Nonlinearity on the SAVIS Device

The excessive stroke of semi-active variable stiffness-tuned mass damper (SATMD) which causes large distortion is common in practice. The effects of the geometrical nonlinearity of the semi-active variable stiffness (SAVIS) device have been investigated and are described in this paper. An expression which includes the stiffness nonlinearity of the device is obtained. A cubic polynomial model of the equivalent stiffness is approximately obtained using the least squares interpolation method. First, the simplified coupled nonlinear equations with no forcing and no damping are approximately solved using the multiple scale method. The results show that the vibration frequency of the primary system can be modulated by the nonlinearity of the SAVIS device, and the 1:1, 1:3 and 3:1 internal resonance may occur in some conditions. Second, using the Runge-Kutta method, the iteration results are obtained under a full period sine-wave pulse and under the El Centro seismic record. Standard deviation (STD) responses and peak responses of the system are calculated for different damping ratios and different local frequency ratios. The power spectra distribution (PSD) of the response of a nonlinear system shows that the local frequency will be shifted, and the effect on the vibration control of the main structure is much better for a nonlinear case than for a linear case as the frequency ratio is less than one under both the sine-wave pulse and the El Centro seismic excitation.

Structures with Semiactive Variable Stiffness Single/Multiple Tuned Mass Dampers

This paper proposes application of single and multiple semiactive variable stiffness tuned mass dampers (STMD/SMTMD) for response control of multistory structures under several types of excitation. A new semiactive control algorithm is developed based on real-time frequency tracking of excitation signal by short time Fourier transform. A parametric study is performed in the frequency domain to investigate the dynamic characteristics and effectiveness of STMDs. Time history responses of single-degree-of-freedom and five-degree-of-freedom structures equipped with STMDs at the roof level, subjected to harmonic, stationary, and nonstationary excitations are presented. STMD/SMTMD are most effective when they have low damping ratios and the excitation frequency can be tracked. They are superior than their passive counterparts in reducing the response of the main structure both under force and base excitations. In case the fundamental frequency changes due to damage or deterioration of the main structure then th...

Short time Fourier transform algorithm for wind response control of buildings with variable stiffness TMD

The new semi-active variable stiffness tuned mass damper (SAIVS-TMD) system, developed by the authors, is capable of continuously varying its stiffness and retuning its frequency in real time. The tuned mass damper (TMD) system can only be tuned to a fixed frequency, which is the first mode frequency of the building. The SAIVS-TMD system is robust to changes in building stiffness and damping. The short time Fourier transform (STFT) is the most widely used method for studying non-stationary signals. The basic idea of short time Fourier transform is to break up the signal into small time segments and Fourier analyze each time segment to ascertain the frequencies that exist in it. For each different time a different spectrum is obtained and the totality of these spectra is the time–frequency distribution. The new idea proposed in this study is to use STFT to identify the dominant frequency of response, and track its variation as a function of time to retune the SAIVS-TMD. The effectiveness of a SAIVS-TMD controlled by the new STFT algorithm for response reduction of a wind excited tall building is investigated in this study. An analytical model of the tall building with time varying stiffness of SAIVS-TMD is developed. The frequency tuning of the SAIVS-TMD is achieved by a new time frequency algorithm based on STFT. It is shown that the SAIVS-TMD can reduce the structural response, when compared to the uncontrolled case and the case with TMD. SAIVS-TMD is particularly effective in reducing the response when the building stiffness changes; the TMD loses its effectiveness under building stiffness variations. The response reductions due to an active tuned mass damper can also be achieved by SAIVS-TMD—with an order of magnitude less power consumption—with the STFT algorithm.

Wind Response Control of Building with Variable Stiffness Tuned Mass Damper Using Empirical Mode Decomposition/Hilbert Transform

The effectiveness of a novel semiactive variable stiffness-tuned mass damper ~SAIVS-TMD! for the response control of a wind-excited tall benchmark building is investigated in this study. The benchmark building considered is a proposed 76-story concrete office tower in Melbourne, Australia. It is a slender building 306 m tall with a height to width ratio of 7.3; hence, it is wind sensitive. Across wind load data from wind tunnel tests are used in the present study. The objective of this study is to evaluate the new SAIVS-TMD system, that has the distinct advantage of continuously retuning its frequency due to real time control and is robust to changes in building stiffness and damping. In comparison, the passive tuned mass damper ~TMD! can only be tuned to a fixed frequency. A time varying analytical model of the tall building with the SAIVS-TMD is developed. The frequency tuning of the SAIVS-TMD is achieved based on empirical mode decomposition and Hilbert transform instantaneous frequency algorithm developed by the writers. It is shown that the SAIVS-TMD can reduce the structural response substantially, when compared to the uncontrolled case, and it can reduce the response further when compared to the case with TMD. Additionally, it is shown the SAIVS-TMD reduces response even when the building stiffness changes by 615% and is robust; whereas, the TMD loses its effectiveness under such building stiffness variations. It is also shown that SAIVS-TMD can reduce the response similar to an active TMD; however, with an order of magnitude less power consumption.