Nonlinear Tuned Mass Damper Research Articles

Equivalent continuous method based novel design of a nonlinear TMD with piecewise stiffness

Tuned mass Dampers (TMDs) are extensively used passive control devices for high-rise buildings to mitigate undesirable responses. In practice, limit devices are frequently applied due to the large displacement of TMD, resulting in the emergence of piecewise nonlinearity. In this study, a TMD with piecewise stiffness (PSTMD) is developed to investigate the piecewise nonlinearity, including piecewise linear stiffness (PLS) and piecewise nonlinear stiffness (PNS). Initially, a novel equivalent continuous method (ECM) is proposed based on the principles of the least squares method (LSM) to approximate the PSTMD using a nonlinear TMD with Duffing stiffness. The equivalent nonlinear TMD is proven to be accurate enough to approximate the PSTMD. Subsequently, frequency response analysis is conducted on the PSTMD designed by linear method, results indicate that the linear method fails to design PSTMD. Thirdly, the optimal parameters of PSTMD are determined based on the ECM and the improved design method for nonlinear TMD proposed by the author. Results indicate that this novel design method effectively enhances the performance of PSTMD and mitigates the effect of piecewise nonlinearity. Finally, the influence of parameters of PSTMD on the optimal tuning frequency is investigated. The influence of damping ratio of PSTMD is explored by numerical simulation, with results indicating that employing the damping ratio suggested by traditional linear design method as the optimal parameter is reasonable. In summary, the novel method proposed in this study holds significance for the engineering design of TMDs with piecewise characteristics.

Application of a new two dimensional nonlinear tuned mass damper in bi-directional vibration mitigation of wind turbine blades

A new two-dimensional non-linear tuned mass damper inerter (2d-NTMDI) is proposed in the present paper with the aim of suppressing bi-directional vibrations. The proposed 2d-NTMDI includes a single mass and two sets of springs, dashpots and inerters configured in two axes. With respect to the displacements in two axes, the resulting restoring forces have nonlinear characteristics. While the proposed novel 2d-NTMDI has the capability of mitigating bi-directional vibrations simultaneously, the nonlinearity of the system makes the optimization a challenging task. The particle swarm optimization (PSO) algorithm is adopted to obtain the optimum design parameters of the 2d-NTMDI. To evaluate the effectiveness, the proposed 2d-NTMDI is deployed in a 5MW-wind turbine blade suffering from bi-directional vibrations in the edgewise and flapwise directions. Therefore, an analytic model of a wind turbine blade with a 2d-NTMDI is derived. The aerodynamic loading is computed using blade element momentum theory. The effectiveness of the 2d-NTMDI is tested under different loading conditions. Also, the fatigue damage of the wind turbine blades is calculated according to the rain-flow cycle counting approach and Miner’s law. It is concluded that the optimized design 2d-NTMDI can prolong the blade fatigue life by 24.6%.

Research on Vibration Suppression of Nonlinear Tuned Mass Damper System Based on Complex Variable Average Method

Tuned mass dampers (TMDs) are widely used as vibration damping devices in engineering practice. However, during use, TMDs inevitably exhibit some nonlinear characteristics that may negatively impact engineering applications. To improve the practical performance of TMDs, the cubic nonlinear stiffness of the TMD is considered, and a nonlinear design is implemented. A numerical model of a single-degree-of-freedom main structure controlled by an NTMD is developed, and the steady-state amplitude solution of the system is obtained using the complex variable averaging method. The results show that a jump phenomenon may occur in the structure. To address this, a multivalued solution discrimination formula based on the complex variable averaging method is proposed. The discriminant formula for the jump phenomenon obtains the frequency ratio and nonlinear coefficient curves of the critical jump state, and four different system response areas are obtained. This helps the structure avoid the jump phenomenon while ensuring stability of the main structure and improving the control performance of the NTMD.

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.

Comparative study on seismic performance of structure with TMD and particle TMD considering SSI effects

Tuned mass dampers (TMDs) are widely adopted to suppress structural response under dynamic loads. Some novel nonlinear TMDs have been developed to improve control performance, such as particle TMD (PTMD). The damping mechanism of TMD and PTMD are linear and nonlinear, respectively. Ignoring soil-structure interaction (SSI) effects may lead to inaccurate evaluation for the structural seismic responses and effectiveness of TMDs. In this study, the seismic control performance of the linear TMD and the nonlinear PTMD considering SSI effects are explored. Based on the shaking table test results, the mitigation effects of TMD and PTMD on floor acceleration and displacement responses are compared, in terms of average decreasing amplitude ratios and root-mean-square decreased ratios. Furthermore, to provide insights into the mitigation mechanism of TMD and PTMD including SSI effects, the recorded signals are decomposed and the energy response analysis is conducted using wavelet packet transform. The results show that when SSI effects are included, the performance of the linear TMD and the nonlinear PTMD on acceleration response is close, but the effectiveness of the linear TMD on displacement response and energy response is superior to that of PTMD. This study improves the understanding of TMDs’ effectiveness in SSI system subjected to seismic excitations.

Optimal Design and Analysis of Nonlinear Tuned Mass Damper System

The tuned mass damper (TMD), as a representative passive control device, has been widely used in various fields such as mechanical vibration and civil engineering. In practical engineering applications, nonlinear characteristics of the TMD inevitably occur due to the installation of limiting devices or large displacements. Neglecting such nonlinearity may adversely affect the control performance of the TMD. Based on this situation, the parameters of the nonlinear tuned mass damper (NTMD) were analyzed, considering the linear and cubic nonlinear stiffness of the TMD, in order to improve its control performance. In this paper, a numerical model of a single-degree-of-freedom controlled structure using an NTMD was established, and the complex variable averaging method was employed to derive the response expression of the structure under the 1:1 resonance condition. Subsequently, the nonlinear design equation for the NTMD frequency was obtained. Based on this nonlinear design formula, the design accuracy was analyzed under 1:1 resonance, undamped and softened stiffness conditions. The results indicate that the NTMD based on a nonlinear design exhibits good control performance.

Analysis and Design of Nonlinear Tuned Mass Damper Based on Complex Variable Averaging Method

As one of the most representative passive control devices, tuned mass dampers (TMDs) are widely used in civil engineering, aerospace, machinery, and other fields, after years of research and improvement. However, due to their large displacement and the use of a limiting device, they inevitably exhibit some nonlinear characteristics in practical engineering applications. This nonlinearity is often ignored; however, neglecting it in the design process can adversely affect the control performance. Therefore, considering the nonlinearity of a TMD while designing TMD parameters can make the calculation results closer to reality and benefit the structural design. In this paper, we derived the approximate analytical solution of TMD amplitude using the complex variable averaging method by considering the nonlinearity generated by a TMD in the vibration process. Theoretical optimal design parameters were obtained by analytical comparison, and we compared the computational time consumption of this method and the numerical method. The results showed that the optimized parameters of the TMD obtained by nonlinear design possessed a good vibration reduction effect both before and after the TMD generated nonlinear characteristics. Additionally, the complex averaging method generated frequency response curves tens of times faster than the numerical method.

An experimental study on the equivalent nonlinear model for a large-sized tuned liquid damper

A fire-suppression water tank is usually required at the top of a tall building. It would be economical to design a fire-suppression tank as a tuned liquid damper (TLD) during preliminary building design. A TLD has obvious advantages in terms of economy, maintenance, and damping efficiency with small vibrations. The sloshing nonlinearity of a TLD increases design difficulty. The purpose of this study is to investigate the nonlinear dynamic response of a large-scale TLD and provide an equivalent model for the TLD under small excitation suitable for the vibration comfort control of tall buildings. The nonlinear dynamic response was investigated through shaking table experimental results. An experiment was conducted with a TLD with a rectangular tank size of 2500 mm × 1750 mm and a sloshing period of 3.2–6.2 s. A series of TLD tests were performed with different flow-damping devices, water depths, and excitations. The time history of the water sloshing wave height was obtained using a video recognition method; the base shear force of the tank was measured simultaneously. A new nonlinear stiffness and damping model (NSD-h) was proposed that simplified the TLD as a nonlinear tuned mass damper (TMD) to predict the tank base force. In the NSD-h model, the equivalent wave height was introduced to describe the sloshing amplitude of the TLD. The nonlinear frequency and damping ratio of the TLD were calculated using the equivalent wave height. Verified in wind conditions, the NSD-h model demonstrated significantly higher accuracy than the nonlinear stiffness and damping model (NSD) with similar simple equations.

Research on Vibration Damping of Tuned Mass Damper for Wheeled Excavator

Background: When driving and working, the engine, working equipment and uneven road surface will cause severe vibrations to the wheeled excavator, which can affect efficiency and comfort. This paper discusses various patents and presents a new method of vibration reduction for excavators. Objective: The research aims to design the excavator's counterweight as a tuned mass damper (TMD) to reduce body vibration. Methods: The recent patents of TMD were investigated in this research. In this paper, the counterweight of the excavator is designed as a non-linear TMD system. The vibration models were established under the driving and crushing conditions, respectively. The vibration response of the vehicle body was calculated and analyzed through MATLAB/Simulink under driving and crushing conditions. Finally, the damping characteristics of the TMD system were discussed. Results: The vibration of the car body can be reduced by TMD. The improvement rates in vertical acceleration were 8.05%, 11.85% and 11.15% for the three classes of road surfaces for the driving conditions. The improvement rates of vertical accelerations for the three powers of crushing conditions are 16.18%, 18.32% and 23.48%, respectively. Conclusion: The vibration damping performance of the excavator was effectively improved by TMD in the main working conditions. The variation of body vertical acceleration with TMD parameters indicates the existence of optimal damping characteristics parameters for the TMD system at a fixed road surface and vehicle speed.

Research on Dynamic Characteristics of Joint of RC Frame Structure with NES

The NES (nonlinear energy sink) is a new type of nonlinear tuned mass damper that is connected to the shock-absorbing main structure through strong nonlinear stiffness and viscous damping. The vibrational energy in the main structure is transferred to the NES oscillator by means of target energy transfer. A shaking table test of a 1:4 scaled RC (Reinforced Concrete) frame structure model with a new type of NES shock absorber was conducted to study the damping effect of the NES shock absorber, especially for the influence of joint strength and deformation. The NES used in this experiment has a relatively large nonlinear stiffness and a wide vibration absorption frequency band. The variation of reinforcement strains, node failure mode, and structural natural frequency of 1 story and two-layer joints of the model frame structure with NES were studied. The test results showed that NES could effectively reduce the strains of longitudinal reinforcement and stirrup in beams and columns and delay the plastic hinge development at the bottom and the top of the column. The frame model with NES installed has failures at the beam ends and shear failures at the nodes, realizing the seismic mechanism of solid columns and weak beams. Compared with ordinary seismic structures, the NES can effectively reduce the shear stress of concrete at the joints and alleviate the shear failure of joints. The final failure of the NES shock absorbing structure was the yielding of the steel bars at the bottom of the column and the crushing of the concrete at the foot of the column, and the connection between the column foot and the backplane became loose simultaneously. The decreasing rate of the vibration frequency declined due to the NES with varied broadband absorbing capability. It can be seen that the NES shock absorber not only has a good effect on reducing the seismic response of the structure, but more importantly, the damage of the structural nodes is greatly reduced, and therefore, the seismic capacity of the structure improved.

Analysis of a nonlinear tuned mass damper by using the multi-scale method

1. Alexander N.A., Schilder F., 2009, Exploring the performance of a nonlinear tuned mass damper, Journal of Sound and Vibration, 319, 1-2, 445-462. CrossRef Google Scholar

Enhanced suppression of longitudinal vibration transmission in propulsion shaft system using nonlinear tuned mass damper inerter

This study proposes the use of a novel nonlinear tuned mass damper inerter device in vibration suppression of the ship propulsion shafting system and evaluates its performance. The device consists of an axial inerter and a pair of lateral inerters to create geometric nonlinearity. The system response subjected to propeller forces is determined by using the harmonic balance method with alternating-frequency-time technique and a numerical time-marching method. The force transmissibility and energy flow variables are employed to assess the performance of the device. The results show that the proposed device can reduce the peak force and energy transmission to the foundation while increase the energy dissipation within the device. Its use can lead to an improved vibration attenuation effect than the traditional mass-spring-damper device for low-frequency vibration. The configurations of the nonlinear inerter-based device can be adjusted to obtain an anti-peak at a resonance frequency of the original system, providing superior vibration suppression performance.

Optimum design of nonlinear tuned mass damper for dynamic response control under earthquake and wind excitations

Optimum design of nonlinear tuned mass damper for dynamic response control under earthquake and wind excitations

A novel three dimensional nonlinear tuned mass damper and its application in floating offshore wind turbines

This paper proposes a novel three-dimensional non-linear tuned mass damper (3d-NTMD) to effectively mitigate three-dimensional structural responses. The 3d-NTMD consists of a mass and three pairs of springs and dash-pots configured in three axes. The resultant restoring forces are nonlinear with respected to the displacements in the three axes. While the proposed 3d-NTMD has the potential to simultaneously mitigate triaxial vibrations, the system nonlinearity complicates the optimization. A numerical search approach is adopted to determine the optimum design. The National Renewable Energy Laboratory spar floating wind turbine (FWT) model is used to evaluate the performance of the 3d-NTMD in reducing the motion of the FWT in three directions: pitch, roll and heave. To this end, an analytical model of a spar FWT with a 3d-NTMD in the spar is established. The wind loading is determined using blade element momentum method and the wave loading is calculated using JONSWAP spectrum and Morison equation. The effectiveness of the 3d-NTMD is examined under operational and parked conditions. Results show that the 3d-NTMD outperforms linear TMDs and can effectively reduce the response of the FWT in three directions. The proposed 3d-NTMD has the potential to mitigate three-dimensional vibrations of a large set of civil/mechanical systems.

Interval type-2 fuzzy decentralised event-triggered H ∞ control for nonlinear interconnected systems with time delays

This paper studies the interval type-2 fuzzy decentralised event-triggered control design problem for the nonlinear time-delay interconnected systems. The considered plant is first represented by an interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy time-delay interconnected system and then an event-triggered mechanism is established through using the sampled states. By using the PDC algorithm, a fuzzy decentralised event-triggered controller is developed. Furthermore, the asymptotic stable conditions with a performance of closed-loop system are obtained, which are formulated in the form of linear matrix inequalities. Finally, an example of the nonlinear Tuned Mass Damper system with time delays is given to illustrate the effectiveness of the proposed fuzzy decentralised controller.

Analytical analysis for optimizing mass ratio of nonlinear tuned mass dampers

To reduce the adverse vibrations of buildings, tuned mass dampers (TMDs), which are the most representative passive control devices, have been widely used and studied in aerospace, machinery, civil engineering, and other fields for many years. Most scholars used to treat the TMD as a linear damper, but they show some nonlinear characteristics owing to the use of limit devices and large displacements. It is necessary to consider the nonlinear coefficient of the TMD when designing its parameters. In this study, the mass ratio of the TMD was optimized by considering the nonlinear coefficient of the TMD. The complex variable average method and multiscale method were used for analysis. A mass ratio interval was found on the “\(\varepsilon - N_{2}\)” curve in which modulation response can occur, and then an analytical method for obtaining the optimal mass ratio of TMD was derived based on this phenomenon. The numerical results showed that taking the midpoint of this mass ratio interval as the optimal mass ratio can yield a better damping effect and robustness than using the traditional linear design method.

A nonlinear X-shaped structure based tuned mass damper with multi-variable optimization (X-absorber)

Installing a tuned mass damper (TMD) is a promising vibration control method in many engineering applications which can suppress excessive vibration of a primary structure by transferring and dissipating vibration energy from the primary structure to the TMD. To overcome some limitations and drawbacks of traditional tuned mass dampers in practice, a bio-inspired X-shaped structure/mechanism is utilized to design a novel tunable and nonlinear TMD (X-absorber) in this study. To this aim, multi-variable optimization analysis, tunable stiffness and damping properties, nonlinear influence and vibration suppression performance of the new X-absorber are systematically investigated. The X-absorber can provide beneficial nonlinear damping and tunable quasi-zero stiffness which can significantly improve system parametric robustness, widen vibration suppression bandwidth with a widened anti-resonance, effectively suppress resonant peaks of very low frequencies, and eliminate potential instabilities (e.g., bifurcation, jump) inherently existing in Duffing systems, compared with traditional absorbers. The effectiveness and robustness of the X-absorber with different excitations compared with a traditional spring-mass absorber are verified in experiments. The X-absorber presents a new insight into the design of nonlinear passive absorbers of high performance, and a more flexible and reliable solution to many engineering problems.

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

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

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.

Design of Nonlinear Tuned Mass Damper by Using the Harmonic Balance Method

AbstractAs a passive control device, tuned mass dampers (TMDs) are widely used in structural vibration control. Due to the nonlinear characteristics of a TMD, it is important to consider nonlineari...