Nonlinear Tuned Mass Damper Research Articles

A Simplified Optimization Strategy for Nonlinear Tuned Mass Damper in Structural Vibration Control

AbstractIn this paper, a simplified optimization strategy for the nonlinear tuned mass damper (TMD) is presented, and the optimal parameter setting can be simply determined, by which the nonlinear TMD is effective over a wide frequency range. In the given numerical model, the nonlinear TMD is attached to the structure, which is represented by a single‐degree‐of‐freedom system, and the environmental load is assumed to be the Gaussian white noise process. Governing differential equations of motion of the coupled structure‐TMD system are derived, and the equivalent linearization method is introduced in the numerical calculation. The standard deviation of the structural displacement is adopted as the optimized objective function. Furthermore, it is pointed out that the response of the system can be controlled in a case of multiple probable steady‐state processes caused by the nonlinearity of the stiffness element. Different from the linear TMD, the performance of the nonlinear TMD may be influenced by the excitation. Thus, the performance sensitivity of optimal nonlinear TMD is investigated with different excitation intensities and structural damping ratios. The results show that the sensitivity may limit the engineering applications of nonlinear TMD.

Optimal design formulas for viscous tuned mass dampers in wind-excited structures

SUMMARY Optimal design for tuned mass dampers (TMDs) with linear or nonlinear viscous damping is formulated in order for design practitioners to directly compute the optimal parameters of a TMD in a damped structure subjected to wind excitations. The optimal TMD tuning frequency ratio and damping coefficient for a viscous TMD system installed in a damped structure under 10 white noise excitations are determined by using the time-domain optimization procedure, which minimizes the structural response. By applying a sequence of curve-fitting schemes to the obtained optimal values, design formulas for optimal TMDs are then derived. These are expressed as a function of the mass ratio and damping power-law exponent of the TMD as well as the damping ratio of the structure. The feasibility of the proposed optimal design formulas is verified in terms of formulary accuracy and of comparisons with existing formulas from previous research works. In addition, one numerical example of the Taipei 101 building with a nonlinear TMD, which is redesigned according to the proposed optimal formulas, is illustrated in effort to describe the use of the formulas in the TMD design procedure and to investigate the effectiveness of the optimal TMD. The results indicate that the proposed optimal design formulas provide a convenient and effective approach for designing a viscous TMD installed in a wind-excited damped structure. Copyright © 2011 John Wiley & Sons, Ltd.

Experimental verification of seismic vibration control using a semi‐active friction tuned mass damper

SUMMARYA tuned mass damper (TMD) system consists of an added mass with properly functioning spring and damping elements for providing frequency‐dependent damping in a primary structure. The advantage of a friction‐type TMD, that is, a nonlinear TMD, is its energy dissipation via a friction mechanism. In contrast, the disadvantages of a passive friction TMD (PF‐TMD) are its fixed and predetermined slip load and loss of tuning and energy dissipation capabilities when it is in a stick state. A semi‐active friction TMD (SAF‐TMD) is used to overcome these disadvantages. The SAF‐TMD can adjust its slip force in response to structure motion. To verify its feasibility, a prototype SAF‐TMD was fabricated and tested dynamically using a shaking table test. A nonsticking friction control law was used to keep the SAF‐TMD activated and in a slip state in earthquakes at varying intensities. The shaking table test results demonstrated that: (i) the experimental results are consistent with the theoretical results; (ii) the SAF‐TMD is more effective than the PF‐TMD given a similar peak TMD stroke; and (iii) the SAF‐TMD can also prevent a residual TMD stroke in a PF‐TMD system. Copyright © 2011 John Wiley & Sons, Ltd.

Reliability of structures with tuned mass dampers under wind-induced motion: a serviceability consideration

Excessive wind-induced motion in tall buildings can cause discomfort, affect health, and disrupt the daily activities of the occupants of a building. Dynamic vibration absorbers such as the tuned mass dampers (TMDs) can be used to reduce the wind-induced motion below a specified tolerable serviceability limit state (SLS) criterion. This study investigates whether the same probability of not exceeding specified wind-induced motion levels can be achieved by torsionally sensitive structures without/with linear/nonlinear TMDs subjected to partially correlated wind forces, if they are designed to just meet the same SLS criterion. For the analyses, different structures and the uncertainty in the response, wind load and perception of motion is considered. Numerical results indicate that for structures that are designed or retrofitted without or with optimum linear TMDs and satisfying the same SLS criterion, their probability of exceeding the considered criterion is very consistent, if the inherent correlation between the wind forces is considered in design. However, this consistency deteriorates if nonlinear TMDs are employed. Furthermore, if the correlation is ignored in the design, in many cases a slightly unconservative design, as compared to the designed by considering correlation, is achieved.

Development of a chaotic nonlinear tuned mass damper for optimal vibration response

In this article an efficient method is developed for optimal design of a nonlinear tuned mass damper (N-TMD) system. Using several horizontal linear springs coming into action sequentially, system nonlinearity can be achieved with ease as a novel method. Friction force between tuned mass and the structure is variably produced by a vertical linear spring that follows a specified controlling curved path allowing reduction of the desired tuned mass. Chaotic behavior of the introduced tuned mass is investigated in terms of the existing parameters in the system. Lyapunov characteristic exponents are determined to demonstrate the chaotic behavior of the system. It is confirmed by comparison that the proposed scheme is able to retrofit structures in a superior way than some other devices such as multiple tuned mass damper systems. The optimization procedure is performed by sequential Simplex algorithm, while Newmark’s beta method for step by step integration is used to find the dynamic response of the structure.

Feasibility study of nonlinear tuned mass damper for machining chatter suppression

In order to improve the performance of the tuned mass damper (TMD) for machining chatter suppression, a new-type of nonlinear TMD is proposed in this paper. Compared with the common linear TMD, the nonlinear TMD is equipped with an additional series friction-spring element. The capability of the nonlinear TMD in suppressing machining chatter vibration is investigated in this paper. The harmonic balancing method (HBM) is used to estimate the frequency response function (FRF) of the machining system to which the nonlinear TMD is attached. Considering the special nature of the machining stability problem, the optimal design parameters of this nonlinear TMD are those that minimize the magnitude of the real part of the FRF of the nonlinear TMD damped machining system. This paper also demonstrates the performance of the optimally tuned nonlinear TMD for machining stability improvement by calculating the stability diagrams for the milling of the nonlinear TMD damped workpiece. The calculation results show that more than 30% improvement in the critical limiting cutting depth can be obtained, compared to the optimally tuned linear TMD.

Bifurcation Phenomena Caused by Multiple Nonlinear Vibration Absorbers

The characteristics of two, three, and four nonlinear vibration absorbers or nonlinear tuned mass dampers (NTMDs) attached to a structure under harmonic excitation are investigated. The frequency response curves are theoretically determined using van der Pol’s method. When the parameters of the absorbers are equal, it is found from the theoretical analysis that pitchfork bifurcations may occur on the part of the response curves, which are unstable in the multi-absorber systems, but are stable in a system with one NTMD. Multivalued steady-state solutions, such as three steady-state solutions for a dual-absorber system with different amplitudes, five steady-state solutions for a triple-absorber system, and seven steady-state solutions for a quadruple-absorber system, appear near bifurcation points. The NTMDs behave in that one of them vibrates at high amplitudes while the others vibrate at low amplitudes, even if the dimensions of the NTMDs are identical. Namely, “localization phenomenon” or “mode localization” occurs. After the pitchfork bifurcation, Hopf bifurcations may occur depending on the values of the system parameters, and amplitude- and phase-modulated motions, including chaotic vibrations, appear after the Hopf bifurcation when the excitation frequency decreases. Lyapunov exponents are numerically calculated to prove the occurrence of chaotic vibrations. Bifurcation sets are also calculated to investigate the influence of the system parameters on the response of the systems.

Design and implementation of nonlinear TMD for chatter suppression: An application in turning processes

A new-type nonlinear tuned mass damper (TMD) containing an additional element of elastic support dry friction compared with the common linear TMD is proposed to suppress machining chatter. The design and tuning process of this nonlinear TMD have used a combination of analytical modeling with experimentally measured frequency response function (FRF) of the machining system. Theoretical studies and experimental results show that the proposed nonlinear TMD can remarkably improve the machining stability by effectively suppressing the magnitude of the real part of the FRF of the damped machining system.

Optimal design theories of tuned mass dampers with nonlinear viscous damping

Optimal design theory for linear tuned mass dampers (TMD) has been thoroughly investigated, but is still under development for nonlinear TMDs. In this paper, optimization procedures in the time domain are proposed for design of a TMD with nonlinear viscous damping. A dynamic analysis of a structure implemented with a nonlinear TMD is conducted first. Optimum design parameters for the nonlinear TMD are searched using an optimization method to minimize the performance index. The feasibility of the proposed optimization method is illustrated numerically by using the Taipei 101 structure implemented with TMD. The sensitivity analysis shows that the performance index is less sensitive to the damping coefficient than to the frequency ratio. Time history analysis is conducted using the Taipei 101 structure implemented with different TMDs under wind excitation. For both linear and nonlinear TMDs, the comfort requirements for building occupants are satisfied as long as the TMD is properly designed. It was found that as the damping exponent increases, the relative displacement of the TMD decreases but the damping force increases.

Protection of seismic structures using semi‐active friction TMD

AbstractAlthough the design and applications of linear tuned mass damper (TMD) systems are well developed, nonlinear TMD systems are still in the developing stage. Energy dissipation via friction mechanisms is an effective means for mitigating the vibration of seismic structures. A friction‐type TMD, i.e. a nonlinear TMD, has the advantages of energy dissipation via a friction mechanism without requiring additional damping devices. However, a passive‐friction TMD (PF‐TMD) has such disadvantages as a fixed and pre‐determined slip load and may lose its tuning and energy dissipation abilities when it is in the stick state. A novel semi‐active‐friction TMD (SAF‐TMD) is used to overcome these disadvantages. The proposed SAF‐TMD has the following features. (1) The frictional force of the SAF‐TMD can be regulated in accordance with system responses. (2) The frictional force can be amplified via a braking mechanism. (3) A large TMD stroke can be utilized to enhance control performance. A non‐sticking friction control law, which can keep the SAF‐TMD activated throughout an earthquake with an arbitrary intensity, was applied. The performance of the PF‐TMD and SAF‐TMD systems in protecting seismic structures was investigated numerically. The results demonstrate that the SAF‐TMD performs better than the PF‐TMD and can prevent a residual stroke that may occur in a PF‐TMD system. Copyright © 2009 John Wiley & Sons, Ltd.

Parametric Identification of Structures with Nonlinearities Using Global and Substructure Approaches in the Time Domain

This paper presents further research on the parametric identification of structures with non-linearities in stiffness and damping properties. Parametric identification is carried out using acceleration responses in the time domain and is useful for structural health monitoring. Cubic nonlinearities in springs and quadratic nonlinearities in dampers are considered. Structural parametric identification is modeled as an inverse problem, based on minimizing the difference between measured responses and calculated responses from a mathematical model. The results of both global and substructural identification approaches are compared. The substructural approach allows us to identify a smaller domain while ignoring external parameters, resulting in a reduced model, but on the other hand the formulation is more complex. Genetic algorithms (GA) are used for filtering the unknown parameter values from within a given range. Simple real coded GA as well as a superior hybrid version obtained by combining with the Levenberg-Marquardt (LM) have been studied. Several numerical examples, including variations of a 10 DOF non-linear lumped mass system and a 12 member truss with several non-linear tuned mass dampers have been studied. The effect of measurement noise have been considered. The substructural method is shown to be superior overall in terms of speed, accuracy and economy (number of sensors) although the global identification approach implemented in conjunction with hybrid GA performs well in some cases.

Exploring the performance of a nonlinear tuned mass damper

We explore the performance of a nonlinear tuned mass damper (NTMD), which is modeled as a two degree of freedom system with a cubic nonlinearity. This nonlinearity is physically derived from a geometric configuration of two pairs of springs. The springs in one pair rotate as they extend, which results in a hardening spring stiffness. The other pair provides a linear stiffness term. We perform an extensive numerical study of periodic responses of the NTMD using the numerical continuation software AUTO. In our search for optimal design parameters we mainly employ two techniques, the optimization of periodic solutions and parameter sweeps. During our investigation we discovered a family of detached resonance curves for vanishing linear spring stiffness, a feature that was missed in an earlier study. These detached resonance response curves seem to be a weakness of the NTMD when used as a passive device, because they essentially restore a main resonance peak. However, since this family is detached from the low-amplitude responses there is an opportunity for designing a semi-active device.

Tuned mass damper with nonlinear viscous damping

This paper investigates the effect of tuned mass dampers with nonlinear viscous damping elements. The tuned mass damper is assumed to be attached to a single-degree-of-freedom system excited by white noise. Statistical linearization is used to analyze the system and the accuracy of this procedure is verified by stochastic simulation. The optimal linear tuned mass damper is defined in terms of minimizing the standard deviation of the structural displacement. The structural damping is shown to have little influence on the optimal parameter values for the linear tuned mass damper. The (approximate) optimal nonlinear tuned mass damper is defined as the system, which by statistical linearization identifies an optimal equivalent linear tuned mass damper. This is shown to lead to explicit expressions for the optimal parameter values of the nonlinear tuned mass damper. The fact that statistical linearization leads to very accurate results, implies that the optimal nonlinear tuned mass damper is practically as effective as a linear tuned mass damper. However, the nonlinear tuned mass damper must be tuned to a specific amplitude and excitation intensity, in contrast to a conventional linear tuned mass damper. The theory is demonstrated for a tuned mass damper with viscous power-law damping and for a tuned mass damper with Bingham-type damping. The probability distribution of the displacement of the structure seems to be a close approximation to a Gaussian distribution despite the nonlinearity. Furthermore, it is shown by stochastic simulation, that the approximate optimal nonlinear tuned mass damper (identified via statistical linearization) is in fact very close to the true optimum.

T-S fuzzy controllers for nonlinear interconnected systems with multiple time delays

This paper investigates the effectiveness of a passive tuned mass damper (TMD) and fuzzy controller in reducing the structural responses subject to the external force. In general, TMD is good for linear systems. We proposed here an approach of Takagi-Sugeno (T-S) fuzzy controller to deal with the nonlinear system. To overcome the effect of modeling error between nonlinear multiple time-delay systems and T-S fuzzy models, a robustness design of fuzzy control via model-based approach is proposed in this paper. A stability criterion in terms of Lyapunov's direct method is derived to guarantee the stability of nonlinear multiple time-delay interconnected systems. Based on the decentralized control scheme and this criterion, a set of model-based fuzzy controllers is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time-delay interconnected system and the H/sup /spl infin// control performance is achieved at the same time. Finally, the proposed methodology is illustrated by an example of a nonlinear TMD system.

Fuzzy controllers for nonlinear interconnected tmd systems with external force

This paper investigates the effectiveness of a passive tuned mass damper (TMD) and active fuzzy controllers in reducing structural responses under external forces. In general, TMD is good for linear systems. We propose here a fuzzy controller to deal with nonlinear systems. For the fuzzy controller, a stability criterion in terms of Lyapunov's direct method is derived to guarantee the stability of interconnected TMD systems. Based on decentralized control and this criterion, a set of model‐based fuzzy controllers are then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear interconnected TMD system. Finally, an example is given to illustrate the concepts discussed throughout this paper.

Nonlinear Tuned Mass Damper for self-excited oscillations

The effects of a class of nonlinear Tuned Mass Dampers on the aeroelastic behavior of SDOF systems are investigated. Unlike classical linear TMDs, nonlinear constitutive laws of the internal damping acting between the primary oscillator and the TMD are considered, while the elastic properties are keept linear. The perturbative Multiple Scale Method is applied to derive a set of bifurcation equations in the amplitude and phase and a parametric analysis is performed to describe the postcritical scenario of the system. Both cubic- and van der Pol-type dampings are considered and the dependence of the limit-cycle amplitudes on the system parameters is studied. These new results, compared with the previously obtained bifurcation scenario of a SDOF aeroelastic oscillator equipped with a linear TMD, show a detrimental effect on the maximum limit-cycle amplitude reduction of the nonlinear TMD. However, the analyses evidence that in the parameter region away from the perfect tuning condition the nonlinear connection can be used to tune the system with an enhancement of the limit-cycle amplitude reduction.

Wind tunnel study of the across-wind response of a slender tower with a nonlinear tuned mass damper

The effectiveness of a class of nonlinear tuned mass dampers (TMDs) in suppressing across-wind structure oscillations was examined through a wind tunnel test. The nonlinear TMD employed a wire rope spring to replace both the spring and the damper required in a typical system. First, a single degree of freedom aeroelastic stick model of a slender structure with a square cross-section was tested under different levels of damping. The measurements obtained from the tests were used to determine the root-mean-square (RMS) of the lift coefficient and other aerodynamic parameters. In the second phase of testing, the nonlinear TMD system was attached near the tip of the aeroelastic model. The response reduction achieved by adding the TMD was considerable and was quantitatively expressed in terms of an equivalent viscous damping. A comparison between the nonlinear TMD and an equivalent optimized linear TMD was made. Probability-based procedures were developed to estimate the equivalent damping provided by the nonlinear TMD. The estimated damping was compared with that obtained experimentally to evaluate the accuracy of the prediction method.

Mass Damper Using Friction-Dissipating Devices

The paper proposes and studies a nonlinear mass damper that uses friction dampers acting transversely to the direction of the motion of the mass damper as a means for energy dissipation. The resistant scheme of this mass damper shows a hysteretic damping mechanism in which the dissipation of energy is quadratic in the amplitude of deformation. The effectiveness of the mass damper in reducing vibrations of the main structural system to which it is attached is investigated. The statistical linearization technique is used to estimate the mean square response of the system subjected to random excitation. The optimum parameters of this mass damper are defined as those that minimize the mean square deformation of the main structural system subjected to random excitation. The study confirms that the efficacy of this nonlinear tuned mass damper (TMD) system is comparable to that of a linear TMD system for a wide range of excitation intensity.