Nonlinear Tuned Mass Damper Research Articles

Effect of inertia nonlinearity on dynamic response of an asymmetric building equipped with tuned mass dampers

This study investigates the effect of nonlinear inertia on the dynamic response of an asymmetric building equipped with Tuned Mass Dampers (TMDs). In the field of structural engineering, many researchers have developed models to study the behavior of nonlinear TMDs, but the effect of nonlinear inertia has not received as much attention for asymmetric buildings. To consider nonlinear inertia, the equations of motion are derived in a local rotary coordinates system. The displacements and rotations of the modeled building and TMDs are defined by five-degree-of-freedom (5-DOFs). The equations of motion are derived by using the Lagrangian method. Also in the proposed nonlinear model, the equations of motion are different from a conventional linear model. In order to compare the response of the proposed nonlinear model and a conventional linear model, numerical examples are presented and the response of the modeled buildings are derived under harmonic and earthquake excitations. It is shown that if the nonlinear inertia is considered, the response of the modeled structures changes and the conventional linear approach cannot adequately model the dynamic behavior of the asymmetric buildings which are equipped with TMDs.

Analytical analysis for the design of nonlinear tuned mass damper

A tuned mass damper is a passive control device that has been widely used in aerospace, mechanical, and civil engineering as well as many other fields. Tuned mass dampers have been studied and improved over the course of many years. In practical engineering applications, a tuned mass damper inevitably produces some nonlinear characteristics due to the large displacement and the use of the limiting devices, but this nonlinearity is often neglected. The simulation results in this study confirm that neglecting the nonlinearity in the design process can produce adverse effects on the control performance. This paper takes into account the nonlinearity of the tuned mass damper produced in the process of vibration and deduces an optimum formula for the frequency of a tuned mass damper by the complexification averaging method and multiscale method. Based on this formula, a modified design method for the frequency of a tuned mass damper is presented. The numerical results show that the nonlinear tuned mass damper after modification is better than a linear tuned mass damper in terms of control performance.

Numerical and Experimental Investigation of a Cable-based Nonlinear Tuned Mass Damper to Reduce Free and Forced Vibrations

Numerical and Experimental Investigation of a Cable-based Nonlinear Tuned Mass Damper to Reduce Free and Forced Vibrations

Conditions for the existence of isolated backbone curves.

Isolated backbone curves represent significant dynamic responses of nonlinear systems; however, as they are disconnected from the primary responses, they are challenging to predict and compute. To explore the conditions for the existence of isolated backbone curves, a generalized two-mode system, which is representative of two extensively studied examples, is used. A symmetric two-mass oscillator is initially studied and, as has been previously observed, this exhibits a perfect bifurcation between its backbone curves. As this symmetry is broken, the bifurcation splits to form an isolated backbone curve. Here, it is demonstrated that this perfect bifurcation, indicative of a symmetric structure, may be preserved when the symmetry is broken under certain conditions; these are derived analytically. With the symmetry broken, the second example—a single-mode nonlinear structure with a nonlinear tuned mass damper—is considered. The evolution of the system's backbone curves is investigated in nonlinear parameter space. It is found that this space can be divided into several regions, within which the backbone curves share similar topological features, defining the conditions for the existence of isolated backbone curves. This allows these features to be more easily accounted for, or eliminated, when designing nonlinear systems.

Effects of hysteretic damping on the seismic performance of tuned mass dampers

SummaryA tuned mass damper (TMD) as a convenient passive device in average to tall buildings has limitations specifically against broad band seismic excitations. According to evidences from the literature, this drawback can be dominated by using nonlinear stiffness in TMDs; however, past studies did not explore this issue, and observations are not sufficient to reach a conclusion about seismic performance of nonlinear TMDs. This paper considers seismic performance of a nonlinear TMD developed by adding a martensitic shape memory alloy spring with significant stable features to conventional TMDs. To this end, single degree of freedom structures (from short to large periods) equipped with the nonlinear TMD are investigated subjected to set of ground motions, and through numerical analyses, effects of hysteretic damping and energy absorption capacity of the nonlinear TMD are examined. In addition, features of the proposed TMD configuration and effects of the excitation properties have been scrutinized through graphing frequency response curves by the arc length continuation method. Results indicate that the proposed configuration can make the nonlinear TMD robust against variations of the loading properties. Moreover, due to significant hysteretic damping of the shape memory alloy, spring seismic performance of the nonlinear TMD is better than conventional TMDs.

Seismic performance evaluation of steel frame structures equipped with tuned liquid dampers

An economical solution to reduce building motions to an acceptable level, under dynamic loadings, is to provide additional damping. A passive damping device shown to be effective as a vibration control mechanism is tuned liquid damper (TLD). A TLD is a passive control system which utilizes fluid-sloshing motion to dissipate the lateral excitation energy. In this paper, the TLD was modeled as an equivalent nonlinear-tuned mass damper. Furthermore, the validity of the numerical procedure in predicting the structural response equipped with TLD under seismic loading is also investigated with two studies. To study the effectiveness of implementing TLDs, three existing intermediate steel moment-resisting frames were taken into consideration, and nonlinear response history analysis was carried out for structural models with and without TLDs. It was observed that TLDs can be utilized as seismic response mitigation devices and can also be employed for seismic rehabilitation of the existing steel structures. Even though the natural frequency of the TLD is always chosen to match the natural frequency of the structure, any change in the frequency of the primary structure or amplitude-dependent frequency of the TLD results in a detuned TLD system. Therefore, this paper also evaluates the efficiency of a detuned TLD system for some tuning ratios (0.8–1.2) by sensitivity analysis. The results showed that tuning ratio in the range of 0.9–1.1 has a slight influence on the seismic response of the structure.

Damping effects of linear and nonlinear tuned mass dampers on nonlinear hinged-hinged beam

This study analyzes the vibration reduction of a tuned mass damper (TMD) applied to a hinged-hinged nonlinear Euler-Bernoulli beam. We compare the effects of linear and nonlinear tuned mass dampers (LTMD/NLTMD) and obtain results undiscovered in previous studies. We analyze the frequency responses (fixed points) of the system using the method of multiple scales (MOMS) and obtain analytical solutions for the NLTMD in the frequency and time domains using Dimensional Analysis and the Perturbation Method. The present study shows that when the damping coefficient (λ), TMD mass (mD), TMD initial displacement (A) and nonlinear spring constant (β) of the NLTMD fulfill a function relationshipλ=3mDβA, the damping and nonlinear elastic effects cancel each other out, and the nonlinear damping frequency coincides with the linear natural frequency. With a fixed damping coefficient and an LTMD or NLTMD at a fixed position, optimal damping is achieved when the product of the TMD mass and spring constant are at fixed values. Finally, we use the Floquet transition matrix of the system and Floquet multipliers (F.M.) to create the basin of attraction (BOA) and analyze the stability of the system under aerodynamic forces.

Analysis of systems with nonlinear auxiliary mass dampers by means of a special selection of linear generating functions

Nonlinear vibration isolation systems have a wider range of effective damping than linear ones. However, their analysis with an arbitrary load is quite laborious. In the article the method of special selection of linear generating systems for analyzing nonlinear systems proposed by professor Chernov Yu T is used. The linear generating system is chosen in such a way that the difference between the solutions of the linear and nonlinear systems in the first approximation for the first harmonic is minimal. Such an approach makes it possible to reduce the complexity of constructing the amplitude-frequency characteristics of nonlinear systems. In this paper, the amplitude-frequency characteristics were constructed to evaluate the efficiency of nonlinear auxiliary mass dampers at different frequencies of the external load. Tuned mass damper (TMD) was chosen as the type of auxiliary mass damper. The article looks at numerical examples of two systems with nonlinear TMD as a three degrees of freedom system. In the first numerical example, a stand with an equipment installed on it was analyzed. The TMD is installed on the stand. In the second numerical example the equipment is installed on a pedestal. The equipment is equipped with a nonlinear TMD. In both examples, there is cubic reaction-displacement relationship in the link that attaches the TMD. The amplitude-frequency characteristics for both systems are constructed for different variants: with a nonlinear, linear TMD and without a damper. The linear TMD was tuned to the first natural frequency of oscillations of the system without a damper. A comparative analysis of the options is given. The efficiency of using nonlinear TMD is determined from the numerical examples. There is a three times reduction in displacements in the nonlinear system as compared to the linear system.

Lifecycle cost effectiveness of translational and pendulum tuned mass dampers for the seismic mitigation of building structures

Lifecycle cost (LCC) analysis is increasingly used by researchers and designers worldwide as a comprehensive and objective tool to evaluate the performance of structural systems, and particularly of dynamic mitigation strategies. Very recently, it has been successfully adopted to assess the cost-effectiveness of linear tuned mass dampers (TMDs) on inelastic building structures under earthquake hazard. In this paper, the analysis is extended to nonlinear TMDs of the pendulum type, where modelling nonlinearities are both geometrical (large angular displacements) and mechanical (collision against the fail-safe bumper). By analysing three benchmark structural models representative of typical office buildings in the Los Angeles area, a comparison between the translational (linear) and the pendulum (nonlinear) alternatives is presented. Results show that the cost-effectiveness of the pendulum TMD is similar to that of the translational TMD in many cases, but may be significantly diminished in the case of short-period structures and small mass ratios, particularly if premature bumping is permitted.

Lifecycle cost effectiveness of translational and pendulum tuned mass dampers for the seismic mitigation of building structures

Lifecycle cost (LCC) analysis is increasingly used by researchers and designers worldwide as a comprehensive and objective tool to evaluate the performance of structural systems, and particularly of dynamic mitigation strategies. Very recently, it has been successfully adopted to assess the cost-effectiveness of linear tuned mass dampers (TMDs) on inelastic building structures under earthquake hazard. In this paper, the analysis is extended to nonlinear TMDs of the pendulum type, where modelling nonlinearities are both geometrical (large angular displacements) and mechanical (collision against the fail-safe bumper). By analysing three benchmark structural models representative of typical office buildings in the Los Angeles area, a comparison between the translational (linear) and the pendulum (nonlinear) alternatives is presented. Results show that the cost-effectiveness of the pendulum TMD is similar to that of the translational TMD in many cases, but may be significantly diminished in the case of short-period structures and small mass ratios, particularly if premature bumping is permitted.

Fundamental insight on the performance of a nonlinear tuned mass damper

To try and enhance the performance of a tuned mass damper, nonlinear stiffness can be introduced to good use. In this paper, an investigation is performed on the characteristics of a nonlinear tuned mass damper when attached to a linear oscillator. The whole system is modelled as a two degree-of-freedom system with cubic stiffness nonlinearity, and the effect of the nonlinearity and mass ratio of the attachment is investigated for both a softening and a hardening stiffness characteristics, using an analytical formulation. The corresponding linear case is presented as a benchmark, and the main critical issues are discussed. Depending on the frequency to which the vibration reduction is desired, recommendations are highlighted for proper tuning and parameters selection.

Novel Design Approach of a Nonlinear Tuned Mass Damper with Duffing Stiffness

AbstractIn practical engineering, a tuned mass damper (TMD) inherently exhibits nonlinear behavior owing to its large displacement or the application of a limiting stopper. This paper studies the c...

Control-based continuation: Bifurcation and stability analysis for physical experiments

Control-based continuation is technique for tracking the solutions and bifurcations of nonlinear experiments. The idea is to apply the method of numerical continuation to a feedback-controlled physical experiment such that the control becomes non-invasive. Since in an experiment it is not (generally) possible to set the state of the system directly, the control target becomes a proxy for the state. Control-based continuation enables the systematic investigation of the bifurcation structure of a physical system, much like if it was numerical model. However, stability information (and hence bifurcation detection and classification) is not readily available due to the presence of stabilising feedback control. This paper uses a periodic auto-regressive model with exogenous inputs (ARX) to approximate the time-varying linearisation of the experiment around a particular periodic orbit, thus providing the missing stability information. This method is demonstrated using a physical nonlinear tuned mass damper.

Steady-state response attenuation of a linear oscillator–nonlinear absorber system by using an adjustable-length pendulum in series: Numerical and experimental results

Response attenuation of a linear primary structure (PS)–nonlinear tuned mass damper (NTMD) dynamic system with and without an adaptive-length pendulum tuned mass damper (ALPTMD) in a series configuration is studied by using numerical and experimental methods. In the PS–NTMD system, coexisting high and low amplitude solutions are observed in the experiment, validating previous numerical efforts. In order to eliminate the potentially dangerous high amplitude solutions, a series ALPTMD with a mass multiple orders of magnitude smaller than the PS is added to the NTMD. The ALPTMD is used in order to represent the steady-state behavior of a smart tuned mass damper (STMD). In the experiment, the length of the pendulum is adjusted such that its natural frequency matches the dominant frequency of the harmonic ground motions. In the present study, the proposed ALPTMD can be locked so that it is unable to oscillate and influence the dynamics of the system in order to obtain the benefits provided by the NTMD. The experimental data show good qualitative agreement with numerical predictions computed with parameter continuation and time integration methods. Activation of the ALPTMD can successfully prevent the transition of the response from the low amplitude solution to the high amplitude solution or return the response from the high amplitude solution to the low amplitude solution, thereby protecting the PS.

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.

Experimental investigation of vibration attenuation using nonlinear tuned mass damper and pendulum tuned mass damper in parallel

The present paper experimentally and numerically explores the response attenuation of a hardening Duffing oscillator using a nonlinear tuned mass damper (NTMD) and an adaptive-length pendulum tuned mass damper (APTMD). The three degrees-of-freedom system is excited by harmonic ground motions. The cubic nonlinearity of the primary structure is obtained using an adaptive passive stiffness (APS) device. When an NTMD is used alone, a high amplitude detached resonance branch in the lower frequency range is identified in the experiment, which validates the results reported in earlier numerical research. In order to attenuate this high amplitude resonance branch, an APTMD with an adaptive frequency realized by means of a variable pendulum length is used in parallel with the NTMD. In the experiment, length of the APTMD is adjusted such that its natural frequency matches the dominant frequency of the harmonic ground motions. Results indicate that the high amplitude resonance branch in the case of an NTMD alone can be greatly attenuated using the APTMD, and significant attenuation of the structural responses over a large frequency range can be obtained. In addition, the APTMD can prevent the occurrence of the “jump phenomenon” existing in the forcing response curve of the nonlinear dynamic system, thereby protecting the primary nonlinear structure effectively when the forcing amplitude varies. Therefore, the present paper provides an effective and viable solution to control the hazardous bifurcations in a Duffing oscillator-NTMD dynamic system.

Efficient Sensitivity Analysis of Structures with Local Modifications. I: Time Domain Responses

The time evolution of the parameter sensitivity of a nonlinear dynamical system is essential to its successful design, control, and identification. For an important class of systems, the governing equations of motion can be expressed as a linear system of ordinary differential equations augmented with a low-rank parameter-dependent (generally nonlinear) vector function. This paper builds on previous efforts by the authors to devise an approach for computing not only the responses of such systems but also the sensitivities of their responses to changes in design parameters in a computationally efficient manner. The proposed solution procedure first segregates the degrees of freedom appearing in the augmented functions from those that involve only linear deterministic operations. Second, the responses and sensitivities of the augmented terms are determined by solving the Volterra integral equations of reduced dimension. Finally, the responses and sensitivities of all remaining desired outputs are computed through a convolution approach using the fast Fourier transform to further increase the computational efficiency. The proposed method is applied to two examples, one simple linear model where exact solutions can be computed, and a second, more realistic, example of a wind-excited 20-story building augmented with nonlinear tuned mass dampers on its roof. The proposed method is shown to possess accuracy levels similar to those obtained through the time integration of the corresponding analytical sensitivity equations; however, it is several orders of magnitude faster than conventional sensitivity analysis approaches.

Electromechanical semi-passive nonlinear tuned mass damper for efficient vibration damping

Vibrations often lead to fatigue or damage which is harmful to structures. In order to efficiently limit such vibrations, Tuned Mass Dampers (TMD) have been investigated since the last century. In this study, a new concept for TMD design is proposed, which combines an electromechanical TMD featuring piezoelectric elements with the nonlinear Synchronized Switch Damping on Inductor (SSDI) semi-passive technique. The proposed electromechanical semi-passive nonlinear TMD includes a switching circuit connected in parallel to the piezoelectric element which is periodically turned on for a brief time period in order to quickly invert the piezovoltage. Theoretical investigations using a Two-Degree of Freedom (TDOF) model and Finite Element (FE) approach, validated through experimental measurements, demonstrated that the proposed electromechanical semi-passive nonlinear TMD significantly outperforms purely mechanical TMDs and electromechanical passive TMDs with same dynamical parameters, allowing to further improve the control performance of such techniques.

Hardening Düffing oscillator attenuation using a nonlinear TMD, a semi-active TMD and multiple TMD

This paper investigates the response attenuation of a hardening Düffing oscillator utilizing a Nonlinear Tuned Mass Damper (NTMD), a Semi-Active Tuned Mass Damper (STMD), and a multiple TMD (MTMD) consisting of the two in parallel. A high amplitude “detached” solution branch in the frequency-response of the primary structure is observed in the case of an NTMD. By adding an STMD to the NTMD in parallel, the study indicates that the high amplitude detached resonance can be significantly attenuated. The MTMD (NTMD+STMD) is found effective in suppressing both the steady-state and transient responses. A parametric study of the design parameters of the MTMD is conducted. It is found that the addition of an STMD with a small mass ratio and small damping ratio in parallel with an NTMD results in significant reduction of steady-state response. For transient response reduction, the study shows that the damping ratio of NTMD has a significant effect while the other parameters have minimal effects. Increasing the damping ratio of the NTMD (up to a critical value) increases the decay rate of the transient responses. These results indicate that the design parameters for the MTMD should be appropriately selected to ensure that the MTMD attenuates both the steady-state and transient response effectively.

Attenuation of a linear oscillator using a nonlinear and a semi-active tuned mass damper in series

In this paper, the behavior of a three degrees-of-freedom system is examined, consisting of a linear primary structure (PS), a tuned mass damper with a small cubic stiffness nonlinearity and a semi-active tuned mass damper (STMD) connected in series—each element with a mass approximately two orders of magnitude smaller than the previous. Using numerical simulations, it is determined that an STMD with a mass four orders of magnitude smaller than the PS is able to greatly reduce the amplitude of the PS response by acting to keep the nonlinear tuned mass damper within its linear range. Effective attenuation is dependent on appropriate selection of design parameters—selecting an appropriate STMD mass ratio given its damping, the strength of the stiffness nonlinearity, and the largest forcing amplitude expected. Using a standard tuning approach for the STMD (modulating its stiffness to match the natural frequency of the STMD to the excitation frequency) and comparing its performance with an optimal passive linear tuned mass damper (TMD), the STMD provides a wider-band frequency-response amplitude reduction but often increases the response amplitude slightly above the resonance frequency. A piecewise linear tuning approach for the STMD is proposed which combines the performance benefits of the STMD and the TMD to improve performance and further reduce power requirements.