Conventional Tuned Mass Damper Research Articles

Vibration attenuation of dual periodic pipelines using interconnected vibration absorbers

Pipelines are crucial elements in various engineering applications. However, unexpected vibrations from different sources can jeopardize the operational performance and potentially damage the piping structures and other connected units. This study explores flexural wave propagation and attenuation characteristics of the pipes supported periodically on a rack. Also, a specific case of a rack with infinite stiffness (simple support) is investigated. The dispersion relations pertinent to pipe rack scenario is obtained through transfer matrix method (TMM) in conjunction with Floquet-Bloch’s theorem, and the accuracy of ensuing band gaps (BGs) are confirmed through finite element (FE) models. Following this, the modal analysis is performed to ascertain the minimum number of unit-cells necessary for the FE model to accurately mimic the attenuation and propagation characteristics of the corresponding infinite structure. The findings indicate that a pipe supported on rack displays resonance and Bragg-type BGs, arising from local resonance and spatial periodicity, respectively, while the pipe on simple support exhibits only Bragg-type BGs. To control low-frequency vibrations in dual pipelines placed on the rack, a novel configuration using interconnected dynamic vibration absorbers (DVAs) is proposed. The DVA consisting of two spring-damper units along with a mass is connected across the center of each span of the two pipelines. The proposed DVA is designed via genetic algorithm-based optimization. It was found that the designed DVA significantly reduces the vibration of the two pipelines. The performance of DVAs improves with an increase in the mass ratio. Additionally, the performance of pipes connected with conventional tuned mass damper (TMD) is evaluated and compared with the proposed DVA. The effectiveness of DVAs is also verified by employing a white Gaussian noise as input. The proposed DVAs are efficient in scenarios involving multiple pipes within a rack, leveraging other pipe’s mass, stiffness, and damping properties to mitigate vibrations in the considered pipes.

Mechanical behavior and seismic control performance of a metallic torsional damper for flexible structures

The use of metallic dampers is an effective way to reduce seismic responses and dissipate excessive vibration energy for civil structures. Conventional metallic dampers employed energy dissipation by plastic deformation under bending or shear modes are hard to design, and may cause uniform distribution of stress in the metallic components. In this paper, employing the high plastic deformation capacity of aluminum materials, a metallic torsional damper using a gear and rack device (MTDGRD) is proposed to enhance the control effectiveness for the structural response reduction under earthquakes. The static mechanical behavior and energy dissipation of aluminum metallic components under torsional deformation are experimentally studied. Moreover, the configuration and working principle of the proposed damper are introduced. The dynamic behavior of the proposed damper is experimentally studied. For precise modeling in simulations, the elastic-plastic theory of torsional deformation is used to derive the mechanical model of the proposed damper and the model accuracy is validated by experimental data. Finally, numerical simulations under different seismic ground motions controlled by a proposed MTDGRD are compared to that controlled by a conventional tuned mass damper (TMD) for a 10-floor flexible structure. The results show that aluminum 6061# of the energy dissipation capacity is higher than aluminum 1060#. The dynamical tests show that the loading frequency and operational cycles have very limited effect on mechanical behavior and energy consumption capacity of the MTDGRD. The proposed dynamic mechanical model of the MTDGRD has considerable accuracy in numerical simulations and seismic control simulations show the better performance of the proposed damper in reducing structural displacement responses than the conventional TMD with a mass ratio of 0.5 %.

Control of edgewise vibration of a pre-twisted rotating beam with shunted piezoelectric tuned mass damper

The edgewise vibration control of a pre-twisted beam, rotating in the vertical plane, is considered in this study. A piezoelectric tuned mass damper (PTMD) comprising a spring–mass–damper system and a piezoelectric transducer with its associated shunt circuit is considered the control device. A finite element formulation of the pre-twisted rotating beam with the attached PTMD is developed while considering the effect of centrifugal stiffening due to rotation and the effect of gravity force. The natural frequencies of the beam (without PTMD) obtained using the present formulation are corroborated by comparing them with the results derived from Ansys. A single PTMD attached at the tip end of the beam can effectively suppress the response of the beam subjected to a distributed load in the edgewise direction. The best values of resistance and inductance of the shunt circuit are obtained through a parametric study on the peak and root mean square value of the beam tip response. A qualitative difference in the uncontrolled as well as in the controlled responses can be noticed while considering the effect of the gravity load component in the edgewise direction. Further, it has been observed that the conventional Tuned Mass Damper (TMD) provides better control than the PTMD system for ideally tuned conditions, however, the control performance of TMD degrades rapidly as compared to the PTMD in the presence of detuning. This demonstrates the effectiveness of PTMD in a practical implementation where achieving the perfectly tuned condition is seldom realized. The control performance of PTMD marginally degrades when the beam is subjected to multi-directional excitation. Hence, the proposed control system has the potential for application in rotating beam-type structures, such as wind turbine blades.

Optimization of column-in-column system based on non-conventional TMD concept

Previous studies showed that the non-conventional tuned mass damper (TMD) with large mass ratio outperforms the traditional one in respect to the structural vibration control efficiency and robustness. The authors recently proposed a novel control system based on the non-conventional TMD concept, namely the column-in-column (CIC) system, which was composed of a primary column, a secondary column and a series of interconnected springs/dashpots. In this novel system, the secondary column connected to the primary one with springs/dashpots could act as a large TMD to attenuate adverse vibration of the primary structure, and its control effectiveness was preliminarily verified through numerical investigations. However, the control robustness was found not sufficient based on the existing optimal formulae in the literature for CIC optimization. This paper presents a new design method for optimizing the CIC system for better harnessing its control effectiveness and robustness in reducing structural response. The CIC system consists of two columns with distributed mass and uniform flexural rigidity, connected by springs along the column height. The effective modal mass and modal stiffness of a specific vibration mode of the system can be straightforwardly calculated by using the Euler-Bernoulli beam theory. Considering the fundamental vibration mode of the system as the target response mode for vibration control, the multiple degree-of-freedom (DOF) CIC is simplified into a two DOF with three springs (2DOF3S) structural model, the design parameters, i.e., the optimal tuning frequency ratio and damping ratio of this system are derived to minimize the displacement response of the primary structure. To demonstrate the proposed design method, the effectiveness and robustness of the CIC system in controlling seismic induced structural vibrations are assessed in both the frequency and time domains. Results show that the derived optimum formulae are applicable for optimizing the TMD system with consideration of the distributed mass and deformation of the mass damper, i.e., a column in this study. The optimized CIC system has good control robustness even if the CIC is mistuned with its design parameters deviate from the optimal values by ±50 %. The conventional TMD system with lumped mass as the mass damper is a special case of the proposed CIC system. The optimized CIC system has favorable control efficiency in mitigating the seismic responses of structures with reduction ratios averagely varying within the range of 15 % ∼ 55 % with a probability of 92.67 %. It is concluded that the proposed method is reliable and can be used for the optimum design and control of the CIC system.

H∞ closed-form solution of tuned mass damper enhanced with negative stiffness element (TMD-NS) for structural vibration control

Negative stiffness element has been applied to improve the control performance of tuned mass dampers (TMDs) recently, and two tuned mass dampers enhanced with negative stiffness (TMD-NS) element, namely KDamper (Without loss of generality, it is referred to as TMD-NS I in the present study) and Extended KDamper (EKD, TMD-NS II), have been developed. Previous studies have demonstrated the control effectiveness of TMD-NS I and II. However, there still exist some issues to be addressed: (1) previous studies normally optimize TMD-NS via the intricate and time-consuming numerical methods, the analytical solutions for the optimal design parameters of TMD-NS II remain unknown; (2) a comprehensive and exhaustive evaluation that compares the control effectiveness of TMD-NS I and II is absent from existing literature. To fill these research gaps, this study derives closed-form optimum solutions for TMD-NS II using the H∞ approach. The control effectiveness of TMD-NS I and II in suppressing the seismic responses of structures is investigated systematically. Specifically, the analytical model of an undamped SDOF system equipped with TMD-NS I or II is first developed within a unified framework, and corresponding dynamic equations of motion are formulated. Subsequently, the optimal parameters of TMD-NS I and II are derived based on the classical “fixed-point” theory. Based on the derived optimal parameters, the control effectiveness of TMD-NS I and II are examined by using a damped SDOF system subjected to harmonic excitations and real earthquake ground motions. Finally, a 5-storey isolated benchmark building model is adopted to further investigate the effectiveness of TMD-NS in the seismic protection of engineering structures. The results reveal that the derived closed-form solutions are accurate in capturing the optimal parameters of TMD-NS. In addition, both the optimized TMD-NS I and II outperform the conventional TMD in reducing the seismic responses of structures. Furthermore, TMD-NS I proves more effective in reducing the absolute acceleration of the isolated building, whereas TMD-NS II demonstrates better performance in mitigating the isolating deformation. In a nutshell, both the TMD-NS I and II are highly effective alternatives to conventional TMDs, showcasing superior performance in vibration reduction and robustness.

Fluid inerter-based vibration control of multi-modal structures subjected to vertical vibration

The so-called inerter is an attracting device that offers a solution to the goal of realizing or improving structural control devices with high mass ratios while avoiding the undesirable increase in dead load. The research presented here focuses on evaluating the performance of a fluid inerter in mitigating vertical vibrations of structures that exhibit multi-modal behavior, such as plates. First, a numerical study based on previous experimental data investigates the properties of the connection between the inerter and the structure to be controlled. Considering that a flexible connection has been shown to introduce a linearization effect, while a rigid connection of the inerter to the controlled structure can achieve significant displacement reductions, the influence of these two connection types over different inertance ratios is analyzed. To evaluate the practical suitability of the flexible connection to reduce the inherent nonlinear effects associated with the device, a novel application of the fluid inerter for vibration control in multi-modal structures is presented, exemplified by a cross-laminated timber panel, and compares its control performance with that of a conventional Tuned Mass Damper (TMD). This provides insight into the effectiveness of the inerter in controlling vertical vibrations. In addition, optimization procedures are employed to determine connection parameters that enhance the effectiveness of both the TMD and the inerter in mitigating vertical vibrations.

Enhancing seismic resilience of nonlinear structures through optimally designed additional mass dampers

Reducing dynamic responses in structures subjected to external excitations like earthquakes and strong winds is crucial for ensuring safety and serviceability. Conventional tuned mass dampers (CTMDs) have limitations in mitigating nonlinear vibrations efficiently. This research proposes the use of additional mass dissipation (AMD) devices to control nonlinear dynamic responses more effectively than CTMDs. The AMD concept involves installing an auxiliary mass–damper system atop the primary structure. An analytical approach is developed to determine the optimal design parameters of AMDs for linear and nonlinear single-degree-of-freedom systems using H2 and H∞ optimization techniques. Transfer function and harmonic balance methods are employed to evaluate the dynamic response reduction capabilities. Compared to optimally designed CTMDs, the proposed H2 and H∞ optimized AMDs demonstrate remarkably superior vibration mitigation achieving up to 77 % and 73.71 % greater reductions in dynamic responses, respectively. The Newmark-beta numerical validation confirms AMDs outperforming CTMDs by 16.06 % in minimizing structural vibrations. The novel AMD concept, coupled with the derived optimal design formulations, offers a highly effective vibration control strategy for both linear and nonlinear structural systems under harmonic and random excitations. This analytical solution paves the way for implementing AMDs in practice to enhance structural safety and longevity against external dynamic loads.

Damping enhancement of nodal modes for stay cables using a single-sided pounding tuned mass damper (SS-PTMD)

Extra long stay cables, owned characteristics of light weight and low damping, may produce large-amplitude vibrations in modes with relatively high frequencies under a moderate wind speed. Installing a transverse fluid viscous damper near the cable anchorage to add maximum damping to the first few cable modes is a traditional method to improve the cable modal damping ratio. However, the installation location of the damper may be coincide with the nodal point of some high vibration modes, and diminishing the damping effect to a large extent. To tackle this nodal mode issue, a single-sided pounding tuned mass damper (SS-PTMD), which exhibits superior control performance over a conventional tuned mass damper (TMD), is adopted to enhance the damping ratio of nodal modes. The coupled equations of motion of a cable equipped with a SS-PTMD are established, and impact force between damper mass and the cable are considered by a impact force model. Free pounding tests are performed to study the pounding behavior with different viscoelastic (VE) material layers and various types of pounding strikers. Numerical simulations are carried out to investigate the damping enhancement and vibration mitigation effect of the SS-PTMD on the cable under various loading cases, including harmonic and simulated turbulent wind excitations. Field performance validations of the SS-PTMD is performed on a cable numbered A10 of the Dongting Lake Bridge. The results from free pounding tests show that the selection of the VE material layers and strikers can greatly affect the pounding behavior of the SS-PTMD. The Numerical simulation of the coupled cable-SS-PTMD system reveals that the SS-PTMD can effectively enhance the damping ratio of the target mode by a SS-PTMD with only 1.08% mass ratio. The numerical results show that SS-PTMD is effective in mitigating the high-oder nodal mode vibration of the cable. Field tests show that after the installation of SS-PTMD, the 2nd-mode modal damping ratio of the cable increases from 0.15% to 1.8%.

Metamaterial-based vibration control for offshore wind turbines operating under multiple hazard excitation forces

Wind energy holds growing investment perspectives due to its renewable and sustainable energy production potential. The harvesting capability of wind turbines is directly related to their size. Therefore, those wind energy generators still encounter challenges related to excessive vibrations aggravated by environmental factors, compromising energy generation and resulting in fatigue damage and downtime. Various vibration control strategies have been explored to address these issues, with passive control emerging as a preferred choice due to its ease of manufacture, cost-effectiveness, and simple installation. Nevertheless, the limitations of these controls lie in their substantial size and weight associated with optimal installation positions for achieving a good performance. Recently, mechanical metamaterials have demonstrated tremendous advancements in efficiency regarding band isolation and vibration mitigation, coupled with enhanced manufacturing possibilities. Hence, this paper proposes a novel approach to control the vibration of wind turbines employing mechanical metamaterials in their design. A spectral approach is used to model the metamaterial turbine and its interaction with external excitations, such as wind, waves, and blade rotation. The numerical results show the efficiency of the metamaterial turbine by its tunable stopband features and vibration amplitude reduction under multiple hazard excitations, emphasising its superior suppressing vibrations compared to conventional tuned mass damper. Thus, the proposed wind turbine metastructures offer a compelling combination of effective vibration attenuation while reducing dynamic resonators’ overall stiffness, mass, and size. The outcome advances wind turbine design and energy technology for reliable wind energy production.

Control of seismic induced response of wind turbines using KDamper

Earthquake-induced vibrations of wind turbines may compromise structural serviceability and safety. Most previous studies adopted passive control devices to mitigate the seismic responses of wind turbines. However, their control effectiveness is heavily dependent on the mass ratio between control devices and wind turbines, and they were typically housed at the tower top or within the nacelle. The restricted space within the hollow tower and the nacelle imposes considerable challenges for the implementation of such devices, rendering the application of large-scale control devices unfeasible for structural vibration control of wind turbines. To this end, this paper integrates a negative stiffness element within a conventional tuned mass damper (TMD), termed KDamper, to mitigate vibrations of wind turbine towers under seismic loads. Specifically, the widely used NREL 5 MW wind turbine is selected as a prototype structure and its tower is modelled as a multiple-degree-of-freedom system. Then KDamper is incorporated into the developed model and its parameters are optimized based on the H2 criterion. Subsequently, the control effectiveness of KDamper is investigated and compared with TMD in the frequency domain, and the control performances in terms of the effectiveness and robustness of KDamper are further examined under a series of earthquake records. Results show that KDamper has superior control effectiveness and robustness than TMD, indicating it has considerable potential for application in improving wind turbine performances against earthquake hazards.

Experimental verification of seismic vibration control of high-rise buildings with friction-type multiple tuned mass dampers

In recent decades, tuned mass damper (TMD) devices have been implemented in numerous high-rise buildings in the world. The vibration of tall buildings caused by natural or man-made dynamic loading poses a challenge. In this study, to ensure structural safety and resident comfort, a friction-type multiple TMD (FT-MTMD) system was investigated and its ability to reduce the seismic response of high-rise buildings was evaluated. The proposed FT-MTMD system comprises multiple TMD units in a parallel arrangement and has a greater frequency bandwidth than a conventional TMD system. To address practical issues, a prototype FT-MTMD system was designed and fabricated to control a scale-down test model which has similar fundamental modal properties to a real 36-story building. Because of the nonlinearity of friction, the parameters of the FT-MTMD system were determined using a proposed optimal design method. First, a component test was conducted to ensure that the parameters of the FT-MTMD agreed with the designed values. Then, the FT-MTMD was installed on the long-period test model and its control performance was experimentally evaluated. Shaking table test results indicated that the FT-MTMD system favorably reduced the seismic response in the test model, indicating that the proposed optimal design method is reliable. A theoretical structure–MTMD model was also developed to simulate the system response with unsynchronized stick-slip motion of the FT-MTMD system. The predicted system response agreed well with the measured response. In addition, to avoid damage to the FT-MTMD system during a severe earthquake, a fail-safe device was employed to lock the TMD when its stroke reached the maximum allowable value.

Latching control: A wave energy converter inspired vibration control strategy

Latching control is a phase optimization control mechanism for improving the energy conversion efficiency of a wave energy converter (WEC). This paper, for the first time, extends the latching mechanism to vibration control to improve energy dissipation efficiency. An innovative semi-active latched mass damper (LMD) is proposed in this paper by integrating conventional tuned mass dampers (TMD) and the latching mechanism. First, the theoretical models of WEC and TMD are compared. Second, the mathematical model of an LMD installed on a single-degree-of-freedom structure is established, and three latching control strategies with different latching time instants, latching durations, unlatching time instants, and required information feedback are tested. Subsequently, the performance of the LMD is evaluated through the comparison with the detuned and optimally tuned TMDs. The characteristics of the latching control force are analyzed in terms of phase, component, energy dissipation, and damping enhancement effect. Lastly, the feasibility and effectiveness of the proposed LMD with three different latching strategies are proven. The latching control can reduce the stiffness component and increase the damping component of the control force, thereby optimizing the phase lag between the control force and the structural response. The proposed latching mechanism and strategies for vibration control can provide an innovative solution to improve the effectiveness of high-frequency detuned dampers, facilitate the design of long-period dampers, and develop adaptive semi-active dampers in the future.

Multiple Tuned Mass Dampers and Double Tuned Mass Dampers for Soft Story Structures: A Comparative Study

Recent seismic events have highlighted the vulnerability of reinforced concrete buildings, especially soft-story structures, to damage and collapse during strong earthquakes due to the ground's vibrational response. This study aims to mitigate these adverse vibrations using passive control mechanisms, particularly tuned mass dampers (TMDs). Conventional TMDs require a substantial mass to effectively influence the structure's lateral reactions. The research explores the use of multi-tuned mass dampers (MTMDs) and double-tuned mass dampers (DTMDs) in a soft-story building. The study uses MATLAB to estimate TMD parameters and subject the models to seismic loading. The comparative assessment of these models reveals the potential benefits of using MTMD and DTMD systems to enhance the seismic resilience of soft-story structures.

Simplified optimization of inerter-enabled tuned mass damper for lightweight-oriented seismic response mitigation of long-span domes

Suspending tuned mass dampers (TMDs) from long-span domes has been studied to mitigate seismic responses of long-span domes. However, the strict weight limitations on the suspension mass in conventional tuned mass dampers (TMDs) hinder their widespread adoption. To address this issue, we introduce the inerter-enabled tuned mass damper (IeTMD) that consists of a suspension mass, tuning spring, and a tuned viscous mass damper (TVMD) sub-system into the seismic vibration mitigation of long-span domes. Under the assumption that long-span domes remain within the elastic range and adhere to the small deformation hypothesis, we have proposed simplified design formulae for IeTMDs, guided by the lightweight-based seismic vibration control criterion. Parametric studies are conducted to illustrate the degree to which an IeTMD can improve the performance of the long-span dome when its key parameters change within certain ranges. The effectiveness of the design strategy in exploiting the damping enhancement effect is confirmed. Time history responses of a benchmark long-span dome demonstrate that the IeTMD has high control efficiency, as bi-directional displacements, accelerations, and base shear are significantly reduced. Comparative analyses between the proposed IeTMD and conventional TMD are conducted. Results show that the IeTMD designed by the simplified design formulae can achieve the target control performance with less suspension mass. Furthermore, the frequency analysis shows that the proposed IeTMD contains a wider control frequency band than conventional TMD, illustrating the promising approach for long-span domes.

A Double-Tuned Pendulum Mass Damper Employing a Pounding Damping Mechanism for Vibration Control of High-Rise Structures

Recently, enhancing conventional tuned mass dampers (TMDs) with a pounding damping mechanism is demonstrated to be an efficient way for vibration control of flexible structures. In this paper, a double-tuned pendulum mass damper employing a pounding damping mechanism (DTPMD-PD) is proposed. DTPMD-PD dissipates energy through the collision between distributed balls with a smaller mass and viscoelastic (VE) boundary, which can effectively reduce noise during operation compared to conventional impact dampers. Moreover, DTPMD-PD utilizes a double-tuning mechanism, and its control performance is significantly enhanced. The motion equations of a multiple degree of freedom (MDOF) structure equipped with DTPMD-PD are formulated. Based on the H∞ optimization criterion, a numerical optimization is performed to obtain the optimal design parameters of DTPMD-PD. Additionally, the pounding dissipation capacity and the parametric identification of the impact force model are investigated through free pounding experiments, and the control performance and robustness of DTPMD-PD are experimentally studied in the laboratory. The results show that the proposed numerical modeling method has considerable accuracy through experimental verifications. The restitution coefficient of the pounding layer has a significant influence on the performance of proposed DTPMD-PD. Optimized DTPMD-PD has better effectiveness than conventional TMDs under harmonic and seismic loads.

The optimum enhanced viscoelastic tuned mass dampers: Exact closed-form expressions

This paper introduces the inertial amplifier viscoelastic tuned mass dampers (IAVTMD). The viscoelastic materials are implanted inside the core material of the inertial amplifier tuned mass dampers. The standard linear solid models are applied mathematically to formulate the viscoelastic material. H2 and H ∞ optimization mechanisms apply to derive the exact mathematical closed-form formulations for optimal design parameters for novel inertial amplifier viscoelastic tuned mass dampers. The optimum IAVTMD installs at the top of the structures to mitigate the dynamic responses, determining the dynamic responses analytically through transfer function formation. At first, IAVTMD’s dynamic response reduction capacity compares with the conventional tuned mass damper’s (CTMD) dynamic response reduction capacity. As a result, H2 optimized IAVTMD’s dynamic response reduction capacity is significantly 20.87% and 26.47% superior to two well-established H2 optimized conventional tuned mass damper’s dynamic response reduction capacity. In addition, H ∞ optimized IAVTMD has 15.48% more dynamic response reduction capacity than H ∞ conventional tuned mass damper. H2 and H ∞ optimized tuned mass damper inerters with optimal closed-form solutions are introduced in this paper. A higher damper mass ratio and a lower inerter mass ratio are recommended to produce H2 and H ∞ optimized tuned mass damper inerter (TMDI) with a lower frequency and damping ratio in an affordable range. Accordingly, H2 and H ∞ optimized IAVTMD’s dynamic response reduction capacities are significantly 6.94% and 23.29% superior to H2 and H ∞ optimized TMDI’s dynamic response reduction capacity. The closed-form expressions for optimal design parameters of inertial amplifier viscoelastic tuned mass dampers and tuned mass damper inerters are mathematically correct and effective for practical applications.

Seismic protection of land-based wind turbine towers using the tuned inerter damper

The tuned inerter damper (TID) has recently emerged in the literature as a bona fide resonant vibration absorber for the seismic protection of building structures by relaxing the requirement for large secondary mass employed in conventional tuned mass dampers (TMDs). This is achieved by leveraging the inertia property of lightweight inerter devices, called inertance. This paper extends the application of the TID to address the seismic response reduction of the supporting towers of land-based wind turbines (WTs). To this aim, a novel vibration suppression strategy is proposed for WT towers in which a TID is attached at two different locations inside and along the height of the tower and is tuned to the tower’s dominant natural frequency. Numerical assessment is supported by developing a finite-element model of the benchmark NREL 5 MW WT equipped with an ad hoc TID model placed at different locations in the tower and with different inertance values. The assessment includes time-domain response history analyses for 28 earthquake ground motions (GMs) with and without pulses under concurrent thrust wind forces for 4 different mean wind speeds. Improved TID vibration suppression performance is noted by installing the TID closer to the tower top and by increasing the inertance and/or the distance of the attachment locations. Further, the TID achieves significant reductions of tower top peak displacement and acceleration as well as peak base shear and bending moment for all the different combinations of GMs and wind speeds, outperforming a conventional TMD with 5% secondary mass ratio placed in the nacelle.

A unified method for parameter optimization and dynamic characteristics analysis of tuned mass damper inerter

To enhance the performance of the tuned mass damper (TMD), an inerter has recently been incorporated into a conventional TMD system to constitute a new type of an inerter-based passive control system, namely, tuned mass damper inerter (TMDI). The present study proposes a unified design idea for the TMDI based on the Kramers–Kronig relations in the complex effective mass. The TMDI is equivalent to a combination of a static mass and a conventional TMD, and the theoretical links between the TMDI and conventional TMD have been established. Based on the proposed method, the performance of the TMDI is investigated combined with the existing dynamic characteristics of the conventional TMD. It is concluded that the proposed design idea is feasible, and the previously reported dynamic characteristics of the TMDI can be well demonstrated. Moreover, the mass ratio of the equivalent TMD can be used to compare the control performance of the TMDI and TMD, and when it is larger than the physical mass ratio, the inerter enhances the control performance of the TMD.

The Optimum Inertial Amplifier Tuned Mass Dampers for Nonlinear Dynamic Systems

The optimum inertial amplifier tuned mass dampers (IATMD) for vibration reduction of linear and nonlinear dynamic systems are introduced in this paper. [Formula: see text] and [Formula: see text] optimization methods are applied to derive the exact closed-form expressions for optimal design parameters such as frequency and viscous damping ratios in simplified form mathematically for IATMD. From the parametric study, using these optimal closed-form solutions, a higher damper mass ratio, a higher amplifier mass ratio, and a lower inertial angle are recommended to design optimum IATMD to achieve robust dynamic response reduction capacity having moderate viscous damping and lower frequency ratios at an affordable range. The optimum IATMD systems are installed on top of linear and nonlinear single-degree-of-freedom systems to mitigate their dynamic responses of them. The linear dynamic responses are determined through transfer matrix formations, and nonlinear dynamic responses are derived using the harmonic balance (HB) method. [Formula: see text] optimized IATMD is significantly [Formula: see text] and [Formula: see text] superior to the [Formula: see text] optimized conventional tuned mass damper one (CTMD1) and conventional tuned mass damper two (CTMD2). Furthermore, [Formula: see text] optimized IATMD is significantly [Formula: see text] superior to the [Formula: see text] optimized conventional tuned mass damper (CTMD). According to the nonlinear dynamic analysis, [Formula: see text] optimized IATMD systems are significantly [Formula: see text], [Formula: see text], and [Formula: see text] superior to the [Formula: see text] optimized CTMD. Furthermore, [Formula: see text] optimized IATMD systems are significantly [Formula: see text], [Formula: see text], and [Formula: see text] superior to the [Formula: see text] optimized CTMD. The results of this study are mathematically accurate and feasible for practical applications.

Robustness of a tuned viscous mass damper (TVMD) controlled system

A tuned viscous mass damper (TVMD) is a novel type of vibration absorber which exhibits outstanding vibration control performance. In this study, an experiment was conducted to investigate the robustness of a TVMD for the vibration control of a typical single degree of freedom (SDOF) structural system. To that end, a new eddy-current TVMD (EC-TVMD) was developed as a representative TVMD device. The TVMD-controlled SDOF system was investigated using a series of shaking table tests. The influence of variations in stiffness of the primary structure and TVMD damping (including damping amplitude and damping nonlinearity) was assessed. The variation in TVMD damping exerted a smaller influence on control performance than the variation in primary structure stiffness. The robustness of TVMD control was enhanced by increasing the inertance-to-mass ratio. Parametric analyses using a numerical model further confirmed the experimental observations, and indicated that a TVMD exhibits improved robustness compared with a conventional tuned mass damper (TMD) which is sensitive to the detuning effect. The vibration control mechanism and robustness characteristics of the TVMD were further revealed by a Kelvin-Voigt model. Finally, the influence of damping nonlinearity was verified by the nonlinear time history analysis of a finite element model of the test structure. The results indicate that damping nonlinearity has limited influence on the control of a TVMD with nonlinear damping as long as this TVMD has the same peak displacement amplification ratio as the optimal linear design.