Inerter-based Dynamic Vibration Absorber Research Articles

Parameter Optimization of Tuned Inerter Damper for Vibration Suppression in Structures with Damping

This study investigates the parameter optimization of tuned inerter damper (TID) in a single degree of freedom (SDOF) system, with a focus on vibration mitigation. As a type of inerter based dynamic vibration absorber (IDVA), TID achieves vibration suppression of the primary structure by replacing the mass block in traditional dynamic vibration absorber (DVA) with an inerter, thereby minimizing the increase in physical mass. With the displacement response of the primary structure as the objective function, this study first employs the classical fixed point theory (FPT) to derive the analytical formulations for the optimal parameters of TID following the H∞ optimization approach and neglecting the inherent damping of primary structure. The influence of optimal parameter deviations on the vibration mitigation effect of TID is also analyzed, revealing that the deviation of the optimal natural frequency ratio has a significant impact on the vibration mitigation performance. By flattening the amplitude curve of the displacement transfer function of primary structure between the fixed points, this study derives the analytical solution for the optimal damping ratio of TID using the extended fixed point theory (EFPT). When the inherent damping of primary structure is considered, this study employs the approximate extended fixed point theory (AEFPT) to derive the approximate optimal parameters of TID. A comparative study of the optimal natural frequency ratios obtained using FPT, AEFPT and numerical searches reveals that the discrepancies among the three methods are minimal for structures with low inherent damping. However, as the inherent damping ratio of the primary structure increases, the optimal natural frequency ratio obtained using FPT deviates significantly from the exact value, whereas the approximate optimal natural frequency ratio derived using AEFPT can significantly reduce this deviation. Combining the conclusion that the vibration mitigation effect of TID is significantly influenced by the natural frequency ratio, this study suggests that for highly damped primary structures, the use of AEFPT can yield more optimal TID parameters, thereby enhancing the robustness of vibration mitigation performance.

Quenching Vibration on a Symmetric Laminated Composite Plate Excited by Multiple Harmonics Using Inerter-based Dynamic Vibration Absorbers

Abstract In this paper a simple and efficient method is developed to quench the steady state vibration of a symmetric laminated composite rectangular plate subjected to multiple harmonics with distinct excitation frequencies. The introduction of the inerter into the traditional dynamic vibration absorber enlarges the solution space for both the feasible attachment locations and the absorber parameters. For a given set of attachment locations, when the traditional vibration absorbers yield physically unrealizable absorber parameters, i.e., negative absorber parameters, an inerter-based vibration absorber can be used such that the absorber parameters become strictly positive. Using the assumed modes method, the governing equations of the laminated composite plate carrying the inerter-based dynamic vibration absorbers are first formulated. A set of constraint equations is established by enforcing nodes at user-specified locations on the plate. Harmonic excitations consisting of a single or multiple distinct excitations are considered. In addition, two attachment scenarios are analyzed: when the attachment and node locations coincide, and when they are distinct. Numerical experiments show that the absorbers parameters can be readily determined for both cases, and validate the proposed method of enforcing the desired node locations when the plate is subjected to either a single or multiple harmonic excitations.

Analytical optimization of inerter-based dynamic vibration absorbers with negative stiffness (INDVAs) using a reduced 2-degree-of-freedom (2DOF) model

The incorporation of an inerter, with its mass amplification capability, along with a negative stiffness spring characterized by high static-low dynamic stiffness, can significantly enhance the vibration control performance of traditional tuned mass dampers (TMDs). The previous analytical solution for the optimal parameters of inerter-based dynamic vibration absorbers with negative stiffness (INDVAs) is a generalized single-degree-of-freedom (GSDOF) model with INDVAs attached. When utilizing INDVAs for controlling wind-induced responses in high-rise buildings, the accuracy of the GSDOF model is compromised. Therefore, a multi-degree of freedom (MDOF) model is initially reduced to a simplified 2-degree of freedom (2DOF) model using a clustering algorithm in this study. The H-∞ optimization method is then employed to derive simplified analytical solutions for the optimal parameters of the three types of INDVAs. The robustness of the parameters and the control effect of these optimal INDVAs are subsequently compared with those of numerical solutions generated through a multiobjective genetic algorithm and with those of analytical solutions based on the GSDOF model. The results demonstrate that for the same type of INDVA, compared with the multiobjective genetic algorithm, the optimal INDVA calculated by the 2DOF model can achieve the same control effect on the structural wind-induced response, while the time cost is lower. In addition, the optimal INDVA obtained by the 2DOF model has a superior control effect on the wind-induced displacement and acceleration response compared to those of the GSDOF model, especially when the INDVA has a substantial inertance ratio and spans multiple floors.

Analytical optimization of an inerter‐based dynamic vibration absorber for suppressing plate vibration

AbstractAn inerter‐based dynamic vibration absorber (IDVA) is proposed and applied to suppress the vibration of a plate. The dynamic model of a thin rectangular plate attached with an IDVA is established and the frequency response function of the transverse displacement of the plate is derived through the classical vibration theory and the analysis in the domain. In addition, the equation for frequency ratios of fixed points is obtained, and the condition for the existence of four fixed points is found by investigating the problem of solving quartic equations. Moreover, the extended fixed‐point method is employed to analytically obtain the optimal parameters of the IDVA attached to a plate, the expressions of the optimal damping ratio and other dimensionless qualities are presented.

Analysis of virtual inerter-based passive absorber for active chatter control

This paper presents a novel approach to active chatter control in milling operations using a new concept called the virtual inerter-based dynamic vibration absorber (VIDVA). While passive control methods, such as tuned mass damper (TMDs), have their merits, they may not provide optimal performance and adaptability in certain scenarios. Moreover, the realisation of an idealised inerter-based absorber as a localisation addition can be a difficult task to achieve. In response of these challenges, the integration of the inerter concept into virtual passive absorber (VPA) control to improve chatter stability performance is proposed. Four IDVAs are numerically evaluated to enhance the absolute chatter stability limit, and the numerical results are experimentally validated using cutting tests with a proof-mass actuator providing the control force. The study also includes robustness and actuator saturation analysis to provide a comprehensive evaluation of the proposed virtual IDVA. The findings demonstrate that the virtual IDVA offers improved chatter suppression performance, making it a promising solution for active chatter control and application of IDVAs in milling operations.

Performance Evaluation of Inerter-Based Dynamic Vibration Absorbers for Wind-Induced Vibration Control of a Desulfurization Tower

High-rise flue gas desulfurization towers are susceptible to wind loads, which can cause instability and failure in the along-wind and across-wind directions. The tuned mass damper (TMD) has been widely applied in the wind-induced vibration control of high-rise structures. To enhance the control performance and reduce the auxiliary mass of TMD, this study focuses on inerter-based dynamic vibration absorbers (IDVAs) for controlling the vibration response of a desulfurization tower. The dynamical equations of the tower–IDVA systems are established under wind loads, and a parameter optimization strategy for IDVAs is proposed by using the genetic algorithm. The performance of the traditional TMD and six IDVAs in the vibration control of the tower are systematically compared. Numerical simulations demonstrate that both the TMD and IDVAs can substantially mitigate the vibration response of the tower. However, compared to the TMD with the same response mitigation ratio, more than 34% of the auxiliary mass can be reduced by two optimal IDVAs. In addition, the energy dissipation enhancement and lightweight effect of the two IDVAs are explained through parametric studies.

Optimal grounded inerter-based dynamic vibration absorber for controlling inertial force-induced vibrations in rotating machines

ABSTRACT This paper proposes the optimal design of GIDVA for inertial force-induced vibrations reduction in rotating machinery considered as primary system. For this purpose, simple-to-use closed-form suboptimal design solutions were first derived based on the extended fixed point theory (EFPT). Then, the H ∞ optimization problem was formulated, which was reduced to solving a constrained system of multi-variable nonlinear equations. Thus, by considering the analytical solutions based on the EFPT as a starting point in order to accelerate the convergence of the system, the Newton-Raphson method was applied to numerically solve the nonlinear system equations for the range values of the mass ratio 1 % ≤ μ ≤ 10 % . For this range of values, the proposed GIDVA was compared with the traditional dynamic vibration absorber (TDVA) and the non-traditional dynamic vibration absorber (NDVA). The results of comparison shown that the proposed GIDVA is 47.76–70.66% and 44.82–70.54% superior to the optimized TDVA and NDVA, respectively, in the steady state vibrations suppression of primary system under inertial excitation, and can widen the effective frequency band 70.22–80.98% and 64.07–80.95% superior to TDVA and NDVA, respectively. These results were confirmed in the time domain simulation of the primary system response considered as a centrifuge pump. For this range of values, the proposed GIDVA was compared with the TDVA and the NDVA. The results of comparison shown that the proposed GIDVA is 47.76–70.66% and 44.82–70.54% superior to the optimized TDVA and NDVA, respectively, in the steady state vibrations suppression of primary system under inertial excitation and can widen the effective frequency band 70.22–80.98% and 64.07–80.95% superior to TDVA and NDVA, respectively. These results were confirmed in the time domain simulation of the primary system response considered as a centrifuge pump.

Vibration reduction of primary structure using optimum grounded inerter-based dynamic vibration absorber

Vibration reduction of primary structure using optimum grounded inerter-based dynamic vibration absorber

Dynamics analysis and parameter optimization of a vibration absorber with geometrically nonlinear inerters

The inerter-based dynamic vibration absorber (DVA) is a promising technique for vibration control. In most studies, the inerter is usually mounted in the same direction as that of the motion, which may not adequately reflect the vibration suppression capability and the two-terminal inertial feature of the inerter, and even weakens the performance of vibration absorbers. Considering the potentiality of improving the control performance by unconventional mounting methods, a rarely studied structure of geometrically nonlinear inerters is introduced into the vibration absorber system. This novel vibration absorber is presented to investigate the following issues, that is, the unknown coupled dynamical behavior between the complex nonlinear force with inertia, damping, and stiffness terms generated by this structure and the vibration absorber system, the possibility of vibration absorption facilitated by this structure, and the full utilization of the two-terminal inertial feature of the inerter. The approximate solutions of the system are obtained using the harmonic balance method. The influence of each variable on the system response is analyzed, and the system parameters are optimized by using the grey wolf algorithm. In addition to the ordinary resonance phenomenon, there are also dynamic features such as soft characteristic jump behavior and response loops at certain parameter range. As a nonlinear system, this model is more stable than the nonlinear energy sink (NES). The optimized amplitude-frequency curves are equal-peak stable, similar to the linear vibration absorbers. The robustness of system parameters is high for small inerter-mass ratios or excitation amplitudes, which is better than DVAs. Compared to the classical linear vibration absorber, NES, and improved NES, the vibration suppression capacity and damping bandwidth of this model are enhanced. In comparison, it is also found that this model has smaller optimum parameters than the classical NES and equivalent inerter-enhanced DVA and NES. This model offers a new solution for the design and implementation of passive vibration absorbers with comprehensive performance.

Vibration reduction performance for the novel grounded inerter-based dynamic vibration absorber controlling a primary structure under random excitation

This paper investigates the control performance of a novel grounded inerter-based dynamic vibration absorber (GI-DVA) for random vibration reduction. First, the dynamics equations of the coupled system are written and the transfer function is obtained based on the Laplace transform. Then, assuming that the primary structure is under random white noise excitation, the displacement variance of the primary structure is calculated based on the exact definition of the H2 norm, by solving the Lyapunov equation. By imposing that the partial derivatives of the response variance of the primary structure with respect to the system parameters are simultaneously equal to zero, the optimum design values of the H2 optimized GI-DVA were derived numerically for given different mass ratio. It can be found that the optimal design parameters as the inerter-to-mass ratio, the stiffness ratio and the damping ratio increase, while the frequency ratio decreases with the increase in the mass ratio. Under the optimal conditions, the response analysis showed that the primary structure response controlled by the H2 optimized GI-DVA can decrease with the increase in the mass ratio, but is less sensitive to large mass ratios, and can be robust to the mistuning on the optimum design parameters. Then, the control performance evaluation is first performed in the frequency domain, which reveal that the dynamic response reduction capacity of the H2 optimized GI-DVA are significantly 62% and 48% superior to the H2 optimized classic DVA (CDVA) and high-performance passive nontraditional inerter-based DVA (NIDVA-C4), respectively. Furthermore, for the root mean square response evaluation (H2 performance), the H2 optimized GI-DVA can provide significantly H2 performance 58% and 50% than the H2 optimized CDVA and NIDVA-C4, respectively. To obtain more realistic results, the time domain simulation is performed, which showed that the GI-DVA can provide significantly performance for random vibration reduction.

Implementation of Inerter-Based Dynamic Vibration Absorber for Chatter Suppression

AbstractChatter is one of the major issues that cause undesirable effects limiting machining productivity. Passive control devices, such as tuned mass dampers (TMDs), have been widely employed to increase machining stability by suppressing chatter. More recently, inerter-based devices have been developed for a wide variety of engineering vibration mitigation applications. However, no experimental study for the application of inerters to the machining stability problem has yet been conducted. This article presents an implementation of an inerter-based dynamic vibration absorber (IDVA) to the problem of chatter stability, for the first time. For this, it employs the IDVA with a pivoted-bar inerter developed in the study by Dogan et al. (2022, “Design, Testing and Analysis of a Pivoted-Bar Inerter Device Used as a Vibration Absorber, Mechanical Systems and Signal Processing,” 171, p. 108893) to mitigate the chatter effect under cutting forces in milling. Due to the nature of machining stability, the optimal design parameters for the IDVA are numerically obtained by considering the real part of the frequency response function (FRF), which enables the absolute stability limit in a single degree-of-freedom (SDOF) to be maximized for a milling operation. Chatter performance is experimentally validated through milling trials using the prototype IDVA and a flexible workpiece. The experimental results show that the IDVA provides more than 15% improvement in the absolute stability limit compared to a classical TMD.

Flexural Wave Bandgaps in a Prestressed Multisupported Timoshenko Beam with Periodic Inerter-Based Dynamic Vibration Absorbers

Locally resonant (LR) metamaterial structures possess bandgaps in which wave propagation is significantly attenuated. In this paper, we discuss flexural wave bandgaps in an LR beam subjected to a global axial force and multiple vertical elastic supports. An array of inerter-based dynamic vibration absorbers (IDVAs) was periodically attached to the LR beam. The flexural wave band structure of this prestressed multisupported LR beam was first derived using the transfer matrix method (TMM) and then explicitly illustrated through a numerical example. Four bandgaps were identified: a bandgap located in the low-frequency zone, a Bragg band generated by Bragg scattering, and two LR bands generated by the local resonance of the IDVAs. The effects of the IDVA parameters, axial force, and vertical elastic support on the properties of the bandgaps were evaluated. In particular, the bandgaps merged accompanied by an exchange of their edge frequencies. The bandwidth of the merged bandgap was nearly equal to the sum of the bandwidths of the bandgaps involved, indicating a method for controlling broadband flexural vibration through the bandgap splicing mechanism.

Optimization design and stability analysis for a new class of inerter-based dynamic vibration absorbers with a spring of negative stiffness

This article investigates the parameter optimization problem for a novel inerter-based dynamic vibration absorber (IDVA) system with a grounded negative stiffness spring, which can be applied to many vibration control systems, such as building vibrations, bridge vibrations, vehicle suspensions, etc. The passive mechanical network in the IDVA system of this article is the parallel connection of a passive spring and a three-element damper-spring-inerter series network. First, the motion equations of the IDVA system are established based on Newton’s second law, and the transfer function in the dimensionless form is derived. Then, the H ∞ optimization problem is formulated for the given values of the mass ratio and negative stiffness ratio. Since it is found that the frequency response curves of this system pass through four fixed points that are independent of the damping ratio, the extended fixed-point method is adopted to optimize the system. Then, the analytical solutions of the optimal parameter values in terms of the mass ratio and negative stiffness ratio are derived, and the necessary and sufficient condition for the IDVA system with optimal parameter values to be stable is obtained by the Hurwitz criterion. Compared with other four optimal DVAs in the existing literature, the optimal IDVA system with a grounded negative stiffness spring can provide better H ∞ performance, and the numerical examples illustrate that the system can provide better time-domain performances under random excitations.

Impulsive resistant optimization design of tuned viscous mass damper (TVMD) based on stability maximization

Recently, inerter based dynamic vibration absorbers (IDVAs) have been extensively investigated to control the harmonic and stochastic vibrations. Numerous studies on the theoretical H∞ and H2 optimizations and numerical analysis have been presented for various structures under different excitations. The variance of the stochastic vibration responses can be largely reduced by using these approaches. However, for excitations with non-stationary impulsive characteristics, such as near-fault earthquake and transient gusty wind, the control of peak responses is also concerned. But there are few related investigations on this topic. In order to address this problem, this paper investigates the vibration control performance of tuned viscous mass damper (TVMD) for impulsive stochastic excitations. Firstly, the transfer function (TF) and impulsive response function (IRF) of the vibrating system are analytically derived. Subsequently, the stability maximization (SM) result is obtained by optimizing poles of TF. The control performances of TVMD and TID based on H∞ and SM solutions subjected to impulsive excitations are compared, and the effectiveness of the SM-based TVMD is demonstrated. Considering the practical requirement of TVMD, an integrated optimization procedure that considers the balance of damping force and control performance is proposed. The corresponding empirical formulas for the optimal TVMD design are established. Through a numerical example, the effectiveness of the proposed method and empirical formulas are validated. In addition, the resulting optimal TVMD design outperforms the design based on H∞ optimization. Statistically, the resulting peak responses induced by the impulsive earthquake and wind can be reduced up to 41.0% and 22.1%, respectively.

Realization of low-frequency stop band in Timoshenko beam with periodic IDVAs

The most prominent dynamic characteristic of metamaterials is that they possess the frequency pass bands and band gaps. In the bandgap, the elastic waves will attenuate significantly, and this property is potentially used to control low-frequency vibrations in civil engineering. To open the low-frequency bandgap of the Timoshenko beam, inerter-based dynamic vibration absorbers (IDVAs) are arranged periodically in the beam. An analytical methodology based on transfer matrix method was developed to predict the flexural wave dispersion characteristics, and was validated by test and numerical experiments. The band gaps can be simultaneously tuned by the parameters of the IDVAs, including spring stiffness, inertance and attached mass. Moreover, the band gaps generated by single IDVAs are independent of each other, and a super-wide bandgap can be achieved by splicing the band gaps for metamaterial beams with graded IDVAs. Explicit formulas with respect to the parameters of IDVAs have been developed to determine the condition of bandgap merging, which can broaden the bandwidth effectively. Finally, a computer-based program was presented to determine the reasonable design parameters.

Low frequency band gap for box girder attached IDVAs

Elastic metamaterial is a kind of periodic structures in which the locally resonators are periodically arranged. The most prominent dynamic characteristic of the metamaterials is that they possess the frequency pass bands and band gap. In the band gap, the elastic waves will attenuate significantly and this property is potentially used to control low frequency engineering vibration. Although many efforts have been made to lower the band gap frequency and broaden the band width, the host beams are usually imaginary Euler beam with rectangular section, not Timoshenko beam with box-section in engineering, in which the effects of rotary inertia and shear deformation shall be considered. Moreover, how to design the metamaterial beam with light-weight and low frequency band gap is still a big challenge because the conflict between the frequency band gap and mass of resonators. To address this issue, the inerter-based dynamic vibration absorbers (IDVAs) are adopted to realize the low frequency band gap due to its amplification mechanism. Band gap structure of Timoshenko beam with IDVAs has been developed based on the spectral element method and validated by the test and numerical experiments. And then, a simplify method to predict the starting frequency of band gap has been presented and the band width has been broadened by band gap merging mechanism. Finally, a computer based design method of metamaterial box girder with IDVAs has been presented and applied to control the vertical vibration of footbridge box girder.

Parameter Optimization for a Novel Inerter-based Dynamic Vibration Absorber with Negative Stiffness

A novel dynamic vibration absorber(DVA) model with negative stiffness and inerter-mass is presented and analytically studied in this paper. The research shows there are still two fixed points independent of the absorber damping in the amplitude frequency curve of the primary system when the system contains negative stiffness and inerter-mass. The optimum frequency ratio is obtained based on the fixed-point theory. In order to ensure the stability of the system, it is found that inappropriate inerter coefficient will cause the system instable when screening optimal negative stiffness ratio. Accordingly, the best working range of inerter is determined and optimal negative stiffness ratio and approximate optimal damping ratio are also obtained. At last the control performance of the presented DVA is compared with three existing typical DVAs. The comparison results in harmonic and random excitation show that the presented DVA could not only reduce the peak value of the amplitude-frequency curve of the primary system significantly, but also broaden the efficient frequency range of vibration mitigation.

Design, testing and analysis of a pivoted-bar inerter device used as a vibration absorber

In this paper a new design for a small scale inerter-based dynamic vibration absorber (IDVA) is presented, based upon a pivoted-bar mechanism. There are several new innovations in this study. The first is to design, build and test an inerter-based device that does not need to be grounded, or placed between different parts of the structure in order to create relative motion. Instead, the relative motion is created between an auxiliary mass and the host structure. Secondly, the pivoted-bar mechanism is designed to act as a pure inerter, and avoids unbalanced inertance effects such as those that occur in the dynamic antiresonant vibration isolator (DAVI). Thirdly, the effects of parasitic mass are minimised by using (i) the appropriate device arrangements, (ii) numerical optimisation, and (iii) fine tuning of the device by adding small additional masses. Fourth, the optimum device damping values are obtained by using a gel damper that can be modelled as a hysteretic damper. In addition, the design uses frictionless flexure hinges that have a small amount of stiffness that can affect the device performance. It is shown how this can also be compensated for using the design optimisation and fine tuning strategies. Detailed design and analysis methodologies are provided, in order to extend the existing work on inerters towards practical design and implementation. In terms of applications, it is anticipated that the design would be suitable for small-size restricted-space applications. A prototype of the design for a small-scale and relatively high frequency application is manufactured. Experimental and numerical results show that the device provides a 18% improvement in performance compared to a classical tuned mass damper (TMD).

Innovative negative-stiffness inerter-based mechanical networks

This paper presents the optimal design for novel negative-stiffness non-traditional inerter-based dynamic vibration absorbers called NS-NIDVAs. The underlying idea of negative-stiffness inerter-based mechanical networks (NS-IMNs) was inspired by the negative-stiffness technology concept. Firstly, the non-dimensional mathematical models for NS-NIDVAs are established considering the harmonic force excitation case, and then the dimensionless frequency response functions of the primary structure are computed for optimization purposes. Therefore, a dynamic stability analysis was conducted in order to determine the allowable boundary on negative stiffness variable. Moreover, the Extended Fixed Points Technique (EFPT) has been proposed as an optimal calibration procedure taking in account the undamped system case. In order to ensure a trade-off among the invariant points of the primary structure's FRFs, a constraint equation was added to the EFPT's optimality approach. It was proved that the allowable negative stiffness solution computed by the constraint equation is in accordance with that provided by the Routh- Hurwitz stability criterion. The short optimal explicit functions revealed that the NS-NIDVA-C4 has a similar optimal tuning magnitude as the NS-NIDVA-C6 and C3, with the devices providing the same dynamic performance. In view of this dynamic characteristic, the H∞ performance measure is computed for both NS-NIDVAs devices considering a practical application mass ratio range. When the NS-NIDVA-C4’s performance is compared to the other passive high-performance devices, an improvement of more than 50% in DMF reduction is obtained. Additionally, the NS-NIDVA-C4 can broaden the effective operating bandwidth from 46% to 82% when compared to the classic DVA. Therefore, it has been proved that NS-NIDVA-C4 has the versatility of yielding high-performance with a small physical mass of the DVA, which is the significant finding of this work.

Random Response of Nonlinear System with Inerter-based Dynamic Vibration Absorber

Random Response of Nonlinear System with Inerter-based Dynamic Vibration Absorber