Feasibility study of nonlinear tuned mass damper for machining chatter suppression

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

Suppression of maglev vehicle-girder self-excited vibration using a virtual tuned mass damper

The self-excited vibration that occurs between a stationary Electromagnetic Suspension (EMS) maglev vehicle and a girder is a practical problem that greatly degrades the performance of a maglev system. As of today, this problem has not been fully solved. In this article, the principle underlying the self-excited vibration problem is explored, and it is found that the fundamental resonance frequency of the maglev girder plays a vital role in the initiation of the self-excited vibration. To suppress the self-excited vibration, a scheme applying a tuned mass damper (TMD) to the maglev girder is proposed, and the stability of the combined system is analyzed. Furthermore, a novel concept of a virtual TMD is introduced, which uses an electromagnetic force to emulate the force of a real TMD acting on the girder. However, in the presence of the time delay caused by the inductance of the electromagnets, the stability analysis of the levitation system combined with the virtual TMD becomes complex. Analysis of the stability shows that there exist some repeated time delay zones within which the overall system is stable. Based on this rule, time delay control is introduced to stabilize the system with a virtual TMD, and a procedure to determine the optimal time delay and gain is proposed. Numerical simulation indicates that the proposed virtual TMD scheme can significantly suppress the self-excited vibration caused by one unstable vibration mode, and is suitable for application to EMS maglev systems.     

Generalized framework for robust design of tuned mass damper systems

The primary purpose of this contribution is to develop a novel framework for generalized robust design of tuned mass damper (TMD) systems as passive vibration controllers for uncertain structures. This versatile strategy is intended to be free of any restriction on the structure-TMD system configuration, the performance criterion, and the number of uncertain parameters. The main idea pursued is to adopt methods and concepts from the robust control literature, including: (1) the linear fractional transformation (LFT) formulation pertaining to the structured singular value (μ) framework; (2) the concept of weighted multi-input multi-output (MIMO) norms for characterizing performance; and (3) a worst-case performance assessment method to avoid the unacceptable computation burden involved with exhaustive search or Monte Carlo methods in the presence of multiple uncertainties. Based on these, the robust design framework is organized into four steps: (1) modeling and casting the overall dynamics into the proposed LFT framework that isolates the TMD system as the controller, and the uncertainties as a structured perturbation to the nominal dynamics; (2) setting up the optimization problem based on generalized indices of nominal performance, robustness, and worst-case performance; (3) implementing a genetic algorithm (GA) for solution of the optimization problem; and (4) post-processing the results for systematic visualization, validation, and selection of preferred designs. This strategy has been implemented on several illustrative design examples involving a seismically excited multi-story building with different combinations of assumptions on the uncertainty, TMD configuration, excitation scenarios, and performance criteria. The resulting solution sets have been studied through various post-processing methods, including visualization of Pareto fronts, uncertain frequency response plots, time-domain simulations, and random vibration analysis.     

Extended Kalman filter for modal identification of structures equipped with a pendulum tuned mass damper

Pendulum tuned mass dampers (PTMDs) have been employed in several full-scale applications to attenuate excessive structural motions, which are mostly due to wind. Conducting periodic condition assessments of the devices to ascertain their health is necessary to ensure their continued optimal performance, which involves identifying the modal parameters of the underlying (bare) structure to which they are tuned to. Such an identification is also necessary for the design of control systems such as adaptive tuned mass dampers. Existing methods of arresting the motion of the damper to estimate the modal properties are expensive, time-consuming, and not suitable for online tuning. Instead, in this paper, parameter estimation using the Extended Kalman Filter (EKF) is proposed to undertake this task. The central task accomplished here is to estimate the dynamic characteristics of the bare structure (structure without the PTMD) from response measurements of the coupled main structure and PTMD system. The proposed methodology relies on ambient acceleration measurements of TMD-attenuated responses to estimate the bare structural modal frequencies, damping, and mode shapes, which can then be used either for condition assessment or for control. The application of EKF to modal parameter estimation is not new. However, a methodology to address the problem in wind engineering arising from stochastic disturbances present in both the measurement and state equations, and unknown process and noise covariances arising due to ambient excitations, is presented for the first time. Extensively studied for synthetic data, these two challenges have limited thus far the application of Kalman filtering to practical wind engineering parameter estimation problems using experimentally obtained measurements. In this paper, a detailed methodology is presented to address these challenges by using a modified form of the standard EKF equations, together with an algorithm to estimate the unknown disturbance and measurement noise covariances. Numerical simulations and an experimental study are both presented. Results demonstrate that the method proposed provides reliable estimates for the modal parameters required to perform condition assessment and control tasks for pendulum tuned mass dampers.     

Real-time hybrid shaking table testing method for the performance evaluation of a tuned liquid damper controlling seismic response of building structures

In this paper, a real-time hybrid shaking table testing method (RHSTTM) is experimentally implemented for evaluating the performance of a tuned liquid damper (TLD) controlling a seismically excited building structure. The RHSTTM does not require a physical building structural model in performing the experiment of a TLD-structure interaction system and it only uses a TLD and a shaking table. The structural responses of the interaction system are calculated numerically in real time using an analytical building model, a given earthquake record, and a shear force generated by the TLD, and the shaking table reproduces both the controlled and uncontrolled absolute acceleration of the TLD installed floor by modulating the feedback gain of the shear force signal measured by the load-cell positioned between the TLD and the shaking table. Comparison between the structural responses obtained by the RHSTTM and the conventional shaking table test of a single story steel frame with TLD indicates that the performance of the TLD can be accurately evaluated using the RHSTTM without the physical structural model. Finally, the uncontrolled and TLD-controlled structural responses of a three story structure are obtained by the RHSTTM in both time and frequency domains, showing that TLD can effectively mitigate the seismic responses of building structures.     

Optimum vibration absorber (tuned mass damper) design for linear damped systems subjected to random loads

Optimum design of dynamic vibration absorbers (DVAs) installed on linear damped systems that are subjected to random loads is studied and closed-form design formulas are provided. Three cases are considered in the optimization process: Minimizing the variance of the displacement, velocity and acceleration of the main mass. Exact optimum design parameters for the velocity case, which to the best knowledge of the author do not exist in the literature, are derived for the first time. Exact solutions are found to be directly applicable for practical use with no simplification needed. For displacement and acceleration cases, a solution for the optimum absorber frequency ratio is obtained as a function of optimum absorber damping ratio. Numerical simulations indicate that optimum absorber damping ratio is not significantly related to the structural damping, especially when the displacement variance is minimized. Therefore, optimum damping ratio derived for undamped systems is proposed for damped systems for the displacement case. When acceleration variance is minimized, however, the optimum damping ratio derived for undamped systems is found not as accurate for damped systems. Therefore, a more accurate approximate expression is derived. Numerical comparisons with published approximate expressions at the same level of complexity indicated that proposed design formula yield more accurate estimates. Another important finding of the paper is that for specific applications where all of the response parameters are desired to be minimized simultaneously, DVAs designed per velocity criteria provide the best overall performance with the least complexity in the design equations.     

Analysis of liquid sloshing of a tuned magnetic fluid damper for single and co-axial cylindrical containers

A tuned magnetic fluid damper (TMFD) is a dynamic absorber using a magnetic fluid. A characteristic of the TMFD is changing natural frequency of a magnetic fluid sloshing under a magnetic field. The magnetic fluid sloshing in a coaxial cylindrical container was analyzed theoretically under the axisymmetrical magnetic field. The theoretical results showed that a radial component of the magnetic field also changed the natural sloshing frequency. A policy of the suitable design of the TMFD was presented and the effect of the radial component of the magnetic field was verified experimentally.     

Auxiliary mass throw in a tuned and damped vibration absorber

Dynamic vibration absorbers should be tuned and optimally damped to control the amplitudes of vibration of the primary mass over the whole range of exciting frequencies. The lighter the auxiliary mass the greater is the amplitude of its excursions relative to the primary mass. In the case of the tuned system the maximum steady state throw of the auxiliary mass can be easily calculated from the formulas given. These are most elegantly derived by use of a frequency locus technique. It is shown that is the system is also optimally damped the throw of the auxiliary mass has its minimum value which depends only on the mass ratio.     

Performance analysis of nonlinear vibration isolator with magneto-rheological damper

A nonlinear vibration isolator is considered to study effectiveness of isolation against harmonic force and displacement excitations. Nonlinearity in the magneto-rheological (MR) fluid based damper as well as in the elastic member is taken into account. The MR-damper has been modeled including Bouc–Wen hysteretic element and the spring is taken to have cubic nonlinearity. Analytical expression for the energy dissipation characteristics of the damper has been derived. Near resonant response of the isolated mass is obtained by a modified averaging technique suitable for hysteretic type nonlinearity present in the system. The performance of the isolators is estimated for various nonlinear stiffness values, both hardening and softening types. Different performance measures are also proposed to judge the performance of the nonlinear isolator.     

Closed-form formulas for the optimal pole-based design of tuned mass dampers

This paper deals with the analysis and optimization of tuned mass dampers (TMDs). It provides design formulas for maximizing the exponential time-decay rate (ETDR) of the system transient response. A detailed analysis is presented for the classical TMD configuration, involving an auxiliary mass attached to the main structure by means of a spring and a dashpot. Analytic expressions of the optimal ETDR are obtained for any mass ratio and tuning condition. Then, a further optimization with respect to the latter is performed. The proposed method is applied also to other TMD configurations involving an auxiliary mass connected to both the main structure and the ground, as well as to a piezoelectric damping device. A justification to the well-known heuristic optimality condition based on the enforcement of coincident couples of complex conjugate poles is presented. That condition is shown, however, to fail in providing optimal solutions for some mass ratio values and/or TMD configurations, and the optimality conditions prevailing in those cases are derived. The present analysis, besides its theoretical interest, may be useful in practical applications, e.g., to assess the sensitivity of the optimal ETDR with respect to the design parameters or to promptly adjust some of those parameters during service, after any variation of the operative conditions.     

Hysteretic tuned mass dampers for structural vibration mitigation

The hysteresis exhibited by short steel wire ropes is shown to lend itself as an effective restoring force for nonlinear monodirectional tuned mass dampers. Experiment-driven modeling based on the identified hysteretic restoring forces together with continuation tools enables an optimal design of these dampers through construction of families of frequency–response curves over a wide range of excitation amplitudes. Semi-analytical/numerical and experimental studies are carried out considering a base-excited test structure represented by a simply supported beam together with a prototype of the hysteretic damper subject to either harmonic or filtered Gaussian white noise excitations.     

Effective mass overshoot in single degree of freedom mechanical systems with a particle damper

We study the response of a single degree of freedom mechanical system composed of a primary mass, M, a linear spring, a viscous damper and a particle damper. The particle damper consists in a prismatic enclosure of variable height that contains spherical grains (total mass m_p). Contrary to what it has been discussed in previous experimental and simulation studies, we show that, for small containers, the system does not approach the fully detuned mass limit in a monotonous way. Rather, the system increases its effective mass up and above M+m_p before reaching this expected limiting value (which is associated with the immobilization of the particles due to a very restrictive container). Moreover, we show that a similar effect appears in the tall container limit where the system reaches effective masses below the expected asymptotic value M. We present a discussion on the origin of these overshoot responses and the consequences for industrial applications.     

On the dynamic behaviour of a mass supported by a parallel combination of a spring and an elastically connected damper

This paper presents a consistent and concise analysis of the free and forced vibration of a mass supported by a parallel combination of a spring and an elastically supported damper (a Zener model). The results are presented in a compact form and the physical behaviour of the system is emphasised. This system is very similar to the conventional single-degree-of freedom system (sdof)—(Voigt model), but the dynamics can be quite different depending on the system parameters. The usefulness of the additional spring in series with the damper is investigated, and optimum damping values for the system subject to different types of excitation are determined and compared.There are three roots to the characteristic equation for the Zener model; two are complex conjugates and the third is purely real. It is shown that it is not possible to achieve critical damping of the complex roots unless the additional stiffness is at least eight times that of the main spring. For a harmonically excited system, there are some possible advantages in using the additional spring when the transmitted force to the base is of interest, but when the displacement response of the system is of interest then the benefits are marginal. It is shown that the additional spring affords no advantages when the system is excited by white noise.     

A comparison between different optimization criteria for tuned mass dampers design

Tuned mass sampers (TMDs) are widely used strategies for vibration control in many engineering applications, so that many TMD optimization criteria have been proposed till now. However, they normally consider only TMD stiffness and damping as design variables and assume that the tuned mass is a pre-selected value. In this work a more complete approach is proposed and then also TMD mass ratio is optimized. A standard single degree of freedom system is investigated to evaluate TMD protection efficiency in case of excitation at the support. More precisely, this model is used to develop two different optimizations criteria which minimize the main system displacement or the inertial acceleration. Different environmental conditions described by various characterizations of the input, here modelled by a stationary filtered stochastic process, are considered. Results show that all solutions obtained considering also the mass of the TMD as design variable are more efficient if compared with those obtained without it. However, in many cases these solutions are inappropriate because the optimal TMD mass is greater than real admissible values in practical technical applications for civil and mechanical engineering. Anyway, one can deduce that there are some interesting indications for applications in some actual contexts. In fact, the results show that there are some ranges of environmental parameters ranges where results attained by the displacement criterion are compatible with real applications requiring some percent of main system mass. Finally, the present research gives promising indications for complete TMD optimization application in emerging technical contexts, as micromechanical devices and nano resonant beams.     

Exploring new mass regions with the ISOLTRAP spectrometer

First direct mass measurements on rare earth isotopes around ¹⁴⁶Gd have been performed with the Penning trap mass spectrometer ISOLTRAP at ISOLDE/CERN. More than 40 isotopes of the elements Pr, Nd, Pm, Sm, Eu, Dy and Ho have been measured with an accuracy of typically 1 × 10^-7. In the case of ¹⁴¹Sm isomeric and ground state (ΔE = 175 keV) were resolved. Since isobaric contaminations are present in the ISOLDE beam, these measurements on rare earth isotopes became only possible after the installation of a new cooler trap which acts an isobar separator. This revised version was published online in August 2006 with corrections to the Cover Date.     

Geometrically nonlinear vibrations of rectangular plates carrying a concentrated mass

Nonlinear forced vibrations of rectangular plates carrying a central concentrated mass are studied. The plate is assumed to have immovable edges and rotational springs; numerical results are presented for clamped plates. The Von Kármán nonlinear plate theory is used, but in-plane inertia in both the plate and the mass is retrained. The problem is discretized into a multi-degree-of-freedom (dof) system by using an energy approach and Lagrange equations taking damping into account. A pseudo-arclength continuation method is used in order to obtain numerical solutions. Results are presented as both (i) frequency-amplitude curves and (ii) time domain responses. The effect of gravity and the effect of the consequent initial plate deflection are also investigated.     

Exploring the performance of spatial stochastic simulation algorithms

Since the publication of Gillespie’s direct method, diverse methods have been developed to improve the performance of stochastic simulation methods and to enter the spatial realm. In this paper we discuss a spatial τ-leaping variant (Sτ) that extends the basic leap method. Sτ takes reaction and both outgoing and incoming diffusion events into account when calculating a leap candidate. A performance analysis shall reveal details on the achieved success in balancing speed and accuracy in comparison to other methods. However, performance analysis of spatial stochastic algorithms requires significant effort — it is crucial to choose suitable (benchmark) models and to carefully define model and simulation setups that take problem and simulation design spaces into account.     

On the nonlinear dynamics of a single degree of freedom oscillator with a time-varying mass

In this paper the forced vibrations of an undamped single degree of freedom oscillator with a time varying mass will be studied. An initial value problem for an oscillator equation with a Rayleigh type of nonlinearity will be formulated, and by applying a straight-forward perturbation method the problem will be solved approximately. The approximations of the solutions will be used to construct a map. By using this map the stability properties of the solutions can be determined. The stability properties of the nonlinear problem will be compared to those for the linear problem, which have been studied earlier in the literature. The instability regions in the parameter space and some phase-space figures for the nonlinear problem will be computed numerically. It will also be shown how the behaviour of the solutions changes when the instability regions in the parameter space are crossed.     

Crowd-induced random vibration of footbridge and vibration control using multiple tuned mass dampers

This paper investigates vibration characteristics of footbridge induced by crowd random walking, and presents the application of multiple tuned mass dampers (MTMD) in suppressing crowd-induced vibration. A single foot force model for the vertical component of walking-induced force is developed, avoiding the phase angle inaccessibility of the continuous walking force. Based on the single foot force model, the crowd-footbridge random vibration model, in which pedestrians are modeled as a crowd flow characterized with the average time headway, is developed to consider the worst vibration state of footbridge. In this random vibration model, an analytic formulation is developed to calculate the acceleration power spectral density in arbitrary position of footbridge with arbitrary span layout. Resonant effect is observed as the footbridge natural frequencies fall within the frequency bandwidth of crowd excitation. To suppress the excessive acceleration for human normal walking comfort, a MTMD system is used to improve the footbridge dynamic characteristics. According to the random vibration model, an optimization procedure, based on the minimization of maximum root-mean-square (rms) acceleration of footbridge, is introduced to determine the optimal design parameters of MTMD system. Numerical analysis shows that the proposed MTMD designed by random optimization procedure, is more effective than traditional MTMD design methodology in reducing dynamic response during crowd-footbridge resonance, and that the proper frequency spacing enlargement will effectively reduce the off-tuning effect of MTMD.