Design optimization of a damped hybrid vibration absorber

In this article, the H_∞ optimization design of a hybrid vibration absorber (HVA), including both passive and active elements, for the minimization of the resonant vibration amplitude of a single degree-of-freedom (sdof) vibrating structure is derived by using the fixed-points theory. The optimum tuning parameters are the feedback gain, the tuning frequency, damping and mass ratios of the absorber. The effects of these parameters on the vibration reduction of the primary structure are revealed based on the analytical model. Design parameters of both passive and active elements of the HVA are optimized for the minimization of the resonant vibration amplitude of the primary system. One of the inherent limitations of the traditional passive vibration absorber is that its vibration absorption is low if the mass ratio between the absorber mass and the mass of the primary structure is low. The proposed HVA overcomes this limitation and provides very good vibration reduction performance even at a low mass ratio. The proposed optimized HVA is compared to a recently published HVA designed for similar propose and it shows that the present design requires less energy for the active element of the HVA than the compared design.     

Optimal active absorber with internal state feedback for controlling resonant and transient vibration

An active, standalone vibration absorber utilizing the state feedback taken from the absorber mass is proposed. Expressions of the optimum absorber parameters are obtained both by optimizing the Η_∞ norm of the frequency response function. For improved transient response featuring low peak response and fast attenuation, the design procedure utilizes the mode equalization followed by the maximization of the damping. An interesting feature of the proposed absorber is that the performance of the absorber does not require having its natural frequency close to the natural frequency of the primary system as is generally the case for tuned passive absorbers or other active and semi-active tuned vibration absorbers. In fact, the performance of the proposed system can be progressively enhanced by increasing the absorber frequency. Compared to the optimum passive absorber, the optimal active absorber can yield wider bandwidth of operation around the natural frequency of the primary system and lower frequency response within the suppression band. The active absorber also offers better transient response compared to the passive absorber both optimized for the best transient responses. The efficacy of the absorber is analyzed both for a single-degree-of-freedom and beam like primary structure.     

Optimization of a hybrid vibration absorber for vibration control of structures under random force excitation

A recently reported design of a hybrid vibration absorber (HVA) which is optimized to suppress resonant vibration of a single degree-of-freedom (SDOF) system is re-optimized for suppressing wide frequency band vibration of the SDOF system under stationary random force excitation. The proposed HVA makes use of the feedback signals from the displacement and velocity of the absorber mass for minimizing the vibration response of the dynamic structure based on the H₂ optimization criterion. The objective of the optimal design is to minimize the mean square vibration amplitude of a dynamic structure under a wideband excitation, i.e., the total area under the vibration response spectrum is minimized in this criterion. One of the inherent limitations of the traditional passive vibration absorber is that its vibration suppression is low if the mass ratio between the absorber mass and the mass of the primary structure is low. The active element of the proposed HVA helps further reduce the vibration of the controlled structure and it can provide significant vibration absorption performance even at a low mass ratio. Both the passive and active elements are optimized together for the minimization of the mean square vibration amplitude of the primary system. The proposed HVA are tested on a SDOF system and continuous vibrating structures with comparisons to the traditional passive vibration absorber.     

H2 optimization of a non-traditional dynamic vibration absorber for vibration control of structures under random force excitation

The H₂ optimum parameters of a dynamic vibration absorber of non-traditional form are derived to minimize the total vibration energy or the mean square motion of a single degree-of-freedom (sdof) system under random force excitations. The reduction of the mean square motion of the primary structure using the traditional vibration absorber is compared with the proposed dynamic absorber. Under optimum tuning condition, it is shown that the proposed absorber when compared with the traditional absorber, provides a larger suppression of the mean square vibrational motion of the primary system.     

Dynamics modelling of beams with shunted piezoelectric elements

General modelling of a resonant shunting damper has been made from piezoelectric sensor/actuator equations. It is found that an additional damping, which is augmented to a system, is generated by the shunt damping effect. The transfer function of the tuned electrical absorber is derived for both series and parallel shunt circuit. The governing equations and associated boundary conditions are derived using Hamilton's principle. The shunt voltage equation is also derived from the charge generated in PZT due to beam vibration. The frequency response function of the obtained mathematical model is compared with that of the tuned electrical absorber and experimental work. The vibration amplitude is reduced about 15 dB at targeted second mode frequency.     

Robust non-fragile dynamic vibration absorbers with uncertain factors

In this paper, the design problem for non-fragile dynamic vibration absorbers (DVAs) is investigated. Due to the imprecision of the manufacturing process or the variation during the operation, uncertainty in the parameters of the DVA is unavoidable. The uncertainty may degrade the performance of the designed DVA or even deteriorate the system. Hence, it is practically demanding to propose a design method for a non-fragile DVA, i.e., when the parameters of the DVA vary in an admissible range, an expected vibration suppression level should be guaranteed. The uncertainty of the DVA is feasibly assumed to be norm-bounded. Then, the design problem for the DVA is converted into a static output feedback (SOF) control problem. Sufficient condition for the existence of the non-fragile DVA with a prescribed H_∞ level is derived by using a bilinear matrix inequality (BMI). An iterative linear matrix inequality (ILMI) method is employed to solve the BMI condition. Finally, a design example is given to show the effectiveness of the proposed approach.     

Semi-active on–off damping control of a dynamic vibration absorber using Coriolis force

A passive dynamic vibration absorber (DVA) moving along a pendulum can cause the nonlinear Coriolis damping to reduce the pendulum swing. This paper proposes a simple semi-active on–off damping controller to improve the passive Coriolis DVA. The aim of the on–off damping control is to amplify the DVA resonance motion to increase the energy dissipated. Moreover, the paper finds the analytical solution of the harmonic vibration of semi-active controlled system. The accuracy of the analytical formulas and the superior performance of the semi-active DVA are verified by numerical simulations.     

The effective damping approach to design a dynamic vibration absorber using Coriolis force

In this paper, the vibration reduction of a pendulum structure with dynamic vibration absorber (DVA) using Coriolis force is investigated. When the pendulum structure is subjected to a single harmonic excitation, the effective damping of Coriolis force is used with the second-order approximations to obtain the closed forms of optimal parameters of the DVA. The closed forms obtained show that the natural frequency of the absorber should be tuned to twice that of the pendulum. The closed forms of optimal parameters are verified by numerical optimization. The modified forms of optimal parameters are proposed to be used in case of general excitation. Base on this modified form, the design procedure is demonstrated by the numerical calculation of the free vibration and wind-induced vibration of a ropeway gondola.     

H∞ optimization of fluid viscous dampers for reducing vibrations of high-speed railway bridges

This work deals with the optimization of fluid viscous damper systems (FVDs) to reduce the resonant dynamic structural response of high-speed railway bridges by algebraic and numerical approaches. The presented method chooses the objective function based on the _H∞$H_{\infty }$ norm over the frequency band of interest. This function allows taking into account structural damping properties and minimizing simultaneously the structural response associated with multiple modes. Especially, the proposed objective function may also be extended to nonlinear problems to determine optimal parameters of nonlinear fluid viscous dampers which may be an interesting solution in applications where high force levels are expected in the dampers. Finally, the proposed method is validated through numerical simulations. The simulation results show that the optimal FVD coefficients obtained by using the presented method are more exact than those by the previous method. Besides, the effectiveness of the method for solving the problems with the contribution of high modes and the consideration of nonlinear FVDs is also proved.     

Suppression of random vibration in flexible structures using a hybrid vibration absorber

A design method is proposed to suppress stationary random vibration in flexible structures using a hybrid vibration absorber (HVA). While the traditional vibration absorber can damp down the vibration mainly at the pre-tuned mode of the primary structure, active damping is generated by the proposed HVA to damp down all resonant modes of interest of the vibrating structure and the spatial average mean square motion of the vibrating structure can be minimized. Only one absorber and one feedback signal are required to achieve global vibration suppression of a flexible structure under stationary random excitation. A special pole-placement controller is designed such that all vibration modes of the flexible structures become critically damped. It is proved analytically that the proposed HVA damps the vibration of the entire structure instead of just the attachment point of the absorber. The proposed optimized HVA is tested on a beam structure and it shows a superior performance on global suppression of broadband vibration in comparison to other published designs of passive and hybrid vibration absorbers.     

Vibrations of a beam with an absorber consisting of a viscoelastic beam and a spring-viscous damper

The effectiveness of the dynamic vibration absorber which consists of a double-cantilever viscoelastic beam and a spring-viscous damper is studied. The absorber is attached to the centre of the main beam. The ends of the main beam are built in and excited sinusoidally by the base motion. In the numerical example, the displacement transmissibility, i.e., the ratio of the displacement at the centre of the main beam to that of the base, is investigated. Variations of the resonant peaks are shown when the absorber parameters are changed. Values of the optimum tuning design parameters are presented, and it is verified that two of the main beam resonances are optimized simultaneously.     

Development of a new damper to reduce resonant vibrations in lightweight steel joist floors

Floor vibrations annoying to humans often occur in lightweight constructions. A number of methods to solve the problem of resonant vibrations are reported in the literature. Tuned mass damper, semi-active tuned vibration absorber and active control system are all examples of existing methods. A new method has been tested in laboratory environment on a prefabricated floor containing a resilient ceiling with a size up to 6.8×4.8 m². The method takes advantage of small pieces of visco-elastic material connected between the ceiling joists and the primary beams. A finite element model is used to calculate the correct amount of visco-elastic material. The new damper is especially effective in damping mode shapes where the ceiling oscillates out of phase relative to the floor but shows improvements for other mode shapes as well.     

Studies of the performance of particle dampers under dynamic loads

This paper presents a systematic investigation of the performance of particle dampers (vertical and horizontal) attached to a primary system (single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF)) under different dynamic loads (free vibration, stationary random excitation as well as nonstationary random excitation, with single component or multi-component), and the optimum operating regions are all determined. The amount of dissipated energy due to impact and friction, and the concept of “Effective Momentum Exchange” are shown to be suitable “global” measures to interpret the physics involved in the behavior of particle dampers. Using the well-established discrete element method, the motion of vertical particle dampers can be analyzed and classified into three different regions, and the associated damping characteristics can be interpreted. The first mode of a MDOF primary system can be effectively controlled by a properly designed particle damper; however, the higher modes are more affected by other parameters. Consequently, extensive parametric studies are presented to evaluate the effects of various system parameters, such as: mass ratio, primary system damping, coefficient of restitution, container dimensions, excitation amplitude and components, input locations and damper locations.     

Energy-to-peak control for seismic-excited buildings with actuator faults and parameter uncertainties

This paper deals with the problem of robust reliable energy-to-peak controller design for seismic-excited buildings with actuator faults and parameter uncertainties. It is assumed that uncertainties mainly exist in damping and stiffness of the buildings because they are difficult to be measured precisely. The objective of designing controllers is to guarantee the asymptotic stability of closed-loop systems and attenuate disturbance from earthquake excitation. Energy-to-peak performance is believed to be of great significance when conditions and requirements of active building vibration control are carefully considered. Based on energy-to-peak control theory and linear matrix inequality techniques, a new approach for reliable building vibration control with satisfactory energy-to-peak performance is presented. An n-degree-of-freedom linear building structure under earthquake excitation is analyzed and simulations are employed to validate the effectiveness of the proposed approach in reducing seismic-excited building vibration. Some comparisons are also made between energy-to-peak control systems and H_∞ control systems to further prove the importance of the method raised in this paper.     

Use of modal energy transfer as a new damping device with controllable bandwidth

This paper presents a new design of nonlinear dynamic absorber (NDA) using the phenomenon of modal energy transfer between the symmetric mode and the anti-symmetric mode of a curved beam. It can reduce the resonance vibration of a primary structure with a controllable operational frequency range. The energy transfer is initiated by an autoparametric vibration and the excitation force required is lowest when the ratio of the resonance frequencies of the first symmetric mode (ω₁) and first anti-symmetric mode (ω₂) is close to 2.The resonance frequency of the first anti-symmetric mode (ω₂) can be altered to control the operational frequency range. The autoparametric vibration response can be used to create an energy-dissipative region with a controllable bandwidth. It is also possible to create a non-dissipative region in between two dissipative regions. This is useful for providing damping for a conventional dynamic absorber without adding high damping material. The damping is due to the dissipation of energy to anti-symmetric mode. Numerical calculations indicate that the resonance vibration of a primary structure can be successfully reduced using this approach. The results are verified with experimental data.     

Numerical investigation of coexisting high and low amplitude responses and safe basin erosion for a coupled linear oscillator and nonlinear absorber system

Over the last half century, numerous nonlinear variants of the tuned mass damper have been developed in order to improve attenuation characteristics. In the present study, the performance of a linear oscillator and an absorber with a strongly nonlinear cubic stiffness is evaluated by using numerical methods. This configuration has been of recent interest due to its capability of wide-band energy absorption. However, high amplitude solutions, which would amplify the response of the system, have been shown to often coexist with the low amplitude solutions. The present research is focused on numerically determining the relative strength of the coexisting solutions. Erosion profiles are presented, quantifying the integrity of the system, i.e. the likelihood of converging to a safe, low amplitude response, and providing an indication of the structural safety of a practical absorber system. The results indicate that the high amplitude solutions not only exist but significantly influence the response of the system within the range of expected operating conditions, particularly at excitation frequencies lower than the natural frequency of the linear oscillator. The erosion profiles indicate a 20–40% increase in system integrity for the case of zero damping compared to a small amount of damping, no significant integrity change when adding a small linear stiffness component to the nonlinear absorber, and no significant change in integrity between the midpoint and extreme of the bi-stable range. Additional higher-period solutions are also discovered and evidence of a chaotic response is presented.     

Proportional-plus-integral semiactive control using magnetorheological dampers

Magnetorheological (MR) dampers are a promising alternative to structural active actuators as they provide adjustable damping over a wide range of frequencies without large power requirements. However, the complex dynamics that characterizes these devices makes it difficult to formulate control laws based on the MR damper model. Instead, many semiactive control strategies proposed in the literature have been based on the idea of “clipping” the voltage signal so that the MR damper force “tracks” a desired active control force which is computed on-line. With this idea many algorithms have been proposed using, among others, techniques such as optimal control, H_∞ control, sliding mode control, backstepping and QFT.This work presents a semiactive control strategy based on the same idea of “clipping” the voltage signal but using a simpler PI design. The proportional and integral gains of the controller are calculated so that the controller guarantees stability, minimization of the closed loop response and robustness against modeling errors. Effectiveness of the control strategy is compared to some others techniques and passive cases as well. Simulation results shows that this simple strategy can effectively improve the structural responses and achieve performance index comparable to that of more complex algorithms.     

Experiments on the search for the effect of resonant screening on the probability of Mössbauer absorption of <Superscript>119<Emphasis Type="Italic">m</Emphasis></Superscript>Sn gamma rays

Experiments on the search for the effect of resonant screening on the Mössbauer absorption of ^119m Sn γ rays of energy 23.8 keV emitted by a standard Mössbauer Ca^119m SnO₃ γ source in the resonant SnO₂ absorber of natural isotopic composition are described. Intensities of tin γ rays and X-rays that passed through the absorber were measured with and without a resonant cylindrical screen (which was a black absorber for the 23.8-keV Mössbauer γ line) around the absorber and their ratios were calculated for each radiation separately. No difference beyond the experimental error was found between these ratios measured with the γ source both at rest and when oscillating with a frequency and amplitude enough to completely break the conditions for Mössbauer resonant absorption of 23.8-keV γ rays. The upper limit for the relative decrease, due to the influence of the resonant screen, in the intensities of these γ rays after their passing through the resonant absorber was 0.00030.     

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.