PERFORMANCE AND DYNAMIC STABILITY OF GENERAL-PATH CENTRIFUGAL PENDULUM VIBRATION ABSORBERS

Centrifugal pendulum vibration absorbers are a type of tuned dynamic absorber used for the attenuation of torsional vibrations in rotating and reciprocating machines. They consist of masses that are constrained to move along specific paths relative to the rotational axis of the machine. Previous analytical studies have considered the performance of single absorber systems with general paths and of multi-absorber systems with a specific path type. In this paper, we investigate the performance and dynamic stability of systems comprised of multiple, identical centrifugal pendulum vibration absorbers riding on quite general paths. The study is carried out by considering a scaling of the system parameters, based on physically realistic ranges of dimensionless parameters, which permits application of the method of averaging. It is found that the performance of these systems is limited by two distinct types of instabilities. In one type, the system of absorbers lose their synchronous character, while in the other a classical non-linear jump affects all absorbers identically, leading to highly undesirable system behavior. These results are used to evaluate two common types of absorber paths, namely circles and cycloids, including intentional mistuning of the absorber frequencies. The results are used to make some recommendations about the selection of paths to achieve design goals in terms of absorber performance and operating range. The analytical predictions are confirmed by numerical simulations.     

Modal properties and stability of centrifugal pendulum vibration absorber systems with equally spaced,identical absorbers

This work develops an analytical model of centrifugal pendulum vibration absorber systems with equally spaced, identical absorbers and uses it to investigate the structure of the modal vibration properties. The planar model admits two translational and one rotational degrees-of-freedom for the rotor and a single arclength degree-of-freedom for each absorber. The gyroscopic effects from rotor rotation are taken into account. Examination of the associated eigenvalue problem reveals well-defined structure of the vibration modes resulting from the cyclic symmetry of the absorbers. The vibration modes are classified into rotational, translational, and absorber modes. Characteristics of each mode type are analytically proved. The effects of the absorber tuning order on the modes are derived. The critical speeds and flutter instability of the system are studied numerically and analytically.     

Non-linear vibrations of a harmonically excited autoparametric system

Harmonic forced vibration of a spring-mass-damper system with a parametrically excited pendulum hinged to the mass is investigated. Two types of restoring forces on the pendulum are considered. The method of harmonic balance is used to evaluate the system response. The results are also verified by numerical integration. Non-periodic system responses are possible if the excitation parameter is large. The performance of the pendulum as an absorber is also studied.     

Dynamic vibration absorbers for vibration control within a frequency band

The use of dynamic vibration absorbers to control the vibration of a structure in both narrow and broadbands is discussed in this paper. As a benchmark problem, a plate incorporating multiple vibration absorbers is formulated, leading to an analytical solution when the number of absorbers yields one. Using this analytical solution, control mechanisms of the vibration absorber in different frequency bandwidths are studied; the coupling properties due to the introduction of the absorber into the host structure are analyzed; and the control performance of the absorber in different control bandwidths is examined with respect to its damping and location. It is found that the interaction between the plate and the absorber by means of the reaction force from the absorber plays a dominant role in a narrow band control, while in a relatively broadband control the dissipation by the absorber damping governs the control performance. When control bandwidth further enlarges, the optimal locations of the absorbers are not only affected by the targeted mode, but also by the other plate modes. These locations need to be determined after establishing a trade-off between the targeted mode and other modes involved in the coupling. Finally, numerical findings are assessed based on a simply-supported plate and a fair agreement between the predicted and measured results is obtained.     

ACTIVE-PASSIVE PIEZOELECTRIC ABSORBERS FOR SYSTEMS UNDER MULTIPLE NON-STATIONARY HARMONIC EXCITATIONS

Previous research has shown that piezoelectric materials can be shunted with electrical networks to form devices that operate similarly to a mechanical vibration absorber. These systems can be tuned to provide modal damping (modal tuning) or to attenuate a harmonic disturbance (tonal tuning). Semi-active piezoelectric absorbers have also been proposed for suppressing harmonic excitations with varying frequency, a scenario that cannot be easily controlled using passive devices. However, these semi-active systems have limitations that restrict their applications. In a previous study, the authors have developed a high performance active-passive alternative to the semi-active absorber that uses a combination of a passive electrical circuit and active control actions. The active control consists of three parts: an adaptive inductor tuning action, a negative resistance action, and a coupling enhancement action. This new device has been shown, both analytically and experimentally, to be very effective for the suppression of harmonic disturbances with time-varying frequency. In the present paper, the adaptive active-passive piezoelectric absorber configuration is extended so that it can track and suppress multiple harmonic excitations. A new optimal tuning law is derived, and the stability conditions of the system are investigated. The effectiveness of this new multi-frequency absorber design is demonstrated by comparing its performance and control power requirement to the popular Filtered-x adaptive feedforward control algorithm.     

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.     

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.     

Dynamic analysis and optimal design of a passive and an active piezo-electrical dynamic vibration absorber

This paper is concerned with the dynamic analysis and parameter optimization of both passive and active piezo-electrical dynamic vibration absorbers that are strongly coupled with a single degree of freedom vibrating structure. The passive absorber is implemented by using an R_s∥L_s parallel shunt circuit while the active absorber is implemented by feeding back the acceleration of the structure through a second-order lowpass filter. An impedance-mobility approach is used for the electromechanical coupling analysis of both types of absorbers coupled with the structure. Using this approach it is demonstrated that the passive and active absorbers can be made exactly equivalent. A maximally flat frequency response strategy is used to find the optimal damping ratio of the passive absorber while a robust, optimal control theory is used to find that for the active absorber. It is found that the passive optimization strategy corresponds to an optimal, robust feedback control of 2 dB spillover. Simulations and experiments are conducted to support the theoretical findings.     

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.     

Vibration control of two degrees of freedom system using variable inertia vibration absorbers: Modeling and simulation

Variable inertia vibration absorbers (VIVA) are previously used for the vibration control of single degree of freedom (dof) primary systems. The performance of such absorbers is studied in many investigations. This paper presents the dynamic modeling and simulation of a proposed modified design of such VIVA’s for the vibration control of two dof primary systems. Lagrange formulation is used to obtain its dynamic model in an analytical form. This model, which is highly nonlinear, is used to develop a computational algorithm to study the absorber performance characteristics. This algorithm is programmed and simulated in Matlab. The obtained results are numerically verified using SAMS2000 software. The effect of mass and stiffness of the proposed VIVA on its performance and tuning is discussed. An optimization algorithm is developed to select the best absorber parameters for vibration suppression of a specific primary system. The obtained results show a good agreement with those obtained using similar techniques. In addition, a linearized model of VIVA dynamics is developed, tested and simulated for the same data used in its nonlinear model. The relative deviation between results of the linear and nonlinear models is less than 1%, which confirms the realistic use of this linearized model. The experimental testing and verification of the simulation results of the proposed VIVA is the subject of another paper.     

Impedance approach to designing efficient vibration energy absorbers

The concept introduced previously by the authors on the best sound absorber having the maximum allowable efficiency in absorbing the energy of an incident sound field has been extended to arbitrary linear elastic media and structures. Analytic relations have been found for the input impedance characteristics that the best vibrational energy absorber should have. The implementation of these relations is the basis of the proposed impedance method of designing efficient vibration and noise absorbers. We present the results of a laboratory experiment that confirms the validity of the obtained theoretical relations, and we construct the simplest best vibration absorber. We also calculate the parameters and demonstrate the efficiency of a dynamic vibration absorber as the best absorber.     

ADAPTIVE-PASSIVE ABSORBERS USING SHAPE-MEMORY ALLOYS

The adaptive-passive vibration absorber shows promise for combining the stability and low complexity of passive tuned absorbers with the robust performance of active vibration control schemes. Previous adaptive tuned vibration absorbers (ATVA) had been complex and bulky. Shape memory alloys (SMA), with their variable material properties, offer an alternative adaptive mechanism. Heating an SMA causes a change in the elastic modulus of the material. An ATVA using spring elements composed of three pairs of SMA wires and one pair of steel wires was constructed and tested. On-off actuation of the SMA elements created an ATVA with four discrete tuned frequencies. Characterization testing of the absorber showed variation of the natural frequency of the ATVA of approximately 15%. The ATVA was applied to a primary system and the frequency response of the system at various states of ATVA actuation was determined. Manual tuning of the ATVA actuation during a stepped-sine base excitation of the primary system showed a wider notch of attenuation than was possible with a non-adaptive absorber. Results of the tests indicate that an adaptive absorber incorporating SMA as a tuning element has potential as a simple, high-performance adaptive-passive technique for vibration control.     

Broadband and ultra-low reflection metamaterial absorber embedded with magnetic materials

In this study, we design, prepare and characterize a broadband, ultra-low reflectivity and incidence angle-insensitive metamaterial absorber. The design of this absorber not only provides a novel idea for the design of broadband absorbers, but also enhances the application prospects of metamaterial absorbers. By introducing FeSiAlp/epoxy magnetic composite and optimizing the structural parameters, the absorption performance of the metamaterial absorber has been significantly improved. The effective absorption bandwidth (bandwidth with reflectivity less than −10dB) is increased by 3.4 times from 2.19 GHz to 7.49 GHz, and the RL_min (minimum reflection loss) value reaches −38.31 dB at 17.83 GHz, that is the absorption rate reaches 99.99%. Meanwhile, the experimental results also verify the simulation design results. Therefore, the absorber not only plays the characteristics of strong absorption of metamaterial, but also absorbs the advantages of broadband of magnetic material.     

Stability improvement and regenerative chatter suppression in nonlinear milling process via tunable vibration absorber

In this paper, a tunable vibration absorber set (TVAs) is designed to suppress regenerative chatter in milling process (as a semi-active controller). An extended dynamic model of the peripheral milling with closed form expressions for the nonlinear cutting forces is presented. The extension part of the cutting tool is modeled as an Euler–Bernoulli beam with in plane lateral vibrations (x–y directions). Tunable vibration absorbers in x–y directions are composed of mass, spring and dashpot elements. In the presence of regenerative chatter, coupled dynamics of the system (including the beam and x–y absorbers) is described through nonlinear delay differential equations. Using an optimal algorithm, optimum values of the absorbers' position and their springs' stiffness in both x–y directions are determined such that the cutting tool vibration is minimized. Results are compared for both linear and nonlinear models. According to the results obtained, absorber set acts effectively in chatter suppression over a wide range of chatter frequencies. Stability limits are obtained and compared with two different approaches: a trial and error based algorithm and semi-discretization method. It is shown that in the case of self-excited vibrations, the optimum absorber improves the process stability. Therefore, larger values of depth of cut and consequently more material removal rate (MRR) can be achieved without moving to unstable conditions.     

Active control effort of hybrid piezoelectric absorber for structural control

This paper aims at addressing the active control effort of the active-shunted hybrid piezoelectric absorber for structural vibration suppression. Both active control efforts of the integrated and separated hybrid piezoelectric absorbers are analyzed by using a simple cantilevered beam example. It is recognized that a new hybrid piezoelectric absorber based on a switching operation is capable of reducing the active control effort. A switching type of the hybrid piezoelectric absorber can be developed by the simple combination of integrated and separated hybrid piezoelectric absorbers. It is demonstrated that the switching type of the absorber has the capability of the trade-off between the active control effort and the damping performance.     

Tuneable vibration absorber design to suppress vibrations: An application in boring manufacturing process

Dynamic vibration absorbers are used to reduce the undesirable vibrations in many applications such as electrical transmission lines, helicopters, gas turbines, engines, bridges, etc. Tuneable vibration absorbers (TVA) are also used as semi-active controllers. In this paper, the application of a TVA for suppression of chatter vibrations in the boring manufacturing process is presented. The boring bar is modeled as a cantilever Euler–Bernoulli beam and the TVA is composed of mass, spring and dashpot elements. In addition, the effect of spring mass is considered in this analysis. After formulation of the problem, the optimum specifications of the absorber such as spring stiffness, absorber mass and its position are determined using an algorithm based on the mode summation method. The analog-simulated block diagram of the system is developed and the effects of various excitations such as step, ramp, etc. on the absorbed system are simulated. In addition, chatter stability is analyzed in dominant modes of boring bar. Results show that at higher modes, larger critical widths of cut and consequently more material removal rate (MRR) can be achieved. In the case of self-excited vibration, which is associated with a delay differential equation, the optimum absorber suppresses the chatter and increases the limit of stability.     

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.     

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.     

An investigation and modelling of energy dissipation through sloshing in an egg-shaped shell

Sloshing absorbers work on a similar principle to that of tuned vibration absorbers. A sloshing absorber consists of a tank, partially filled with liquid. The absorber is attached to the structure to be controlled, and relies on the structure's motion to excite the liquid. Consequently, a sloshing wave is produced at the liquid free surface possessing energy dissipative qualities to suppress excessive vibrations of the structure.The hen's egg has evolved to dissipate vibration energy rapidly to protect its contents. An uncooked hen's egg's capability to rapidly dissipate potentially harmful energy, is due to sloshing of its contents. Hence, there may be lessons to learn from the natural design of an egg which could be employed in the engineered (artificial) design of a sloshing absorber.The primary objective of this work is to identify the physical events responsible for effective energy dissipation in an eggshell, at different fill levels. A secondary objective is to demonstrate the suitability of the Smoothed Particle Hydrodynamics (SPH) method for numerical predictions in such an unusually shaped shell. Through numerical predictions, the possibility of modifying the egg's design to further encourage dissipation patterns is explored briefly. Simple experiments are also presented to check the validity of the numerical predictions.