Minimax design of vibration absorbers for linear damped systems

This paper addresses the issue of design of a passive vibration absorber in the presence of uncertainties in the forcing frequency. A minimax problem is formulated to determine the parameters of a vibration absorber which minimize the maximum motion of the primary mass over the domain of the forcing frequency. The limiting solutions corresponding to the forcing frequency being unrestricted and to that where the forcing frequency is known exactly, are shown to match those available in the literature. The transition of the optimal vibration absorber parameters between the extreme two cases is presented and the solutions are generalized by permitting the mass ratio of the absorber mass and the primary mass to be design parameters. For the specific case where the primary system is undamped, detailed analysis is presented to determine the transition of the optimal vibration absorber parameters between three distinct domains of solutions.     

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.     

Hybrid vibration absorber with virtual passive devices

A vibration control scheme integrating a passive mass–spring resonator and a linear actuator is developed. A control algorithm is devised to convert the actuator into an additional set of virtual mass–spring structure of programmable characteristic frequency. The relative motion between the primary body and the reaction mass is measured, as well as the acceleration of the reaction mass. This hybrid dynamic vibration absorber is capable of neutralizing a harmonic disturbance regardless of the detailed dynamics of the primary structure and other passive elements. Stability analysis leads to a simple, explicit stability criterion. Distribution of the counter-disturbance force between the active and passive devices is analyzed, and the transient performance is also investigated. Real-time experiments as well as numerical simulations are conducted to confirm the effectiveness of the proposed scheme.     

Minimization of the mean square velocity response of dynamic structures using an active-passive dynamic vibration absorber

An optimal design of a hybrid vibration absorber (HVA) with a displacement and a velocity feedback for minimizing the velocity response of the structure based on the H(2) optimization criterion is proposed. The objective of the optimal design is to reduce the total vibration energy of the vibrating structure under wideband excitation, i.e., the total area under the velocity 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 very good 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 velocity of the primary system as well as the active force required in the HVA. The proposed HVA was tested on single degree-of-freedom (SDOF) and continuous vibrating structures and compared to the traditional passive vibration absorber.     

An investigation into the simultaneous use of a resonator as an energy harvester and a vibration absorber

A mass–spring–damper system is at the core of both a vibration absorber and a harvester of energy from ambient vibrations. If such a device is attached to a structure that has a high impedance, then it will have very little effect on the vibrations of the structure, but it can be used to convert mechanical vibrations into electrical energy (act as an energy harvester). However, if the same device is attached to a structure that has a relatively low impedance, then the device may attenuate the vibrations as it may act as both a vibration absorber and an energy harvester simultaneously. In this paper such a device is discussed. Two situations are considered; the first is when the structure is excited with broadband random excitation and the second is when the structure is excited by a single frequency. The optimum parameters of the device for both energy harvesting and vibration attenuation are discussed for these two cases. For random excitation it is found that if the device is optimized for vibration suppression, then this is also adequate for maximizing the energy absorbed (harvested), and thus a single device can effectively suppress vibration and harvest energy at the same time. For single frequency excitation this is found not to be the case. To maximize the energy harvested, the natural frequency of the system (host structure and absorber) has to coincide with the forcing frequency, but to minimize vibration of the host structure, the natural frequency of the absorber has to coincide with the forcing frequency. In this case, therefore, a single resonator cannot effectively suppress vibration and harvest energy at the same time.     

Application of dynamic vibration absorbers in floating raft system

To improve the isolation performance of the traditional floating raft system, dynamic vibration absorber (DVA) is introduced into floating raft in this research. The mathematical models of floating raft system consisting of beams are implemented by assembling the mobility matrices of the subsystems. Then the power flow transmission characteristics of the coupled system with/without the DVAs are investigated to evaluate the vibration reduction performance of DVAs. Numerical simulations are performed to explore the influence of several parameters, such as the setting positions, damping and mass of the passive DVAs, on the vibration reduction effects of DVAs. Moreover the vibration reduction performance of the semi-active absorber adjusting its stiffness adaptively is analyzed for the case of time-varying frequency excitation. In addition, the vibration reduction effects of semi-active DVAs under multi-frequency excitation are investigated. The results show that DVAs can significantly improve the isolation performance of floating raft system.     

Autoparametric vibration absorber effect to reduce the first symmetric mode vibration of a curved beam/panel

This paper presents the implementation of autoparametric phenomena to reduce the symmetrical vibration of a curved beam/panel under external harmonic excitation. The internal energy transfer of a first symmetric mode into first anti-symmetric mode in a curved panel is one example of autoparametric vibration absorber effect. This is similar to the vibration energy transfer from the resonance of a primary structure to the resonance of a secondary spring–mass (tuned mass damper). The nonlinear response of a curved beam is analyzed using an equation with two modes, and a shaker test. The effect of different configurations of the curve beam/panel, including damping ratios and excitation levels, on the energy transfer of the first symmetric mode to the first anti-symmetric mode was studied.The conventional tuned mass damper (TMD) can reduce the resonance response by energy transfer using damping dissipation, whereas an autoparametric vibration absorber (AVA) can reduce the resonance response by energy transfer using parametric interaction. The results indicate that there is a non-absorption region in which vibration is amplified. For the AVA, the non-absorption region can be minimized by tuning the resonance frequency of the first anti-symmetric mode to half of the first symmetric mode resonance frequency using additional mass. No additional damping material is required for achieving sufficient vibration reduction. The AVA can maintain reliable performance in hot and corrosive environments where damping material cannot perform effectively. This paper presents the first successful experimental results of an autoparametric vibration absorption mechanism in a curved beam.     

Two-degree-of-freedom rotational-pendulum vibration absorbers

This paper presents experimental as well as analytic results on a rotational-pendulum vibration absorber. The characteristic frequencies of the absorber can be tuned dynamically by adjusting the rotational speed. The device is coupled to the primary structure through a mechanical spring, thus possessing two natural modes of vibrations in the vertical plane. When the primary structure is excited by a harmonic disturbance of which the frequency matches one of the two natural frequencies, the oscillations will be minimized. Whether the pendulum absorber is operating in a resonant mode can be detected by measuring the phase difference between the motions of the primary structure and the absorber, which provides an efficient way to tune the rotational speed for optimal performance. Experimental results confirm the theoretical developments and also demonstrate the effectiveness of the proposed scheme.     

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.     

Active-passive vibration absorber of beam-cart-seesaw system with piezoelectric transducers

In contrast with fully controllable systems, a super articulated mechanical system (SAMS) is a controlled underactuated mechanical system in which the dimensions of the configuration space exceed the dimensions of the control input space. The objectives of the research are to develop a novel SAMS model which is called beam-cart-seesaw system, and renovate a novel approach for achieving a high performance active-passive piezoelectric vibration absorber for such system. The system consists of two mobile carts, which are coupled via rack and pinion mechanics to two parallel tracks mounted on pneumatic rodless cylinders. One cart carries an elastic beam, and the other cart acts as a counterbalance. One adjustable counterweight mass is also installed underneath the seesaw to serve as a passive damping mechanism to absorb impact and shock energy. The motion and control of a Bernoulli-Euler beam subjected to the modified cart/seesaw system are analyzed first. Moreover, gray relational grade is utilized to investigate the sensitivity of tuning the active proportional-integral-derivative (PID) controller to achieve desired vibration suppression performance. Consequently, it is shown that the active-passive vibration absorber can not only provide passive damping, but can also enhance the active action authority. The proposed software/hardware platform can also be profitable for the standardization of laboratory equipment, as well as for the development of entertainment tools.     

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.     

On the efficacy of an active absorber with internal state feedback for controlling self-excited oscillations

An active absorber, utilizing the state feedback of the absorber mass, is proposed for controlling the self-excited vibration of a single degree-of-freedom extended Rayleigh oscillator. The control strategy renders the design standalone. The process of optimizing the control gains is discussed. The analysis reveals that by selecting a suitably high value of the absorber frequency, the overall damping of the system can be made as high as the critical damping irrespective of the amount of negative linear damping present in the primary self-excited system. It is shown that a higher value of the absorber frequency is profitable in almost all respects related to the performance as well as the robustness of the system under parametric uncertainty. The nonlinear analysis of the system reveals that the proposed absorber can control the amplitude of oscillation even in case detuning (up to some limit) of the absorber frequency from its nominal value. The region of global stability increases with the increase in the value of the absorber frequency. However some aspects, like higher absorber deflection, reduced lower bound of the admissible detuning and the lower range of the tolerance on the mass ratio limit using a very high value of absorber frequency. The results of numerical simulations confirm the analytical results.     

Suppression of the primary resonance vibrations of a forced nonlinear system using a dynamic vibration absorber

In a single degree-of-freedom weakly nonlinear oscillator subjected to periodic external excitation, a small-amplitude excitation may produce a relatively large-amplitude response under primary resonance conditions. Jump and hysteresis phenomena that result from saddle-node bifurcations may occur in the steady-state response of the forced nonlinear oscillator. A simple mass-spring-damper vibration absorber is thus employed to suppress the nonlinear vibrations of the forced nonlinear oscillator for the primary resonance conditions. The values of the spring stiffness and mass of the vibration absorber are significantly lower than their counterpart of the forced nonlinear oscillator. Vibrational energy of the forced nonlinear oscillator is transferred to the attached light mass through linked spring and damper. As a result, the nonlinear vibrations of the forced oscillator are greatly reduced and the vibrations of the absorber are significant. The method of multiple scales is used to obtain the averaged equations that determine the amplitude and phases of the first-order approximate solutions to primary resonance vibrations of the forced nonlinear oscillator. Illustrative examples are given to show the effectiveness of the dynamic vibration absorber for suppressing primary resonance vibrations. The effects of the linked spring and damper and the attached mass on the reduction of nonlinear vibrations are studied with the help of frequency response curves, the attenuation ratio of response amplitude and the desensitisation ratio of the critical amplitude of excitation.     

Coupled FEM/BEM for control of noise radiation and sound transmission using piezoelectric shunt damping

In this paper, we present a coupled finite element/boundary element method (FEM/BEM) for control of noise radiation and sound transmission of vibrating structure by passive piezoelectric techniques. The system consists of an elastic structure (with surface mounted piezoelectric patches) coupled to external/internal acoustic domains. The passive shunt damping strategy is employed for vibration attenuation in the low frequency range. The originality of the present paper lies in evaluating the classically used FEM/BEM methods for structural–acoustics problems when taking account smart systems at the fluid–structure interfaces.     

Optimisation of dynamic vibration absorbers to minimise kinetic energy and maximise internal power dissipation

The tuning of a dynamic vibration absorber is considered such that either the kinetic energy of the host structure is minimised or the power dissipation within the absorber is maximised. If the host structure is approximated as a damped single degree of freedom, the optimal values for the ratio of the absorber's natural frequency to the host structure and the optimal damping ratio of the absorber are shown to be the same whether the kinetic energy of the host structure is minimised or the power dissipation of the absorber is maximised. It is also demonstrated that the total power input into the system does not depend on the two parameters but only on the host structure's mass.     

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.     

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.     

Direct energy flow measurement in magneto-sensitive vibration isolator systems

The effectiveness of highly nonlinear, frequency, amplitude and magnetic field dependent magneto-sensitive natural rubber components applied in a vibration isolation system is experimentally investigated by measuring the energy flow into the foundation. The energy flow, including both force and velocity of the foundation, is a suitable measure of the effectiveness of a real vibration isolation system where the foundation is not perfectly rigid. The vibration isolation system in this study consists of a solid aluminium mass supported on four magneto-sensitive rubber components and is excited by an electro-dynamic shaker while applying various excitation signals, amplitudes and positions in the frequency range of 20–200 Hz and using magneto-sensitive components at zero-field and at magnetic saturation. The energy flow through the magneto-sensitive rubber isolators is directly measured by inserting a force transducer below each isolator and an accelerometer on the foundation close to each isolator. This investigation provides novel practical insights into the potential of using magneto-sensitive material isolators in noise and vibration control, including their advantages compared to traditional vibration isolators. Finally, nonlinear features of magneto-sensitive components are experimentally verified.