Autoparametric Vibration Absorber Research Articles

The Response of an Inerter-Based Dynamic Vibration Absorber With a Parametrically Excited Centrifugal Pendulum

AbstractThe inerter has been integrated into various vibration mitigation devices, whose mass amplification effect could enhance the suppression capabilities of these devices. In the current study, the inerter is integrated with a pendulum vibration absorber, referred to as inerter pendulum vibration absorber (IPVA). To demonstrate its efficacy, the IPVA is integrated with a linear, harmonically forced oscillator seeking vibration mitigation. A theoretical investigation is conducted to understand the nonlinear response of the IPVA. It is shown that the IPVA operates based on a nonlinear energy transfer phenomenon wherein the energy of the linear oscillator transfers to the pendulum vibration absorber as a result of parametric resonance of the pendulum. The parametric instability is predicted by the harmonic balance method along with the Floquet theory. A perturbation analysis shows that a pitchfork bifurcation and period doubling bifurcation are necessary and sufficient conditions for the parametric resonance to occur. An arc-length continuation scheme is used to predict the boundary of parametric instability in the parameter space and verify the perturbation analysis. The effects of various system parameters on the parametric instability are examined. Finally, the IPVA is compared with a linear benchmark and an autoparametric vibration absorber and shows more efficacious vibration suppression.

Dynamic Effect of the Parametric Excitation Force on an Autoparametric Vibration Absorber

Autoparametric vibration absorber is a machine invented to suppress vibration and has been widely employed in many fields of engineering. Previous works reported by various researchers have shown that dangerous motions, like the full rotation of the pendulum subsystem or chaotic motion, can emerge due to small perturbations of initial conditions or system parameters. To tackle this problem, a new model of the autoparametric vibration absorber with an attached piezoelectric actuator exciter is proposed in this paper. Under the effects of parametric excitation forces produced by the exciter, the vibration absorber will absorb more vibration energy. The dynamic response of the new system is studied analytically using the method of multiple scales and the results validated numerically using the continuation method and detailed bifurcation analysis. The results show that the vibration amplitudes of the subsystems are reduced, the region over which the absorption takes place gets widened and chaotic regions are removed with the introduction of parametric excitation forces in contrast to that of the original model of the autoparametric vibration absorber.

Effects of nonlinear interactions of flexural modes on the performance of a beam autoparametric vibration absorber

The performance of the cantilever beam autoparametric vibration absorber with a lumped mass attached at an arbitrary point on the beam span is investigated. The absorber would have a distinct feature that in addition to the two-to-one internal resonance, the one-to-three and one-to-five internal resonances would also occur between flexural modes of the beam by tuning the mass and position of the lumped mass. Special attention is paid on studying the effect of these resonances on increasing the effectiveness and extending the range of excitation amplitudes at which the autoparametric vibration absorber remains effective. The problem is formulated based on the third-order nonlinear Euler–Bernoulli beam theory, where the assumed-mode method is used for deriving the discretized equations of motion. The numerical continuation method is then applied to obtain the frequency response curves and detect the bifurcation points. The harmonic balance method is also employed for detecting the type of internal resonances between flexural modes by inspecting the frequency response curves corresponding to different harmonics of the response. Parametric studies on the performance of the absorber are conducted by varying the position and mass of the lumped mass, while the frequency ratio of the primary system to the first mode of the beam is kept equal to two. Results indicated that the one-to-five internal resonance is especially responsible for the considerable enhancement of the performance.

An Active Nonlinear Controller Emulating a Pendulum-Type Auto-parametric Vibration Absorber

In this paper, a nonlinear active vibration control method, which is suitable for the vibration mitigation of both linear and nonlinear structures, is proposed. The main idea of this method is to make the controller emulate a pendulum-type auto-parametric vibration absorber, with the purpose of counteracting the different types of nonlinearity in structures. In this way, the difficulty in the passive realization of the pendulum-type vibration absorber due to the physical unsuitable parameters can also be well released. The idea of introducing an exosystem in Byrnes–Isidori regulator is borrowed to design the nonlinear controller. The steps to choose the parameters of the controller are introduced. The validity and robustness of the controller for the vibration mitigation of both linear and nonlinear oscillators are investigated by numerical examples of application. The simulation results show that the proposed nonlinear controller can effectively mitigate the vibration not only of linear oscillators, but also of nonlinear oscillators with third-, quintic- and seventh-order nonlinearities. The good robustness of the proposed nonlinear controller is also demonstrated.

Optimal dual-functional design for a piezoelectric autoparametric vibration absorber

Abstract The nonlinear saturation principle and 1:2 internal resonance are used in the design of the piezoelectric autoparametric vibration absorber for vibration suppression and energy harvesting. A novel prototype is manufactured. The proposed theoretical model is verified by the experimental data. Synergy optimization is performed based on the approximate analytical solutions obtained using the harmonic balance method and the method of multiple scales. By leveraging the Routh-Hurwitz criterion, the system’s stability boundary is analytically determined and confirmed by the numerical simulation of the original full coupled governing equations. The system undergoes periodic motion, aperiodic motion and chaos successively from the stable region to the center of the unstable region. The unstable region is shown to be adjustable and minimized by the maximal electrical damping to improve the vibration suppression. The design proposed for the minimal base (main structure) displacement at resonance locates in the stable zone. The optimized piezoelectric autoparametric absorber not only effectively mitigates the vibration of the main structure but also harvests large electric power at resonance or near resonance. Such a system is shown to perform well in the environment with small external noises.

On vibration mitigation and energy harvesting of a non-ideal system with autoparametric vibration absorber system

This paper demonstrates that vibration mitigation and energy harvesting can be achieved simultaneously by using of an electricity-generating from autoparametric vibration absorber system (AVAS) and non-ideal system (NIS). The NIS consists of a simple portal frame excited by a small dc motor with eccentric mass, with limited power supply and located on the top. The AVAS consists of a cantilever beam with tip mass parallel coupled to NIS. A piezoelectric material is considered for energy harvesting installed in the base of the AVAS and an electric circuit is connected to the piezoelectric material in order to produce voltage output. Several numerical simulations were carried out focusing on the passage through the resonance of NIS, when the motor rotational frequency is near the portal frame natural frequency and when the non-ideal subsystem frequency is approximately twice the absorber beam frequency (two-to-one internal resonance). The results showed the existence of Sommerfeld effect in NIS and saturation phenomenon in the NIS–AVAS.

Assessment of energy harvesting and vibration mitigation of a pendulum dynamic absorber

Abstract The paper presents a novel system for simultaneous energy harvesting and vibration mitigation. The system consists of two main parts: an autoparametric pendulum vibration absorber and an energy harvester device. The recovered energy is from oscillation of a levitating magnet in a coil. The energy harvesting system is mounted in a pendulum structure. The system allows energy recovery from a semi-trivial solution (pendulum in rest) or/and swinging of a pendulum. The influence of harvester parameters on the system response and energy harvesting in a parametric resonance is studied in detail. The harvester device does not decrease vibration reduction effectiveness.

Optimum Design of a Nonlinear Vibration Absorber Coupled to a Resonant Oscillator: A Case Study

This paper presents the optimal design of a passive autoparametric cantilever beam vibration absorber for a linear mass‐spring‐damper system subject to harmonic external force. The design of the autoparametric vibration absorber is obtained by using an approximation of the nonlinear frequency response function, computed via the multiple scales method. Based on the solution given by the perturbation method mentioned above, a static optimization problem is formulated in order to determine the optimum parameters (mass and length) of the nonlinear absorber which minimizes the steady state amplitude of the primary mass under resonant conditions; then, a PZT actuator is cemented to the base of the beam, so the nonlinear absorber is made active, thus enabling the possibility of controlling the effective stiffness associated with the passive absorber and, as a consequence, the implementation of an active vibration control scheme able to preserve, as possible, the autoparametric interaction as well as to compensate varying excitation frequencies and parametric uncertainty. Finally, some simulations and experimental results are included to validate and illustrate the dynamic performance of the overall system.

Energy harvesting from an autoparametric vibration absorber

The combined control and energy harvesting characteristics of an autoparametric vibration absorber consisting of a base structure subjected to the external force and a cantilever beam with a tip mass are investigated. The piezoelectric sheets are attached to the cantilever beam to convert the vibrations of the base structure into electrical energy. The coupled nonlinear representative model is developed by using the extended Hamiton’s principle. The effects of the electrical load resistance on the frequency and damping ratio of the cantilever beam are analyzed. The impacts of the external force and load resistance on the structural displacements of the base structure and the beam and on the level of harvested energy are determined. The results show that the initial conditions have a significant impact on the system’s response. The relatively high level of energy harvesting is not necessarily accompanied with the minimum displacements of the base structure.

Passive/Active Autoparametric Cantilever Beam Absorber With Piezoelectric Actuator for a Two-Story Building-Like Structure

This work deals with the design and experimental evaluation of a passive/active cantilever beam autoparametric vibration absorber mounted on a two-story building-like structure (primary system), with two rigid floors connected by flexible columns. The autoparametric vibration absorber consists of a cantilever beam with a piezoelectric patch actuator, cemented to its base, mounted on the top of the structure and actively controlled through an acquisition system. The overall system is then a coupled nonlinear oscillator subjected to sinusoidal excitation in the neighborhood of its external and internal resonances. The addition of the piezoelectric patch actuator to the cantilever beam absorber makes active the passive vibration absorber, thus enabling the possibility to control its equivalent stiffness and damping and, as a consequence, the implementation of an active vibration control scheme able to preserve, as possible, the autoparametric interaction as well as to compensate varying excitation frequencies and parametric uncertainty.

439 非線形連成を利用する動吸振器を仮想的に実現した圧電シャントダンピング

Piezoelectric shunt damping is a damping technique using a piezoelectric element which can act both a sensor and an actuator. A circuit attached to the piezoelectric element is called the shunt circuit, and has the characteristics of the absorber. Many studies use the circuits with linear characteristics, but it becomes possible to have more complex characteristics by virtual admittance. In this paper, the nonlinear absorber called autoparametric vibration absorber is realized by piezoelectric shunt damping with the virtual admittance.

Vibration Reduction of a High-$T_{c}$ Superconducting Magnetic Levitation System With an Autoparametric Vibration Absorber

This research proposes reduction in the amplitude of a primary resonance generated in high-Tc superconducting (HTSC) magnetic levitation system using an autoparametric vibration absorber. In general mechanical systems, reduction of the primary resonance or some nonlinear oscillations have been successfully studied using a kind of a nonlinear vibration absorber called an autoparametric vibration absorber through nonlinear coupling, which is called internal resonance. In this study, we assume that the rigid body vibrates only in the vertical direction z. On the rigid body a pendulum is fixed as an autoparametric vibration absorber. Through the nonlinear coupling that is generated, the amplitude of z is reduced. The governing equations in z and θ directions are derived, and the possibility of energy transfer due to internal resonance is suggested. From the equations, analytical results predict that the amplitude of z decreases when internal resonance occurs. Numerical results confirm this prediction.

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.

Amplitude reduction of parametric resonance by dynamic vibration absorber based on quadratic nonlinear coupling

The paper proposes an amplitude reduction method for parametric resonance with a new type of dynamic vibration absorber utilizing quadratic nonlinear coupling. A main system with asymmetric nonlinear restoring force and harmonic excitation causes parametric resonance in the system. In contrast with autoparametric vibration absorber, the natural frequency of the vibration absorber is tuned to be in the neighborhood of twice that of the main system. For such a vibration absorber, we investigate the effect on the amplitude reduction for a parametrically excited main system. Analytical results using the method of multiple scales show that the amplitude of parametric resonance is reduced by the effect of the vibration absorber. The experimental results by a simple apparatus indicate that the parametric resonance is stabilized by the effects of both vibration absorber and Coulomb friction of the main system. Moreover, numerical results considering the Coulomb friction of the main system show that the amplitude of parametric resonance becomes close to zero by the proposed vibration absorber.

Analysis of the dynamics of a pendulum vibration absorber

The nonlinear dynamics of an autoparametric vibration absorber of pendulum type is considered. The conditions of existence of periodic motions in the case of monoharmonic excitation are considered. A comparison of the vibration quenching qualities of the autoparametric absorber and a “classical” (linear) dynamic vibration absorber is presented.

Amplitude reduction of primary resonance of nonlinear oscillator by a dynamic vibration absorber using nonlinear coupling

The paper presents the characteristics of a new type of nonlinear dynamic vibration absorber for a main system subjected to a nonlinear restoring force under primary resonance. The absorber is connected to the main system by a link in order to be excited with twice the frequency of the motion of the main system. The natural frequency of the absorber is tuned to be twice the natural frequency of the main system, in contrast to autoparametric vibration absorber, whose natural frequency is tuned to be one-half the natural frequency of the main system. The presented absorber is not excited through the autoparametric resonance, i.e., no trivial equilibrium state exists. Therefore, the absorber always oscillates because of the motion of the main system and cannot be trapped by Coulomb friction acting on the absorber, in contrast to the autoparametric vibration absorber. Under small excitation amplitude, this absorber does not produce an overhang in the frequency response curve, which occurs because of the use of the conventional autoparametric vibration absorber; the overhang renders the response amplitude larger than that in the case without an absorber. In addition, the absorber removes the hysteresis in the frequency response curve caused by the nonlinearity of the restoring force acting on the main system. Regarding large excitation amplitude, the response amplitude in the main system can be decreased by increasing the damping of the absorber, but that decrease is limited by the nonlinearity in the restoring force acting on the main system. This paper also describes experimental validation of the absorber under small excitation amplitude using a simple apparatus.

Reduction of Primary Resonance by Nonlinear Coupling with Vibration Absorber

In this paper, we propose a nonlinear vibration absorber for linear external resonance. This absorber does not utilize linear coupling to the main system but utilizes nonlinear coupling. Therefore, the attachment of the vibration absorber does not increase the number of degrees of freedom of the main system. Also, comparing with autoparametric vibration absorber, the proposed method is effective over wide range of the excitation frequency. By applying the method of multiple scales, the modulation equations of the main system and the absorber are derived. Comparison of the frequency response curves with and without nonlinear vibration absorber shows validity of the proposed absorber.

412 ストッパーを用いたオートパラメトリック吸振器の改良

The auto-parametric vibration absorber, which is a kind of nonlinear absorber, suppresses the vibration of main system only at around the resonance point. However, because of the existence of another stable solution due to auto-parametric vibration absorber, the vibration of main system may increase when the excitation frequency is slightly apart from the resonance point. In this paper, the improvement of auto-parametric vibration absorber for the suppression of such another stable solution is investigated. A stopper consists of spring element and damper element is set to limit the absorber motion, and the effects of these elements are investigated and clarified.

Dynamics of structures with wideband autoparametric vibration absorbers: experiment

The dynamics of a resonantly excited thin cantilever with an active controller are investigated experimentally. The controller mimics a passive wideband absorber discussed in the accompanying theory paper. Lead-zirconate-titanate patches are bonded to both sides of the beam to actuate it, while an electromagnetic shaker drives the beam near resonance. An active controller consisting of an array of coupled controllers is developed, such that the governing equations for the controller are quadratically coupled to the resonating system. The control signal, in terms of the motion of the controllers, is quadratically nonlinear. It is shown that the slow time-scale equations of this physical system are identical in form to those for the passive wideband vibration absorber. The controller is implemented using modelling software and a controller hardware board. Two sets of experiments are performed: one with a constant excitation frequency and the other with a linearly varying excitation frequency at a slow sweep rate (non-stationary excitation). The experimental results verify the analysis presented for the passive wideband autoparametric vibration absorber. The experiments also demonstrate the effectiveness of the absorber in reducing the response amplitude of structures, and its robustness to frequency mistuning.

Dynamics of structures with wideband autoparametric vibration absorbers: theory

This article analyses the dynamics of a resonantly excited single–degree–of–freedom linear system coupled to an array of nonlinear autoparametric vibration absorbers (pendulums). Each pendulum is also coupled to the neighbouring pendulums by linear elastic springs. The case of a 1:1:…:2 internal resonance between pendulums and the primary oscillator is studied for stationary (harmonic) and non–stationary (slow frequency sweep) excitations. The method of averaging is used to obtain amplitude equations that determine the first–order approximation to the nonlinear response of the system. The amplitude equations are analysed for their equilibrium as well as non–stationary solutions as a function of the parameters associated with the absorber pendulums. For stationary excitation, most steady–state solutions correspond to modes in which only one pendulum and the primary system execute coupled motions. Conditions for the existence of manifolds of equilibria are revealed when the averaged equations are expressed in modal coordinates. In the non–stationary case with linear frequency sweep through the primary resonance region, delays through pitchforks, smooth but rapid transitions through jumps, and transitions from one stable coupled–mode branch to another are studied using numerical simulations of the amplitude equations. The array of autoparametric pendulums is shown to effectively attenuate the large–amplitude resonant response of structures over a wide band of excitation frequencies.