Mechanical Vibration Absorber Research Articles

Tuning of vibration absorbers by an effective modal coupling factor

The simplest family of vibration absorbers comprise inertia absorbers, with an inerter in series with a parallel or series dashpot–spring element, and stiffness absorbers, for which inerter and spring are interchanged. Vibration absorbers are tuned to a structure’s critical resonance, for which scalar structure-absorber equations are derived from an expansion in vibration modes with the absorber in either a free or clamped state. It is demonstrated that the influence from non-targeted residual modes is consistently represented by an effective modal coupling factor (EMCF), evaluated as the relative difference between free and clamped natural frequencies squared. While closely related to the coupling factor for shunted electromechanical transducers, the use of EMCFs determines an entirely new direction for the tuning of mechanical vibration absorbers on a flexible structure. For inertia and stiffness absorbers, the EMCF represents apparent mass or stiffness ratios that also account for the influence from residual modes. Therefore, analytical tuning expressions can be obtained from the derived modal frequency response functions, as demonstrated for a pole-placement method with the EMCF as a new governing absorber parameter. The accuracy of the proposed absorber tuning is validated by a simple numerical example, which shows that analytical tuning expressions can be used directly for vibration damping of flexible structures, provided that the EMCF is included correctly to compensate for the inherent modal interaction.

Mechanical vibration absorber for flexural wave attenuation in multi-materials metastructure

Vibration isolation is a promise to suppress mechanical vibration from a host structure, similarly, a mechanical vibration absorber, a simple but effective device to attenuate flexural wave propagation, which has been implemented in civil and mechanical engineering. This paper presents a type of composite sandwich phononic crystal to attenuate the flexural wave propagation in a beam structure, which can effectively suppress mechanical vibration in a broad band gap by repetitively arranging phononic crystal. First, the elastic wave dispersion characteristic in a composite sandwich beam structure is derived, and a triangular shape phononic crystal for flexural wave attenuation by taking advantage of destructive interference is presented. Then two dimensional phononic crystals are designed by assembling four different unit-cells of metabeam. Finally, numerical experiments are conducted to verify the effectiveness of the proposed mechanical metamaterial absorbers to attenuate flexural wave propagation, the numerical results indicate that the proposed metamaterial is of good performance in mechanical vibration suppression, which can effectively mitigate structure vibration in low-frequency domain than the structure without phononic crystal and single layer metamaterial beam structure. It is the first attempt to design a mechanical metamaterial absorber with the mechanism of destructive interference with composite sandwich phononic crystal.

On Active Vibration Absorption in Motion Control of a Quadrotor UAV

Conventional dynamic vibration absorbers are physical control devices designed to be coupled to flexible mechanical structures to be protected against undesirable forced vibrations. In this article, an approach to extend the capabilities of forced vibration suppression of the dynamic vibration absorbers into desired motion trajectory tracking control algorithms for a four-rotor unmanned aerial vehicle (UAV) is introduced. Nevertheless, additional physical control devices for mechanical vibration absorption are unnecessary in the proposed motion profile reference tracking control design perspective. A new dynamic control design approach for efficient tracking of desired motion profiles as well as for simultaneous active harmonic vibration absorption for a quadrotor helicopter is then proposed. In contrast to other control design methods, the presented motion tracking control scheme is based on the synthesis of multiple virtual (nonphysical) dynamic vibration absorbers. The mathematical structure of these physical mechanical devices, known as dynamic vibration absorbers, is properly exploited and extended for control synthesis for underactuated multiple-input multiple-output four-rotor nonlinear aerial dynamic systems. In this fashion, additional capabilities of active suppression of vibrating forces and torques can be achieved in specified motion directions on four-rotor helicopters. Moreover, since the dynamic vibration absorbers are designed to be virtual, these can be directly tuned for diverse operating conditions. In the present study, it is thus demonstrated that the mathematical structure of physical mechanical vibration absorbers can be extended for the design of active vibration control schemes for desired motion trajectory tracking tasks on four-rotor aerial vehicles subjected to adverse harmonic disturbances. The effectiveness of the presented novel design perspective of virtual dynamic vibration absorption schemes is proved by analytical and numerical results. Several operating case studies to stress the advantages to extend the undesirable vibration attenuation capabilities of the dynamic vibration absorbers into trajectory tracking control algorithms for nonlinear four-rotor helicopter systems are presented.

Simple exact solutions for designing an optimal mechanical dynamic vibration absorber combined with a piezoelectric LR circuit based on the <i>H</i><sub>∞</sub>, <i>H</i><sub>2</sub>, or stability criterion

Simple exact solutions for designing an optimal mechanical dynamic vibration absorber combined with a piezoelectric LR circuit based on the <i>H</i><sub>∞</sub>, <i>H</i><sub>2</sub>, or stability criterion

Enhancement of a dynamic vibration absorber by means of an electromagnetic shunt

In this study, we address the reduction of structural vibrations by means of an electromagnetic shunt damper (EMSD) combined with a mechanical dynamic vibration absorber (DVA). Two architectures, that differs in the placement of the EMSD with respect to the DVA, are tested, showing that one of them enhances the vibration control. In parallel, three shunt architecture are tested: a resistive shunt, a resonant conservative shunt and a resonant dissipative shunt. Optimal values of the EMSD and DVA parameters are obtained; then, the performances of all architecture, according to relevant criteria, are estimated and compared to a single DVA or a single EMSD. The case of a conservative DVA, that creates an anti-resonance, is particularly targeted. It is shown that the performances rely on two free parameters only: the mass ratio for the DVA and the electromagnetic coupling factor for the EMSD, thus giving generic abacuses that can be applied to any practical cases. Finally, experiments are proposed and a good agreement with the theoretical results is obtained, thus validating them.

Design of a rotational type vibration absorber

Mechanical vibration absorbers are mechanical subsystems capable of developing an oscillatory movement, which dynamically compensates for the vibratory motion developed by a mechanical system of interest, which is affected by an action that can produce a movement that directly affects it in a non-desirable way. The system of interest is called the primary system and the absorber is called the secondary system. The way in which both systems interact establishes the conditions in which absorption will take place. Traditional absorbers are made up of systems coupled by means of an elastic element, they can also have viscous type coupling and very complex couplings can be presented by elastic and viscous type combinations. The objective of the present work is to design a rotational type vibration absorber, in which the interaction between both mechanical systems is developed by contact by rotation without sliding and elastic coupling. Euler-Lagrange equations are used to obtain the mathematical model of the system. One of the main characteristics of the rotary absorber is that the absorber can be designed to achieve small amplitudes of the displacement of its center of mass, but large displacements. Results are presented in numerical simulation.

Consistent frequency-matching calibration procedure for electromechanical shunt absorbers

Electromagnetic and piezoelectric shunt damping can be represented by an equivalent mechanical vibration absorber with a spring, dashpot, and inerter in series. A common calibration procedure for multiple electromechanical shunt absorbers is obtained by this equivalence, including a correction for the influence from residual vibration modes by additional modal terms, whose coefficients are consistently identified by frequency matching for the system with rigid absorber dashpots. The accuracy and robustness of the calibration procedure are verified numerically for an unsupported truss structure with rigid body modes.

Micromechanical vibration absorber for frequency stability improvement of DETF oscillator

This article explores a novel way to improve the frequency stability of micromechanical double-ended tuning fork (DETF) resonators. The aim of this work is to use a non-linear vibration absorber to improve the frequency stability of the oscillator. A vibration absorption device is set up on the oscillator to absorb part of the energy of the oscillator. The influence of the vibration absorber on the frequency stability is studied. The short-term frequency stability of the DETF oscillator can be improved from 378 ppb to 202 ppb by coupling it to a mechanical vibration absorber.

Investigation on a mechanical vibration absorber with tunable piecewise-linear stiffness

Abstract The design and characterization of a mechanical vibration absorber are addressed. A distinctive feature of the absorber is its tunable piecewise-linear stiffness, which is realized by means of a slider with two stop-blocks installed constraining the bilateral deflections of the elastic support. A new analytical approach named as the equivalent stiffness technique (EST) is introduced and then employed to obtain the analytical relations of the frequency, amplitude and phase with a view to exhibit a more comprehensive characterization of the absorber. Experiments are conducted to demonstrate the feasibility of the design. The experimental data show good agreement with the analytical results. The final results indicate that the tunable stiffness absorber (TSA) possesses a typical nonlinear characteristic at each given position of the slider, and its stiffness can be tuned in real time over a wide range by adjusting the slider position. Hence the TSA has a large optimum vibration-absorption range together with a wide suppression band around each optimal position, which contributes to its excellent capacity of vibration absorption.

Tremor Reduction at the Palm of a Parkinson's Patient Using Dynamic Vibration Absorber.

Parkinson’s patients suffer from severe tremor due to an abnormality in their central oscillator. Medications used to decrease involuntary antagonistic muscles contraction can threaten their life. However, mechanical vibration absorbers can be used as an alternative treatment. The objective of this study is to provide a dynamic modeling of the human hand that describes the biodynamic response of Parkinson’s patients and to design an effective tuned vibration absorber able to suppress their pathological tremor. The hand is modeled as a three degrees-of-freedom (DOF) system describing the flexion motion at the proximal joints on the horizontal plane. Resting tremor is modeled as dual harmonic excitation due to shoulder and elbow muscle activation operating at resonance frequencies. The performance of the single dynamic vibration absorber (DVA) is studied when attached to the forearm and compared with the dual DVA tuned at both excitation frequencies. Equations of motion are derived and solved using the complex transfer function of the non-Lagrangian system. The absorber’s systems are designed as a stainless steel alloy cantilevered beam with an attached copper mass. The dual DVA was the most efficient absorber which reduces 98.3%–99.5%, 97.0%–97.3% and 97.4%–97.5% of the Parkinson’s tremor amplitude at the shoulder, elbow and wrist joint.

Electromechanical Delayed Resonator Implementation using Piezoelectric Networks

Delayed Resonators (DR) refer to a special type of active vibration absorber system. An intentionally delayed feedback control is used to bring an absorber sub-structure to resonance, in turn canceling vibrations in the primary structure. So far, this theory has been applied to traditional mechanical vibration absorbers with proof masses. This study proposes a new venue for DR-based vibration control using piezoelectric networks. The inherent electro-mechanical coupling of piezoelectric materials has enabled the use of electrical circuits to absorb vibrations in mechanical structures. The DR principles are applied here to create a resonating electrical circuit which offers ideal vibration absorption performance. Experimental studies are also presented to demonstrate the results.

Acoustic metamaterial beams based on multi-frequency vibration absorbers

Abstract Presented here is a new metamaterial beam based on multi-frequency vibration absorbers for broadband vibration absorption. The proposed metamaterial beam consists of a uniform isotropic beam and small two-mass spring-mass-damper subsystems at many locations along the beam to act as multi-frequency vibration absorbers. For an infinite metamaterial beam, governing equations of a unit cell are derived using the extended Hamilton principle. The existence of two stopbands is demonstrated using a model based on averaging material properties over a cell length and a model based on finite element modeling and the Bloch–Floquet theory for periodic structures. For a finite metamaterial beam, because these two idealized models cannot be used for finite beams and/or elastic waves having short wavelengths, a finite-element method is used for detailed modeling and analysis. The concepts of negative effective mass and effective stiffness and how the spring-mass-damper subsystem creates two stopbands are explained in detail. Numerical simulations reveal that the actual working mechanism of the proposed metamaterial beam is based on the concept of conventional mechanical vibration absorbers. For an incoming wave with a frequency in one of the two stopbands, the absorbers are excited to vibrate in their optical modes to create shear forces to straighten the beam and stop the wave propagation. For an incoming wave with a frequency outside of but between the two stopbands, it can be efficiently damped out by the damper with the second mass of each absorber. Hence, the two stopbands are connected into a wide stopband. Numerical examples validate the concept and show that the structure's boundary conditions do not have significant influence on the absorption of high-frequency waves. However, for absorption of low-frequency waves, the structure's boundary conditions and resonance frequencies and the location and spatial distribution of absorbers need to be considered in design, and it is better to use heavier masses for absorbers.

Demonstration of non-collocated vibration control of a flexible manipulator using electrical dynamic absorbers

This paper describes an experimental study into the vibration control of a servo system comprising a servo motor and a flexible manipulator. Two modes of the system are controlled by using the servo motor and an accelerometer attached to the tip of the flexible manipulator. The control system is thus non-collocated. It consists of two electrical dynamic absorbers, each of which consists of a modal filter and, in case of an out-of-phase mode, a phase inverter. The experimental results show that each absorber acts as a mechanical dynamic vibration absorber attached to each mode and significantly reduces the settling time for the system response to a step input.

Design of Micro Power Self-Generation Device

Power supply for micro-system such as wireless sensor network node (WSNN) is an open and interest issue. In this paper, the principle of power self-generation device based on mechanical vibration transformation is introduced, which absorb the energy of mechanical vibration and transform to pressure on piezoelectric materials to produce micro-current, and a mechanical frequency-adjustable vibration absorber based micro electricity self-generation device is designed.

A modal filter approach to non-collocated vibration control of structures

This paper employs modal filters for simultaneous and independent control of multiple vibration modes of a flexible structure embedded with a non-collocated pair of sensor and actuator. Each modal filter of second order is designed to be sensitive to the target mode for control while insensitive to the others. Based on the fact that there are only in- and out-of-phase modes in lightly and proportionally damped finite structures, those in-phase modes are controlled in the same way as that for collocated control using negative feedback, while those out-of-phase modes are controlled exactly in the opposite way using positive feedback. These two are equivalent as far as single mode control is concerned and are electrical realizations of a mechanical dynamic vibration absorber. Feedback control experiments were conducted on a cantilever beam embedded with a piezoelectric actuator at the root and an accelerometer at the end tip. The results reveal a number of peculiar advantages of using non-collocated control over collocated control. Non-collocated plants generally exhibit better high-frequency roll-off characteristics because there are weaker mechanical and electrical feedthrough couplings between non-collocated transducers. Furthermore, the high frequency control spillover can be greatly eliminated by appropriately adjusting the gains of modal filters. It is thus often possible to make the performance and robustness of non-collocated control as well as or even better than those using collocated control.

Intermittent redesign of continuous controllers

The reverse-engineering idea developed by Maciejowski in the context of model-based predictive control is applied to the redesign of continuous-time compensators as intermittent controllers. Not only does this give a way of designing constrained input and state versions of continuous-time compensators but also provides a method for turning continuous-time compensators into event-driven versions. The procedure is illustrated by three examples: an event-driven PID controller relevant to the human balance control problem, a constrained version of the classical mechanical vibration absorber of den Hartog and an event driven and constrained vibration absorber.

Optimum tuning of series and parallel LR circuits for passive vibration suppression using piezoelectric elements

Bending vibration of flexible structures can be suppressed passively using piezoelectric electromechanical transducers and optimally tuned LR circuits. Since these systems include both mechanical and electrical elements, the governing equations consist of electrically coupled equations of motion. This paper describes a new method for deriving the governing equations that describe a system’s vibration suppression based on the equilibrium of force principle and using an equivalent mechanical model of a piezoelectric element. Both series and parallel LR circuits are considered in the modeling approach. The optimum values for a mechanical vibration absorber can be formulated by using the two fixed points method. However, exact optimal values for the resistances of the LR circuits have not been formulated in the research literature thus far, and approximate values have been used. Analytical formulations are derived in this paper, and optimum values of the LR circuits are presented, not only in displacement, but also in terms of velocity and acceleration. The effects of the stiffness of the adhesive bond between the host structure and piezoelectric element, the dielectric loss in a piezoelectric element, and the internal resistance of an inductor are considered in the theoretical analysis. The effectiveness of the described analytical method is validated through simulations and experiments.

Theory of Metamaterial Beams for Broadband Vibration Absorption

This article presents methods for modeling, analysis, and design of metamaterial beams for broadband vibration absorption/isolation. The proposed metamaterial beam consists of a uniform isotropic beam with many small spring-mass-damper subsystems integrated at separated locations along the beam to act as vibration absorbers. For a unit cell of an infinite metamaterial beam, governing equations are derived using the extended Hamilton principle. The existence of stopband is demonstrated using a model based on averaging material properties over a cell length and a model based on finite element modeling and the Bloch-Floquet theory for periodic structures. However, these two idealized models cannot be used for finite beams and/or elastic waves having short wavelengths. For finite metamaterial beams, a linear finite element method is used for detailed modeling and analysis. Both translational and rotational absorbers are considered. Because results show that rotational absorbers are not efficient, only translational absorbers are recommended for practical designs. The concepts of negative effective mass and stiffness and how the spring-mass-damper subsystems create a stopband (i.e., no elastic waves in this frequency range can propagate forward) are explained in detail. Numerical simulations reveal that the actual working mechanism of the proposed metamaterial beam is based on the concept of conventional mechanical vibration absorbers. It uses the incoming elastic wave in the beam to resonate the integrated spring-mass-damper absorbers to vibrate in their optical mode at frequencies close to but above their local resonance frequencies to create shear forces and bending moments to straighten the beam and stop the wave propagation. This concept can be easily extended to design a broadband absorber that works for elastic waves of short and long wavelengths. Numerical examples validate the concept and show that, for high-frequency waves, the structure’s boundary conditions do not have significant influence on the absorbers’ function. However, for absorption of low-frequency waves, the boundary conditions and resonant modes of the structure need to be considered in the design. With appropriate design calculations, finite discrete spring-mass-damper absorbers can be used, and hence expensive micro- or nanomanufacturing techniques are not needed for design and manufacturing of such metamaterial beams for broadband vibration absorption/isolation.

Metamaterial-based Broadband Elastic Wave Absorber

This article presents modeling and analysis techniques for and reveals the actual working mechanism of longitudinal metamaterial bars as elastic wave absorbers. A metamaterial-based elastic wave absorber can be a uniform isotropic bar with many tiny spring-mass subsystems attached at separated longitudinal locations. In the literature, each cell that consists of a bar segment and an attached spring-mass subsystem is modeled as a discrete system of two degrees of freedom by integration and/or finite difference, and the idealized model becomes a dispersive medium for elastic waves and has a stop band that allows no waves to propagate forward. This work shows that these idealized models can be used only for elastic waves having wavelengths much longer than the unit cell’s length. Moreover, it is revealed that a metamaterial-based elastic wave absorber is actually based on the concept of conventional mechanical vibration absorbers, which uses the local resonance of subsystems to generate inertia forces to work against the external load and prevent elastic waves from propagating forward. This concept is extended to design a broadband absorber that works for elastic waves of any wavelengths, including waves having wavelengths shorter than the unit cell’s length. Numerical examples validate the design and reveal the cause of stop band. Moreover, the effect of negative effective mass and acoustic and optical modes are explained.

Automated synthesis of mechanical vibration absorbers using genetic programming

AbstractConceptual innovation in mechanical engineering design has been extremely challenging compared to the wide applications of automated design systems in digital circuits. This paper presents an automated methodology for open-ended synthesis of mechanical vibration absorbers based on genetic programming and bond graphs. It is shown that our automated design system can automatically evolve passive vibration absorbers that have performance equal to or better than the standard passive vibration absorbers invented in 1911. A variety of other vibration absorbers with competitive performance are also evolved automatically using a desktop PC in less than 10 h.