A review of development and implementation of an active nonlinear vibration absorber

Oueini, Shafic S.; Nayfeh, Ali H.; Pratt, Jon R.

doi:10.1007/s004190050245

Cited by 33 publications

(31 citation statements)

References 20 publications

(22 reference statements)

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“…Properly chosen friction can suppress high amplitude motions, which leads to a global stabilization in the entire frequency range. Such a saturation phenomenon is known from active nonlinear absorbers, [8]. Figure 4 shows the corresponding evolution of frequency response curves for the case of a decreasing characteristic.…”

Section: Theoretical Resultsmentioning

confidence: 92%

Passive vibration absorber with dry friction

Hartung

Schmieg

Vielsack

2001

Archive of Applied Mechanics (Ingenieur Archiv)

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Summary The properties of a passive vibration absorber with dry friction signi®cantly differ from those of the classical linear absorber. The exceptional phenomenon is the possibility of suppressing all excited modes. This effect is in¯uenced to a small extent by a special shape of the friction characteristic, but mainly by an appropriately adjusted threshold of the static friction. The theoretical predictions are con®rmed by experimental investigations.Keywords Nonlinear Absorber, Dry Friction, Experiment IntroductionA passive vibration absorber is a mass-spring subsystem coupled to a superstructure to control its oscillations under the action of periodic excitation. A simple form of this arrangement is shown in Fig. 1 where M 1 is a mass emulating the superstructure and K 1 is its mounting spring. The second mass, M 2 , the coupling spring K 2 and a viscous damper d constitute the absorber system. The superstructure is driven by a harmonic base motion with amplitude A and angular frequency X. Let x 1 be the displacement of M 1 and x 2 the displacement of M 2 , respectively. So far, the problem is well known from elementary textbooks on linear vibration theory. Now, a friction device is added to the substructure which turns the problem into a strongly nonlinear mechanical system. The law for the friction force R must be de®ned in a way that R is an active force if the device slides, and a passive one if the device sticks. This gives strict separation between stick and slip phases during motion.Classical investigations on motions of mechanical systems with dry friction are mostly based on deterministic laws which are de®ned by the product of a dynamic friction coef®cient, depending on the relative velocity at the contact area, and the normal pressure, generally depending on time, [1]. In the following, the normal force is assumed to be constant during motion. Then, the dynamic friction force can be reduced to a simple expression R R d sgn _ x 2 a _ x 2 : Introducing the threshold value R s for the static friction force, three possibilities will be investigated as plotted in Fig. 2.The simplest possibility is Coulomb's law (Fig. 2a). Here, R s is equal to R d , and the dynamic force R depends only on the direction of sliding and not on the value of the relative velocity _ x 2 . In the case of a decreasing characteristic (Fig. 2b), the equality R s R d still holds, but the friction force depends linearly on the relative velocity _ x 2 with a negative slope a < 0. In the third case (Fig. 2c), the value R d of dynamic friction remains constant for _ x T 0, but the static friction coef®cient R s is larger than R d .The ®rst question is whether or not different laws lead to signi®cantly different responses and phenomena of the vibration absorber. Secondly, the total behaviour of the mechanical system is of interest, compared with the well-known ef®ciency of the classical linear vibration absorber. And ®nally, experimental investigations should con®rm the theoretical results.

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Section: Theoretical Resultsmentioning

confidence: 92%

Passive vibration absorber with dry friction

Hartung

Schmieg

Vielsack

2001

Archive of Applied Mechanics (Ingenieur Archiv)

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“…Since then there has been a substantial body of work on various types of absorbers, most of which are described in a series of review papers [3][4][5][6]. This paper is concerned with a specific type of nonlinear absorber in which the stiffness of the device is a function of the excitation level.…”

Section: Introductionmentioning

confidence: 99%

Experimental characterization of a nonlinear vibration absorber using free vibration

Tang

Brennan

Gatti

et al. 2016

Journal of Sound and Vibration

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a b s t r a c tKnowledge of the nonlinear characteristics of a vibration absorber is important if its performance is to be predicted accurately when connected to a host structure. This can be achieved theoretically, but experimental validation is necessary to verify the modelling procedure and assumptions. This paper describes the characterization of such an absorber using a novel experimental procedure. The estimation method is based on a free vibration test, which is appropriate for a lightly damped device. The nonlinear absorber is attached to shaker which is operated such that the shaker works in its mass-controlled regime, which means that the shaker dynamics, which are also included in the measurement, are considerably simplified, which facilitates a simple estimation of the absorber properties. From the free vibration time history, the instantaneous amplitude and instantaneous damped natural frequency are estimated using the Hilbert transform. The stiffness and damping of the nonlinear vibration absorber are then estimated from these quantities. The results are compared with an analytical solution for the free vibration of the nonlinear system with cubic stiffness and viscous damping, which is also derived in the paper using an alternative approach to the conventional perturbation methods. To further verify the approach, the results are compared with a method in which the internal forces are balanced at each measured instant in time.

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“…Dynamic vibration absorber, consisting of a (generally small) mass m 2 , attached to the primary vibrating system of (typically larger) mass m 1 is a generic mechanical model described by (1) [1,2].…”

Section: Introductionmentioning

confidence: 99%

Exact Nonlinear Fourth-order Equation for Two Coupled Oscillators: Metamorphoses of Resonance Curves

Kyzioł¹,

Okniński²

2013

Acta Phys. Pol. B

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We study dynamics of two coupled periodically driven oscillators. The internal motion is separated off exactly to yield a nonlinear fourth-order equation describing inner dynamics. Periodic steady-state solutions of the fourth-order equation are determined within the Krylov-BogoliubovMitropolsky approach -we compute the amplitude profiles, which from mathematical point of view are algebraic curves.In the present paper we investigate metamorphoses of amplitude profiles induced by changes of control parameters near singular points of these curves. It follows that dynamics changes qualitatively in the neighbourhood of a singular point.

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A review of development and implementation of an active nonlinear vibration absorber

Cited by 33 publications

References 20 publications

Passive vibration absorber with dry friction

Passive vibration absorber with dry friction

Experimental characterization of a nonlinear vibration absorber using free vibration

Exact Nonlinear Fourth-order Equation for Two Coupled Oscillators: Metamorphoses of Resonance Curves

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