Design Procedure of a Nonlinear Vibration Absorber Using Bifurcation Analysis

A nonlinear energy sink (NES) is characterized by its ability to passively realize targeted energy transfer as well as multimodal damping. This latter feature seems to make this device very well suited for reducing the vibration level of MDOF linear structures. The perspective of dealing with MDOF linear primary structures requires the development of an efficient NES design procedure. This paper poses the basis of such a procedure based upon the bifurcation analysis of a system composed of a linear oscillator coupled to a NES, using the software MatCont

Toward an Optimal Design Procedure of a Nonlinear Vibration Absorber Coupled to a Duffing Oscillator

In the present study, the focus is set on the development of a design methodology for nonlinear vibration absorbers, termed nonlinear energy sink (NES), to optimize the vibrating level reduction on a Duffing oscillator. The idea lies in the assessment of a duality property between, on the one hand, the tuning procedure of the tuned mass damper (TMD) coupled to a linear oscillator and, on the other hand, the assumed design scheme of NES coupled to a purely nonlinear Duffing oscillator. To this end, the basics on the TMD tuning methodology are recalled and extended to the concept of frequency-energy plot (FEP) [1]. Then, based upon this concept, the development of a NES design procedure is undertaken and the related dynamics analyzed. Finally, it is shown how to design a vibration absorber to deal with a general Duffing oscillator

Nonlinear generalization of Den Hartog׳s equal-peak method

This study addresses the mitigation of a nonlinear resonance of a mechanical system. In view of the narrow bandwidth of the classical linear tuned vibration absorber, a nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA), is introduced in this paper. An unconventional aspect of the NLTVA is that the mathematical form of its restoring force is tailored according to the nonlinear restoring force of the primary system. The NLTVA parameters are then determined using a nonlinear generalization of Den Hartog׳s equal-peak method. The mitigation of the resonant vibrations of a Duffing oscillator is considered to illustrate the proposed developments

Spur Gear Vibration Mitigation by Means of Energy Pumping

The dynamic behaviour of a spur gear pair can be studied in terms of transmission error considering a single degree of freedom system. Thus, a mechanical system exhibiting combined parametric excitation and clearance type nonlinearity is examined by means of numerical integrations and continuation methods in an effort to explain its complex behaviour, as it is commonly observed in the steady state forced response of rotating machines. The specific case of a preloaded mechanical oscillator having a periodically time varying stiffness function and subject to a symmetric backlash condition is considered. Even if such an oscillator represents the simplest model able to analyze a single spur gear pair, it exhibits a complex dynamic scenario, namely jumps, superharmonics, subharmonics resonances and dynamic bifurcations. In order to reduce the vibration of the system, a nonlinear absorber is applied. Unlike common linear and weakly nonlinear systems, systems with strongly nonlinear elements are able to react efficiently on the amplitude characteristics of the external forcing in a wide range of frequencies. A strongly and essentially nonlinear, lightweight, with cubic stiffness oscillator is then attached to the main nonlinear system under periodic parametric forcing and the feasibility of a possible application of this nonlinear energy sink (NES) for vibration absorption and mitigation is checked

Nonlinear vibration absorber coupled to a nonlinear primary system: A tuning methodology

This paper addresses the problem of mitigating the vibration of nonlinear mechanical systems using nonlinear dynamical absorbers. One particular feature of the proposed absorber is that it is effective in a wide range of forcing amplitudes. A qualitative tuning methodology is developed and validated using numerical simulations. (C) 2009 Elsevier Ltd. All rights reserved

Design procedure of a nonlinear vibration absorber using bifurcation analysis : application to the drill-string system

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Vibration Mitigation of Nonlinear Vibrating Structures using Nonlinear Energy Sinks

The tuned mass damper (TMD) is a simple and efficient device, but it is only effective when it is precisely tuned to the frequency of a vibration mode. Because nonlinear vibrating structures have resonant frequencies that vary with the amount of total energy in the system, the efficiency of a TMD is questionable in this case. In the present study, the performance of an essentially nonlinear attachment, termed a nonlinear energy sink (NES), is assessed. It is shown that, unlike the TMD, an NES has no preferential resonant frequency, which makes it a good candidate for vibration mitigation of nonlinear vibrating structures

Excitation of nodal diameter mode-shapes of a stator ring of a turbojet engine

peer reviewedCette étude consiste à développer une approche expérimentale, permettant l’isolation de modes à diamètres nodaux spécifiques d’un étage statorique de compresseur basse pression, ayant pour objectif final la calibration de jauges de déformation. Plus spécifiquement, une étude portant sur le nombre minimal de sources d’excitation (shakers) et sur leur répartition circonférentielle optimale a été menée, l’objectif suivi étant d’isoler des modes à diamètres cibles dans des conditions de laboratoire. La première partie de l’étude consiste en une approche théorique, basée sur les concepts d’appropriation modale en régime forcé. La combinaison optimale des positions des différents points d’excitation est choisie de façon à maximiser une fonction objectif, définie comme le rapport entre l’énergie injectée dans le mode cible et la valeur maximale des énergies injectées dans les modes présentant une fréquence naturelle proche du mode d’intérêt. Dans la deuxième partie de l’étude, des simulations numériques sur un modèle éléments finis de la structure ont été menées sur base des résultats théoriques obtenus. Enfin, la troisième partie a permis de valider expérimentalement les prédictions numériques via des analyses d’influence du nombre d’excitateurs et de leur position sur l’amplitude de la réponse fréquentielle

Practical Computation of Nonlinear Normal Modes Using Numerical Continuation Techniques

The concept of nonlinear normal modes (NNMs) is considered in the present paper. One reason of the still limited use of NNMs in structural dynamics is that their computation is often regarded as impractical. However, when resorting to numerical algorithms, we show that the NNM computation is possible with limited implementation effort, which paves the way to a practical method for determining the NNMs of nonlinear mechanical systems. The proposed algorithm relies on two main techniques, namely a shooting procedure and a method for the continuation of NNM motions. The algorithm is demonstrated using two different mechanical systems, a nonlinear two-degree-of-freedom system and a nonlinear cantilever beam discretized by the finite element method