Nonlinear normal modes, Part 1: Useful framework for the structural dynamicist

in Mechanical Systems & Signal Processing (2009), 23

The conceptofnonlinearnormalmodes(NNMs)isdiscussedinthepresentpaperandits companion,PartII.BecausethereisvirtuallynoapplicationoftheNNMstolarge-scale engineeringstructures ... [more ▼]

The conceptofnonlinearnormalmodes(NNMs)isdiscussedinthepresentpaperandits companion,PartII.BecausethereisvirtuallynoapplicationoftheNNMstolarge-scale engineeringstructures,thesepapersareanattempttohighlightseveralaspectsthat mightdrivetheirdevelopmentinthefuture.Specifically,wesupportthat(i)numerical methodsforthecontinuationofperiodicsolutionspavethewayforaneffectiveand practical computationofNNMs,and(ii)time–frequencyanalysisisparticularlysuitable fortheanalysisoftheresultingdynamics.Anotherobjectiveofthepresentpaperisto describe,insimpleterms,andtoillustratethefundamentalpropertiesofNNMs.Thisis achievedtoconvincethestructuraldynamicistnotnecessarilyacquaintedwiththemthat theyareausefulframeworkfortheanalysisofnonlinearvibratingstructures. & 2008ElsevierLtd.Allrightsreserved [less ▲]

Nonlinear normal modes, Part 2: Toward a pratical computation using numerical continuation techniques

in Mechanical Systems & Signal Processing (2009), 23

The conceptofnonlinearnormalmodes(NNMs)isdiscussedinthepresentpaperandits companion,PartI.OnereasonofthestilllimiteduseofNNMsinstructuraldynamicsis that theircomputationisoftenregardedasimpractical ... [more ▼]

The conceptofnonlinearnormalmodes(NNMs)isdiscussedinthepresentpaperandits companion,PartI.OnereasonofthestilllimiteduseofNNMsinstructuraldynamicsis that theircomputationisoftenregardedasimpractical.However,whenresortingto numericalalgorithms,weshowthattheNNMcomputationispossiblewithlimited implementationeffort,whichpavesthewaytoapracticalmethodfordeterminingthe NNMsofnonlinearmechanicalsystems.Theproposedalgorithmreliesontwomain techniques,namelyashootingprocedureandamethodforthecontinuationofNNM motions. Thealgorithmisdemonstratedusingfourdifferentmechanicalsystems,a weakly andastronglynonlineartwo-degree-of-freedomsystem,asimplifieddiscrete modelofanonlinearbladeddiskandanonlinearcantileverbeamdiscretizedbythefinite elementmethod. [less ▲]

Using passive nonlinear targeted energy transfer to stabilize drill-stringsystems

in Mechanical Systems & Signal Processing (2009), 23

Torsional vibrations of drill strings used in drilling oil and gas wells arises from a complex interaction of the dynamics of the drilling structure with speed-dependent effective rock-cutting forces ... [more ▼]

Torsional vibrations of drill strings used in drilling oil and gas wells arises from a complex interaction of the dynamics of the drilling structure with speed-dependent effective rock-cutting forces. These forces are often difficult to model, and contribute substantially to the instability problems of controlling the drilling operation so as to produce steady cutting. In this work we show how nonlinear passive targeted energy transfer to a lightweight attachment can be used to passively control these instabilities. This is performed by means of a nonlinear energy sink (NES), a lightweight attachment which has been shown to be effective in reducing or even completely eliminating self-excited motions in aeroelastic and other systems. The NES is a completely passive, inherently broadband vibration absorber capable of attracting and dissipating vibrational energy from the primary structure to which it is attached, in this case a nonlinear discontinuous model of a drill-string system. In this paper we describe a prototypical drill string-NES system, briefly discuss some of the analytical and computational tools suitable for its analysis, and then concentrate on mathematical results on the efficacy of the NES in this application and their physical interpretation. [less ▲]

Detection of nonlinearity in a dynamic system using deformation modes obtained from the Wavelet Transfrom of measured responses

Conference given outside the academic context (2009)

An efficient approach to Structural Health Monitoring of dynamical systems based on the Wavelet Transform (WT) and the concept of subspace angle is presented. The objective is to propose a detection ... [more ▼]

An efficient approach to Structural Health Monitoring of dynamical systems based on the Wavelet Transform (WT) and the concept of subspace angle is presented. The objective is to propose a detection method that is sensitive to the onset of nonlinear behaviour in a dynamic system. For this purpose, instantaneous frequencies are identified first from output-only vibration signals using the Wavelet Transform. Time varying deformation shapes are then extracted by analyzing the whole measurement data set on the structure. From this information, different dynamic states of the structure may be detected by inspecting time variations of ‘modal’ features. The experimental structure considered here as application example is a clamped beam with a geometric nonlinearity. Detection of nonlinearity is carried out by means of the concept of subspace angles between instantaneous deformation modes extracted from measurement data using the continuous Wavelet Transform. The method consists in controlling the angular coherence between active subspaces of the current and reference states respectively. The proposed technique, which shows a good sensitivity to small changes in the dynamic behaviour of the structure, may also be used for damage detection. [less ▲]

Electrostatic Forces Computed with Extended Finite Element

(2009)

Smart Sensors and MEMS for all over Industrial Application Niches

in Smart Systems Integration (2009)

On modal interactions in strongly nonlinear systems

in Euromech 503, Nonlinear Normal Modes, Dimension Reduction and Localization in Vibrating Systems, Frascati, 2009 (2009)

Dimensionality Reducion using Linear and Nonlinear Transformations

in Boller, C. (Ed.) Encyclopedia of Structural Health Monitoring (2009)

Static and Dynamic experimental investigations of a micro-electromechanical cantilever in air and vacuum

(2009)

The dynamic response of electro-mechanically actuated micro structures is governed by nonlinear effects which directly influence their performance. To date, most work in the field of micro/nano systems is ... [more ▼]

The dynamic response of electro-mechanically actuated micro structures is governed by nonlinear effects which directly influence their performance. To date, most work in the field of micro/nano systems is done experimentally and documented theoretical research consists of nonlinear lumped-mass models as well as continuum mechanics approaches. Existing and codified computational tools for micro-electromechanical systems (MEMS) more and more penetrate the market of designers and fabrication of such devices. The present work is the experimental part of a bench-mark study of a selected microbeam structure investigated with aforementioned analytical and computational techniques and compared to experiments performed with a Polytec MSA400 analyzer. The emphasis of this benchmark study is put on the nonlinear dynamic behavior with respect to qualitative and quantitative explanations of the electro-mechanical actuation and damping mechanisms. [less ▲]

Nonlinear modal analysis and energy localization in a bladed disk assembly

in ASME Turbo Expo 2008: Power for Land, Sea and Air, Berlin, 2008 (2008, June)

The objective of this study is to carry out modal analysis of nonlinear periodic structures using nonlinear normal modes (NNMs). The NNMs are computed numerically with a method developed in [18] that is ... [more ▼]

The objective of this study is to carry out modal analysis of nonlinear periodic structures using nonlinear normal modes (NNMs). The NNMs are computed numerically with a method developed in [18] that is using a combination of two techniques: a shooting procedureand a method for the continuation of periodic motion. The proposed methodology is applied to a simplified model of a perfectly cyclic bladed disk assembly with 30 sectors. The analysis shows that the considered model structure features NNMs characterized by strong energy localization in a few sectors. This feature has no linear counterpart, and its occurrence is associated with the frequencyenergy dependence of nonlinear oscillations. [less ▲]