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Nonlinear modal analysis of aerospace structures Peeters, Maxime ; Kerschen, Gaëtan ; Golinval, Jean-Claude et al in Proceedings of the 3rd International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (2011) The dynamic systems theory is well-established for linear systems and can rely on mature tools such as the theories of linear operators and linear integral transforms. This is why theoretical and ... [more ▼] The dynamic systems theory is well-established for linear systems and can rely on mature tools such as the theories of linear operators and linear integral transforms. This is why theoretical and experimental modal analysis, i.e., the computation of vibration modes from a mathematical model and from experimental data, respectively, is really quite sophisticated and advanced. Even though linear modal analysis served, and is still serving, the structural dynamics community for applications ranging from bridges to satellites, it is commonly accepted that nonlinearity is a frequent occurrence in engineering structures. Because linear modal analysis fails in the presence of nonlinear dynamical phenomena, the development of a practical nonlinear analog of modal analysis would be an extremely timely contribution; it is clearly missing in the structural dynamics literature. A new framework for nonlinear modal analysis of real-world structures, which includes the computation of nonlinear modes from finite element models, is introduced in this paper. This framework will permit a rigorous, yet understandable by the practicing engineer, analysis of nonlinear dynamical phenomena. It will also provide solid theoretical foundations for extending finite element model validation to nonlinear aerospace structures. [less ▲] Detailed reference viewed: 46 (1 ULg)Nonlinear normal modes of real-world structures: application to a full-scale aircraft Peeters, Maxime ; Kerschen, Gaëtan ; Golinval, Jean-Claude et al in Proceedings of the ASME International Design Engineering Technical Conferences (2011) The objective of this paper is to demonstrate that the numerical computation of the nonlinear normal modes (NNMs) of complex real-world structures is now within reach. The application considered in this ... [more ▼] The objective of this paper is to demonstrate that the numerical computation of the nonlinear normal modes (NNMs) of complex real-world structures is now within reach. The application considered in this study is the airframe of the Morane-Saulnier Paris aircraft, whose ground vibration tests have exhibited some nonlinear structural behaviors. The finite element model of this aircraft, elaborated from drawings, has more than 80000 degrees of freedom, and softening nonlinearities exist in the connection between the external fuel tanks and the wing tips. From this model, a reduced-order model, which is accurate in the [0-100Hz] range, is constructed using the Craig- Bampton technique. The NNMs of the reduced model are then computed using a numerical algorithm combining shooting and pseudo-arclength continuation. The results show that the NNMs of this full-scale structure can be computed accurately even in strongly nonlinear regimes and with a reasonable computational burden. Nonlinear modal interactions are also highlighted by the algorithm and are discussed. [less ▲] Detailed reference viewed: 26 (2 ULg)Nonlinear normal modes and band zones in granular chains with no precompression ; ; et al in Nonlinear Dynamics (2011), 63 We study standing waves (nonlinear normal modes—NNMs) and band zones in finite granular chains composed of spherical granular beads in Hertzian contact, with fixed boundary conditions. Although these are ... [more ▼] We study standing waves (nonlinear normal modes—NNMs) and band zones in finite granular chains composed of spherical granular beads in Hertzian contact, with fixed boundary conditions. Although these are homogeneous dynamical systems in the notation of Rosenberg, we show that the discontinuous nature of the dynamics leads to interesting effects such as separation between beads, NNMs that appear as traveling waves (these are characterized as pseudo-waves), and localization phenomena. In the limit of infinite extent, we study band zones, i.e., pass and stop bands in the frequency–energy plane of these dynamical systems, and classify the essentially nonlinear responses that occur in these bands. Moreover, we show how the topologies of these bands significantly affect the forced dynamics of these granular media subject to narrowband excitations. This work provides a classification of the coherent (regular) intrinsic dynamics of one-dimensional homogeneous granular chains with no pre-compression, and provides a rigorous theoretical foundation for further systematic study of the dynamics of granular systems, e.g., the effects of disorders or clearances, discrete breathers, nonlinear localized modes, and high-frequency scattering by local disorders. Moreover, it contributes toward the design of granular media as shock protectors, and in the passive mitigation of transmission of unwanted disturbances. [less ▲] Detailed reference viewed: 33 (2 ULg)Computation of nonlinear normal modes of large structures: application to a full-scale aircraft Peeters, Maxime ; Renson, Ludovic ; Kerschen, Gaëtan et al in Proceedings of the 7th European Nonlinear Dynamics Conference (ENOC 2011) (2011) The objective of this paper is to demonstrate that the numerical computation of the nonlinear normal modes (NNMs) of complex real-world structures is now within reach. The application considered in this ... [more ▼] The objective of this paper is to demonstrate that the numerical computation of the nonlinear normal modes (NNMs) of complex real-world structures is now within reach. The application considered in this study is the airframe of the Morane-Saulnier Paris aircraft, whose ground vibration tests exhibited some nonlinear structural behaviors. The NNMs are computed using a numerical algorithm combining shooting and pseudo-arclength continuation. [less ▲] Detailed reference viewed: 67 (5 ULg)Phase resonance testing of nonlinear vibrating structures Peeters, Maxime ; Kerschen, Gaëtan ; Golinval, Jean-Claude in 28th International Modal Analysis Conference, Jacksonville, 2010 (2011) Detailed reference viewed: 36 (13 ULg)Modal testing of nonlinear vibrating structures based on nonlinear normal modes: Experimental demonstration Peeters, Maxime ; Kerschen, Gaëtan ; Golinval, Jean-Claude in Mechanical Systems & Signal Processing (2011), 25 Detailed reference viewed: 27 (1 ULg)Dynamic testing of nonlinear vibrating structures using nonlinear normal modes Peeters, Maxime ; Kerschen, Gaëtan ; Golinval, Jean-Claude in Journal of Sound & Vibration (2011), 330 Detailed reference viewed: 28 (1 ULg)Nonlinear Normal Modes of a Full-Scale Aircraft Peeters, Maxime ; Kerschen, Gaëtan ; Golinval, Jean-Claude et al in 29th International Modal Analysis Conference, Jacksonville, 2011 (2011) Detailed reference viewed: 37 (5 ULg)Theoretical and Experimental Modal Analysis of Nonlinear Vibrating Structures using Nonlinear Normal Modes Peeters, Maxime Doctoral thesis (2011) Detailed reference viewed: 75 (29 ULg)Detection of nonlinearity in a dynamic system using deformation modes obtained from the wavelet transform of measured responses Nguyen, Viet Ha ; Peeters, Maxime ; Golinval, Jean-Claude in Shock and Vibration (2010), 17(4-5), 491-506 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 ▲] Detailed reference viewed: 66 (17 ULg)Theoretical and experimental modal analysis of nonlinear aerospace structures Peeters, Maxime ; Golinval, Jean-Claude ; Kerschen, Gaëtan in Proceedings of the AIAA Modeling and Simulation Technologies Conference (2010) Because nonlinearity is a frequent occurrence in aerospace applications, there is a need for e cient analysis procedures. In this context, nonlinear normal modes (NNMs) o er a solid mathematical tool for ... [more ▼] Because nonlinearity is a frequent occurrence in aerospace applications, there is a need for e cient analysis procedures. In this context, nonlinear normal modes (NNMs) o er a solid mathematical tool for interpreting a wide class of nonlinear dynamical phenomena. The objective of this study is to highlight the usefulness of NNMs for modeling and testing of nonlinear aerospace structures. Both theoretical and experimental modal analysis are described and are illustrated. [less ▲] Detailed reference viewed: 12 (0 ULg)Modal testing using nonlinear normal modes: experimental demonstration Peeters, Maxime ; Kerschen, Gaëtan ; Golinval, Jean-Claude in Proceedings of the International Conference on Noise and Vibration Engineering (2010) Modal testing and analysis is well-established for linear vibrating structures. While the common practice is to assume linear behavior, nonlinearity is a frequent occurrence in engineering applications ... [more ▼] Modal testing and analysis is well-established for linear vibrating structures. While the common practice is to assume linear behavior, nonlinearity is a frequent occurrence in engineering applications and can drastically alter the behavior of mechanical systems. In this paper, an attempt is made to extend experimental modal analysis methodology to a practical nonlinear analog. In this context, nonlinear normal modes (NNMs) offer a solid theoretical and mathematical tool for interpreting a wide class of nonlinear dynamical phenomena, yet they have a clear and simple conceptual relation to the classical linear normal modes. Based on a nonlinear extension of phase resonance testing (also called force appropriation), the proposed methodology excites the structure to isolate one single NNM during the experiments. Thanks to the invariance principle, the energy dependence of that nonlinear mode (i.e., the NNM modal curves and their frequencies of oscillation) can be extracted from the resulting free decay response using time-frequency analysis. The proposed method is demonstrated using an experimental cantilever beam with a geometrical nonlinearity. [less ▲] Detailed reference viewed: 25 (2 ULg)Nonlinear Normal Modes: Theoretical Curiosity or Practical Concept ?, KEYNOTE LECTURE, Peeters, Maxime ; Golinval, Jean-Claude ; Kerschen, Gaëtan in IMPACT 2010, Djerba, 2010 (2010) Detailed reference viewed: 50 (15 ULg)Experimental modal analysis of nonlinear vibrating structures using nonlinear normal modes Peeters, Maxime ; Kerschen, Gaëtan ; Golinval, Jean-Claude in IV European Conference on Computational Mechanics, Paris, 2010 (2010) Detailed reference viewed: 40 (14 ULg)Energy Transfer and Dissipation in a Duffing Oscillator Coupled to a Nonlinear Attachment Viguié, Régis ; Peeters, Maxime ; Kerschen, Gaëtan et al in Journal of Computational and Nonlinear Dynamics (2009), 4(4), The dynamics of a two-degree-of-freedom nonlinear system consisting of a grounded Duffing oscillator coupled to an essentially nonlinear attachment is examined in the present study. The underlying ... [more ▼] The dynamics of a two-degree-of-freedom nonlinear system consisting of a grounded Duffing oscillator coupled to an essentially nonlinear attachment is examined in the present study. The underlying Hamiltonian system is first considered, and its nonlinear normal modes are computed using numerical continuation and gathered in a frequency-energy plot. Based on these results, the damped system is then considered, and the basic mechanisms for energy transfer and dissipation are analyzed. [DOI: 10.1115/1.3192130] [less ▲] Detailed reference viewed: 38 (11 ULg)Nonlinear normal modes, Part 1: Useful framework for the structural dynamicist Kerschen, Gaëtan ; Peeters, Maxime ; Golinval, Jean-Claude et al 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 ▲] Detailed reference viewed: 144 (28 ULg)Modal Analysis of a Nonlinear Periodic Structure with Cyclic Symmetry ; Peeters, Maxime ; Kerschen, Gaëtan et al in AIAA Journal (2009), 47 The objective of this paper is to examine nonlinear normal modes and their bifurcations in cyclic periodic structures. The nonlinear normal modes are computed using a numerical technique that combines ... [more ▼] The objective of this paper is to examine nonlinear normal modes and their bifurcations in cyclic periodic structures. The nonlinear normal modes are computed using a numerical technique that combines shooting and pseudoarclength continuation. Unlike perturbation techniques, the resulting algorithm can investigate strongly nonlinear regimes of motion. This study reveals that modal interactions may occur without necessarily having commensurate natural frequencies in the underlying linear system. In addition, a countable infinity of such modal Q2 interactions are shown to exist in the system. [less ▲] Detailed reference viewed: 50 (3 ULg)Nonlinear normal modes, Part 2: Toward a pratical computation using numerical continuation techniques Peeters, Maxime ; Viguié, Régis ; Sérandour, Guillaume et al 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 ▲] Detailed reference viewed: 67 (20 ULg)Detection of nonlinearity in a dynamic system using deformation modes obtained from the Wavelet Transfrom of measured responses Nguyen, Viet Ha ; Peeters, Maxime ; Golinval, Jean-Claude 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 ▲] Detailed reference viewed: 107 (29 ULg)On modal interactions in strongly nonlinear systems Peeters, Maxime ; Kerschen, Gaëtan ; Golinval, Jean-Claude in Euromech 503, Nonlinear Normal Modes, Dimension Reduction and Localization in Vibrating Systems, Frascati, 2009 (2009) Detailed reference viewed: 11 (4 ULg) |
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