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COMPUTATION OF NONLINEAR NORMAL MODES, PART I: NUMERICAL CONTINUATION IN MATLAB Peeters, Maxime ; Viguié, Régis ; et al in Sixth EUROMECH Nonlinear Dynamics Conference, Saint Petersbourg, 2008 (2008) The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companion, Part II. Because there is virtually no application of the NNMs to large-scale engineering structures ... [more ▼] The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companion, Part II. Because there is virtually no application of the NNMs to large-scale engineering structures, these papers are an attempt to highlight one aspect that might drive their development in the future. Specifically, we support that numerical methods for the continuation of periodic solutions pave the way for an effective and practical computation of NNMs. In this context, we show that the NNM computation is possible with limited implementation effort. The proposed algorithm, implemented in MATLAB, relies on two main techniques, namely a shooting procedure and a method for the continuation of NNM motions. The algorithm is demonstrated using a 2DOF nonlinear system. A comparison with the results given by the AUTO software is achieved in Part II. [less ▲] Detailed reference viewed: 157 (7 ULg)Vibration Mitigation of Nonlinear Vibrating Structures using Nonlinear Energy Sinks Viguié, Régis ; Peeters, Maxime ; Kerschen, Gaëtan et al in 26th International Modal Analysis Conference, Orlando, 2008 (2008) 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 60 (4 ULg)Empirical Mode Decomposition in the Reduced-Order Modeling of Aeroelastic Systems ; ; et al in 49th AIAA Structural Dynamics and Materials Conference, Shaumberg, 2008 (2008) A relationship between IntrinsicMode Functions (IMFs), derived from the Empirical Mode Decomposition (EMD), and the slow-flow model of a nonlinear dynamical system has been exploited in the development of ... [more ▼] A relationship between IntrinsicMode Functions (IMFs), derived from the Empirical Mode Decomposition (EMD), and the slow-flow model of a nonlinear dynamical system has been exploited in the development of the Slow Flow Model Identification (SFMI) method for strongly nonlinear systems, in which the physical parameters of such systems are identified from experimental data. Both the slow flows and IMFs provide the means to expand a general multicomponent signal in terms of a series of simpler, dominant, monocomponent signals. The slow flows are obtained analytically, for example through application of the method of complexification and averaging (CxA), which transforms the equations of motion into a set of approximate equations in amplitude and phase for each modeled frequency component. In contrast, the EMD characterizes a signal through the envelope and phase of its elemental components, the IMFs. Thus, between nonlinear transitions, the equations derived using the CxA method govern the amplitude and phase of the modeled IMFs. Application of SFMI has, until now, been limited to low-dimensional systems subjected to impulsive excitation. Herein, the method is extended to identification of a planar rigid airfoil [less ▲] Detailed reference viewed: 55 (1 ULg)Targeted Energy Transfers for Suppressing Aeroelastic Instability due to Unsteady Lift ; ; et al in AVT-152 Symposium on Limit Cycle Oscillations, Norway, 2008 (2008) Detailed reference viewed: 22 (0 ULg)Computation of Nonlinear Normal Modes using Numerical Continuation Techniques Peeters, Maxime ; Viguié, Régis ; et al in International Confernce on Advanced Computational Methods in Engineering, Liège, 2008 (2008) Detailed reference viewed: 41 (7 ULg)Efficiency of Targeted Energy Transfers in Coupled Nonlinear Oscillators Associated with 1:1 Resonance Captures ; ; et al in 45th Technical Meeting of the Society of Engineering Science, Urbana Champaign, 2008 (2008) Detailed reference viewed: 24 (1 ULg)Operational Modal Analysis using Second-Order Blind Identification Poncelet, Fabien ; Kerschen, Gaëtan ; Golinval, Jean-Claude in 26th International Modal Analysis Conference, Orlando, 2008 (2008) For modal analysis of large structures, it is unpractical and expensive to use artificial excitation (e.g., shakers). However, engineering structures are most often subject to ambient loads (e.g., traffic ... [more ▼] For modal analysis of large structures, it is unpractical and expensive to use artificial excitation (e.g., shakers). However, engineering structures are most often subject to ambient loads (e.g., traffic and wind) that can be exploited for modal parameter estimation. One difficulty is that the actual loading conditions cannot generally be measured, and output-only measurements are available. This paper proposes to explore the utility of blind source separation (BSS) techniques for operational modal analysis. The basic idea of BSS is to recover unobserved source signals from their observed mixtures. The feasibility and practicality of the proposed method are demonstrated using an experimental application. [less ▲] Detailed reference viewed: 111 (7 ULg)Toward an Optimal Design Procedure of a Nonlinear Vibration Absorber Coupled to a Duffing Oscillator Viguié, Régis ; Kerschen, Gaëtan in International Conference on Noise and Vibration Engineering, Leuven, 2008 (2008) 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 87 (3 ULg)OUFTI-1: The CubeSat developed at the University of Liège, Belgium ; Pisane, Jonathan ; et al Conference (2008) Detailed reference viewed: 165 (25 ULg)Exploration of nonlinear shunting strategies as effective vibration absorbers Viguié, Régis ; Peeters, Maxime ; Kerschen, Gaëtan et al in 45th Technical Meeting of the Society of Engineering Science, Urbana Champaign, 2008 (2008) Detailed reference viewed: 40 (7 ULg)Nonlinear Normal Modes, Part II: Practical Computation using Numerical Continuation Techniques Peeters, Maxime ; Viguié, Régis ; et al in 26th International Modal Analysis Conference, Orlando, 2008 (2008) The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companion, Part I. One reason of the still limited use of NNMs in structural dynamics is that their computation is ... [more ▼] The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companion, Part I. 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. [less ▲] Detailed reference viewed: 68 (6 ULg)In-orbit vibration testing of spacecraft structures Poncelet, Fabien ; Kerschen, Gaëtan ; Golinval, Jean-Claude in International Conference on Noise and Vibration Engineering, Leuven, 2008 (2008) In-orbit modal testing can be an interesting tool for the monitoring of spacecraft structures. In these applications, it is impossible to measure or to control the excitation resulting, for instance, from ... [more ▼] In-orbit modal testing can be an interesting tool for the monitoring of spacecraft structures. In these applications, it is impossible to measure or to control the excitation resulting, for instance, from an impact with a small asteroid or from the working engines. Consequently the only realistic methodology must be an outputonly modal analysis, also called Operational Modal Analysis (OMA). This paper proposes another way of doing OMA where the post-processing (i.e. the physical modal parameter extraction) is simplified and automated. The methodology uses the Blind Source Separation (BSS) techniques which attempt to recover the source signals only from their observed mixtures. In case of structural dynamic responses, the source signals and the mixing matrix are equivalent to the modal coordinates and the mode matrix, respectively. The paper describes the complete methodology including the post-processing, and its feasibility is demonstrated using a numerical application modeling a truss satellite with the FE method. [less ▲] Detailed reference viewed: 127 (12 ULg)Targeted energy transfers in vibro-impact oscillators for seismic mitigation ; ; et al in Nonlinear Dynamics (2007), 50(3), 651-677 In the field of seismic protection of structures, it is crucial to be able to diminish 'as much as possible' and dissipate 'as fast as possible' the load induced by seismic (vibration-shock) energy ... [more ▼] In the field of seismic protection of structures, it is crucial to be able to diminish 'as much as possible' and dissipate 'as fast as possible' the load induced by seismic (vibration-shock) energy imparted to a structure by an earthquake. In this context, the concept of passive nonlinear energy pumping appears to be natural for application to seismic mitigation. Hence, the overall problem discussed in this paper can be formulated as follows: Design a set of nonlinear energy sinks (NESs) that are locally attached to a main structure, with the purpose of passively absorbing a significant part of the applied seismic energy, locally confining it and then dissipating it in the smallest possible time. Alternatively, the overall goal will be to demonstrate that it is feasible to passively divert the applied seismic energy from the main structure (to be protected) to a set of preferential nonlinear substructures (the set of NESs), where this energy is locally dissipated at a time scale fast enough to be of practical use for seismic mitigation. It is the aim of this work to show that the concept of nonlinear energy pumping is feasible for seismic mitigation. We consider a two degree-of-freedom (DOF) primary linear system (the structure to be protected) and study seismic-induced vibration control through the use of Vibro-Impact NESs (VI NESs). Also, we account for the possibility of attaching to the primary structure additional alternative NES configurations possessing essential but smooth nonlinearities (e.g., with no discontinuities). We study the performance of the NESs through a set of evaluation criteria. The damped nonlinear transitions that occur during the operation of the VI NESs are then studied by superimposing wavelet spectra of the nonlinear responses to appropriately defined frequency - energy plots (FEPs) of branches of periodic orbits of underlying Conservative systems. [less ▲] Detailed reference viewed: 39 (1 ULg)LOCALIZATION OF ENERGY IN A PERFECTLY SYMMETRIC BLADED DISK ASSEMBLY DUE TO NONLINEARITIES ; Peeters, Maxime ; Kerschen, Gaëtan et al in ASME Internaional Mechanical Engineering Congress and Exposition, Seattle, 2007 (2007, November) Although a bladed disk is typically designed to have identical blades, manufacturing tolerances, wear, and other causes may cause random deviations among the blades. The blade-to-blade discrepancies ... [more ▼] Although a bladed disk is typically designed to have identical blades, manufacturing tolerances, wear, and other causes may cause random deviations among the blades. The blade-to-blade discrepancies, denoted as mistuning, lead to vibratory responses mostly concentrated in small regions of the bladed-disk assembly, according to a phenomenon called localization. The resulting spatial confinement of the vibration energy causes the responses of some blades to become dangerously high and increases the amplitude of the bladed-disk assembly's overall response. The attendant increase in stresses can lead to premature high cycle fatigue (HCF) of the blades. In this study we investigate whether vibration localization in a perfectly symmetric bladed disk assembly may occur in the presence of nonlinearity. To this end, the nonlinear normal modes (NNMs) of a simplified model of a bladed disk assembly are computed. The NNMs are then carefully examined to highlight possible vibration localization phenomena. [less ▲] Detailed reference viewed: 49 (5 ULg)Suppressing aeroelastic instability by means of broadband targeted energy transfers, part 2: Experiments ; Kerschen, Gaëtan ; et al in AIAA Journal (2007), 45(10), 2391-2400 This paper presents experimental results corroborating the analysis developed in the companion paper, Part I (Lee, Y., Vakakis, A., Bergman, L., McFarland, M., and Kerschen G., "Suppression Aeroelastic ... [more ▼] This paper presents experimental results corroborating the analysis developed in the companion paper, Part I (Lee, Y., Vakakis, A., Bergman, L., McFarland, M., and Kerschen G., "Suppression Aeroelastic Instability Using Broadband Passive Targeted Energy Transfers, Part 1: Theory," AIAA Journal, Vol. 45, No. 3, 2007, pp. 693-711), and demonstrates that a nonlinear energy sink can improve the stability of an aeroelastic system. The nonlinear energy sink was, in this case, attached to the heave (plunge) degree of freedom of a rigid airfoil which was supported in a low-speed wind tunnel by nonlinear springs separately adjustable in heave and pitch. This airfoil was found to exhibit a at flow speeds above the critical ('flutter") speed of 9.5 m/s, easily triggered by an initial heave displacement. After attachment of a single degree of freedom, essentially nonlinear energy sink to the wing, the combined system exhibited improved dynamic response as measured by the reduction or elimination of limit cycle oscillation at flow speeds significantly greater than the wing's critical speed. The design, application, and performance of the nonlinear energy sink are described herein, and the results obtained are compared to analytical predictions. The physics of the interaction of the sink with the wing is examined in detail. [less ▲] Detailed reference viewed: 44 (2 ULg)Broadband passive targeted energy pumping from a linear dispersive rod to a lightweight essentially non-linear end attachment ; ; Kerschen, Gaëtan in International Journal of Non-Linear Mechanics (2007), 42(5), 773-788 We examine non-linear resonant interactions between a damped and forced dispersive linear finite rod and a lightweight essentially non-linear end attachment. We show that these interactions may lead to ... [more ▼] We examine non-linear resonant interactions between a damped and forced dispersive linear finite rod and a lightweight essentially non-linear end attachment. We show that these interactions may lead to passive, broadband and on-way targeted energy flow from the rod to the attachment, which acts, in essence, as non-linear energy sink (NES). The transient dynamics of this s stem subject to shock excitation is examined numerically using a finite element (FE) formulation. Parametric studies are performed to examine the regions in parameter space where optimal (maximal) efficiency of targeted energy pumping from the rod to the NES occurs. Signal processing of the transient time series is then performed. employing energy transfer and/or exchange measures, wavelet transforms, empirical mode decomposition and Hilbert transforms. By computing intrinsic mode functions (IMFs) of the transient responses of the NES and the edge of the rod, and examining resonance captures that occur between them, we are able to identify the non-linear resonance mechanisms that govern the (strong or weak) one-way energy transfers from the rod to the NES. The present study demonstrates the efficacy of using local lightweight non-linear attachments (NESs) as passive broadband energy absorbers of unwanted disturbances in continuous elastic structures, and investigates the dynamical mechanisms that govern the resonance interactions influencing this passive non-linear energy absorption. (c) 2007 Elsevier Ltd. All rights reserved. [less ▲] Detailed reference viewed: 35 (0 ULg)Complex dynamics and targeted energy transfer in linear oscillators coupled to multi-degree-of-freedom essentially nonlinear attachments ; ; Kerschen, Gaëtan et al in Nonlinear Dynamics (2007), 48(3), 285-318 We study the dynamics of a system of coupled linear oscillators with a multi-DOF end attachment with essential (nonlinearizable) stiffness nonlinearities. We show numerically that the multi-DOF attachment ... [more ▼] We study the dynamics of a system of coupled linear oscillators with a multi-DOF end attachment with essential (nonlinearizable) stiffness nonlinearities. We show numerically that the multi-DOF attachment can passively absorb broadband energy from the linear system in a one-way, irreversible fashion, acting in essence as nonlinear energy sink (NES). Strong passive targeted energy transfer from the linear to the nonlinear subsystem is possible over wide frequency and energy ranges. In an effort to study the dynamics of the coupled system of oscillators, we study numerically and analytically the periodic orbits of the corresponding undamped and unforced hamiltonian system with asymptotics and reduction. We prove the existence of a family of countable infinity of periodic orbits that result from combined parametric and external resonance interactions of the masses of the NES. We numerically demonstrate that the topological structure of the periodic orbits in the frequency-energy plane of the hamiltonian system greatly influences the strength of targeted energy transfer in the damped system and, to a great extent, governs the overall transient damped dynamics. This work may be regarded as a contribution towards proving the efficacy the utilizing essentially nonlinear attachments as passive broadband boundary controllers. [less ▲] Detailed reference viewed: 40 (3 ULg)Enhancing Robustness of Instability Suppression by Means of Multi-Degree-of-Freedom Nonlinear Energy Sinks ; ; et al in 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Honolulu, 2007 (2007, April) Multi-degree-of-freedom nonlinear energy sinks (MDOF NESs) are utilized to improve robustness of suppression of limit cycle oscillations (LCOs) due to aeroelastic instability. Bifurcation analysis by a ... [more ▼] Multi-degree-of-freedom nonlinear energy sinks (MDOF NESs) are utilized to improve robustness of suppression of limit cycle oscillations (LCOs) due to aeroelastic instability. Bifurcation analysis by a numerical continuation technique shows that controlling occurrence of a limit point cycle (LPC or saddle-node) bifurcation point above a Hopf bifurcation point is crucial to enhancing robustness. Not only greatly can MDOF NESs enhance the robustness of suppression against even strong external disturbances, but they can also yield a similar e±ciency even with a smaller mass, compared to the SDOF NESs with the same parameter conditions. Nonlinear modal interactions between the aeroelastic modes and the MDOF NES are examined to demonstrate e±ciency of the MDOF NES. [less ▲] Detailed reference viewed: 62 (2 ULg)Theoretical and experimental study of multimodal targeted energy transfer in a system of coupled oscillators Kerschen, Gaëtan ; ; et al in Nonlinear Dynamics (2007), 47 The purpose of this study is the theoretical and experimental investigation of targeted energy transfers from a two-degree-of-freedom primary structure to a nonlinear energy sink (NES). It is demonstrated ... [more ▼] The purpose of this study is the theoretical and experimental investigation of targeted energy transfers from a two-degree-of-freedom primary structure to a nonlinear energy sink (NES). It is demonstrated that an NES can resonate with and extract energy from both modes of the primary structure. By facilitating these energy transfers, notably through excitation of appropriate periodic and quasi-periodic orbits, one can promote dissipation of a major portion of externally induced energy in the nonlinear attachment. [less ▲] Detailed reference viewed: 36 (14 ULg)Identification of nonlinear modal inter. between elastic continua nonlinear attachments ; ; et al in 1st int. Conf. on Computational Dynaics and Earthquake Eng., Rethymno, 2007 (2007) Detailed reference viewed: 6 (0 ULg) |
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