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Efficiency of targeted energy transfers in coupled nonlinear oscillators associated with 1:1 resonance captures:Part II, analytical study ; ; et al in Journal of Sound & Vibration (2009) We study targeted energy transfer in a two degree-of-freedom damped system under the conditionof1:1transient resonance capture. The system consists of a linear oscillator strongly coupled to an ... [more ▼] We study targeted energy transfer in a two degree-of-freedom damped system under the conditionof1:1transient resonance capture. The system consists of a linear oscillator strongly coupled to an essentially nonlinear attachment or nonlinear energy sink. In a companion paper[ Quinnetal., Efficiency of targeted energy transfers in coupled nonlinear oscillators associated with1:1resonance captures: part I, Journal of Sound and Vibration 311 (2008)1228–1248]we studied the under lying structure of the Hamiltonian dynamics of this system ,and showed that for sufficiently small values of viscous damping , nonlinear damped transitions are strongly influenced by the under lying topological structure of periodic and quasi periodic or bits of the Hamiltonian system. In this work direct analytical treatment of the governing strongly nonlinear damped equations of motion is performed through slow/fast partitions of the transient responses, in order to investigate analytically the parameter region of optimal targeted energy transfer .To this end, we determine the characteristic time scales of the dynamics that influence the capacity of the nonlinear attachment to passively absorb and locally dissipate broad band energy from the linear oscillator. Then, we prove that optimal targeted energy transfer is realized for initial energies close to the neighbourhood of a homo clinic or bit of the under lying Hamiltonian system. We study analytically transient orbits resulting as perturbations of the homo clinic or bit in the weak lydamped system, and show that this yields an additional slow-time scale in the averaged dynamics, and leads to optimal targeted energy transfer from the linear oscillator to the nonlinear energy sink in a single ‘‘super-slow’’ half-cycle. We show that at higher energies, this ‘‘super-slow’’ half-cycle is replaced by strong nonlinear beats, which lead to significant but suboptimal targeted energy transfer efficiency. Finally, we investigate numerically targeted energy transfer efficiency in this system over a wide range of system parameter sand verify the analytical predictions. 2009 Elsevier Ltd .All rights reserved. [less ▲] Detailed reference viewed: 115 (7 ULg)Using passive nonlinear targeted energy transfer to stabilize drill-stringsystems Viguié, Régis ; Kerschen, Gaëtan ; Golinval, Jean-Claude et al 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 ▲] Detailed reference viewed: 91 (6 ULg)Passive non linear TET and its application to vibration absorption: a review ; ; et al in Proceedings of the Institution of Mechanical Engineers - Part K - Journal of Multi-body Dynamics (2008), 222 This review paper discusses recent efforts to passively move unwanted energy from a primary structure to a local essentially non-linear attachment (termed a non-linear energy sink) by utilizing targeted ... [more ▼] This review paper discusses recent efforts to passively move unwanted energy from a primary structure to a local essentially non-linear attachment (termed a non-linear energy sink) by utilizing targeted energy transfer (TET) (or non-linear energy pumping). First, fundamental theoretical aspects of TET will be discussed, including the essentially non-linear governing dynamical mechanisms for TET. Then, results of experimental studies that validate the TET phenomenon will be presented. Finally, some current engineering applications of TET will be discussed. The concept of TET may be regarded as contrary to current common engineering practise, which generally views non-linearities in engineering systems as either unwanted or, at most, as small perturbations of linear behaviour. Essentially non-linear stiffness elements are intentionally introduced in the design that give rise to new dynamical phenomena that are very beneficial to the design objectives and have no counterparts in linear theory. Care, of course, is taken to avoid some of the unwanted dynamic effects that such elements may introduce, such as chaotic responses or other responses that are contrary to the design objectives. [less ▲] Detailed reference viewed: 23 (1 ULg)Toward a fundamental understanding of the Hilbert-Huang Transform in nonlinear dynamics Kerschen, Gaëtan ; ; et al in Journal of Vibration & Control (2008) The Hilbert–Huang transform(HHT) has been shown to be effective for characterizing a wide range of nonstationary signals in terms of elemental components through what has been called the empirical mode ... [more ▼] The Hilbert–Huang transform(HHT) has been shown to be effective for characterizing a wide range of nonstationary signals in terms of elemental components through what has been called the empirical mode decomposition (EMD). The HHT has been utilized extensively despite the absence of a serious analytical foundation, as it provides a concise basis for the analysis of strongly nonlinear systems. In this paper, an attempt is made to provide the missing theoretical link, showing the relationship between the EMD and the slow-flow equations of a system. The slow-flow reduced-order model is established by performing a partition between slow and fast dynamics using the complexification-averaging technique in order to derive a dynamical system described by slowly-varying amplitudes and phases. These slow-flow variables can also be extracted directly from the experimental measurements using the Hilbert transform coupled with the EMD. The comparison between the experimental and analytical results forms the basis of a novel nonlinear system identification method, termed the slow-flow model identification (SFMI) method. Through numerical and experimental application examples, we demonstrate that the proposed method is effective for characterization and parameter estimation of multi-degree-of-freedom nonlinear systems. [less ▲] Detailed reference viewed: 40 (2 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)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)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)Suppressing aeroelastic instability by means of broadband passive TET, part 1, theory ; ; et al in AIAA Journal (2007), 45 We study passive and nonlinear targeted energy transfers induced by resonant interactions between a singledegree- of-freedom nonlinear energy sink (NES) and a 2-DOF in-flow rigid wing model. We show that ... [more ▼] We study passive and nonlinear targeted energy transfers induced by resonant interactions between a singledegree- of-freedom nonlinear energy sink (NES) and a 2-DOF in-flow rigid wing model. We show that it is feasible to partially or even completely suppress aeroelastic instability by passively transferring vibration energy from the wing to the NES in a one-way irreversible fashion. Moreover, this instability suppression is performed by partially or completely eliminating its triggering mechanism. Numerical parametric studies identify three main mechanisms for suppressing aeroelastic instability: recurring burstout and suppression, intermediate suppression, and complete elimination.Weinvestigate these mechanisms both numerically by the Hilbert–Huang transform and analytically by a complexification-averaging technique. Each suppression mechanism involves strong 1:1 resonance capture during which the NES absorbs and dissipates a significant portion of energy fed from the flow to the wing. Failure of suppression is associated with restoring the underlying triggering mechanism of instability, which is a series of superharmonic resonance captures followed by escapes from resonance. Finally, using a numerical continuation technique, we perform a bifurcation analysis to examine sensitive dependence on initial conditions and thus robustness of instability suppression. [less ▲] Detailed reference viewed: 44 (0 ULg) |
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