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The harmonic balance method for bifurcation analysis of nonlinear mechanical systems Detroux, Thibaut ; Renson, Ludovic ; Masset, Luc et al in Proceedings of the International Modal Analysis Conference (IMAC) XXXIII (2015) Because nowadays structural engineers are willing to use or at least understand nonlinearities instead of simply avoiding them, there is a need for numerical tools performing analysis of nonlinear large ... [more ▼] Because nowadays structural engineers are willing to use or at least understand nonlinearities instead of simply avoiding them, there is a need for numerical tools performing analysis of nonlinear large-scale structures. Among these techniques, the harmonic balance (HB) method is certainly one of the most commonly used to study finite element models with reasonably complex nonlinearities. However, in its classical formulation the HB method is limited to the approximation of periodic solutions. For this reason, the present paper proposes to extend the method to the detection and tracking of codimension-1 bifurcations in the system parameters space. As an application, the frequency response of a spacecraft is studied, together with two nonlinear phenomena, namely quasiperiodic oscillations and detached resonance curves. This example illustrates how bifurcation tracking using the HB method can be employed as a promising design tool for detecting and eliminating such undesired behaviors. [less ▲] Detailed reference viewed: 168 (36 ULg)Suppression of limit cycle oscillations using the nonlinear tuned vibration absorber Habib, Giuseppe ; Kerschen, Gaëtan in Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences (2015), 471(2176), The objective of this study is to mitigate, or even completely eliminate, the limit cycle oscillations in mechanical systems using a passive nonlinear absorber, termed the nonlinear tuned vibration ... [more ▼] The objective of this study is to mitigate, or even completely eliminate, the limit cycle oscillations in mechanical systems using a passive nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA). An unconventional aspect of the NLTVA is that the mathematical form of its restoring force is not imposed a priori, as it is the case for most existing nonlinear absorbers. The NLTVA parameters are determined analytically using stability and bifurcation analyses, and the resulting design is validated using numerical continuation. The proposed developments are illustrated using a Van der Pol–Duffing primary system. [less ▲] Detailed reference viewed: 20 (1 ULg)Identification of nonlinear normal modes of engineering structures under broadband forcing Noël, Jean-Philippe ; Renson, Ludovic ; Grappasonni, Chiara et al in Mechanical Systems & Signal Processing (2015) The objective of the present paper is to develop a two-step methodology integrating system identification and numerical continuation for the experimental extraction of nonlinear normal modes (NNMs) under ... [more ▼] The objective of the present paper is to develop a two-step methodology integrating system identification and numerical continuation for the experimental extraction of nonlinear normal modes (NNMs) under broadband forcing. The first step processes acquired input and output data to derive an experimental state-space model of the structure. The second step converts this state-space model into a model in modal space from which NNMs are computed using shooting and pseudo-arclength continuation. The method is demonstrated using noisy synthetic data simulated on a cantilever beam with a hardening-softening nonlinearity at its free end. [less ▲] Detailed reference viewed: 21 (3 ULg)Analytic solution for the relative motion of satellites in near-circular low-Earth orbits Martinusi, Vladimir ; Dell'Elce, Lamberto ; Kerschen, Gaëtan in Proceedings of the AAS/AIAA Space FLight Mechanics Meeting (2015) The paper presents the solution to the problem of the relative motion between two satellites orbiting Earth under the influence of the oblateness and atmospheric drag perturbations. Starting from the ... [more ▼] The paper presents the solution to the problem of the relative motion between two satellites orbiting Earth under the influence of the oblateness and atmospheric drag perturbations. Starting from the analytic solution to the problem of the absolute motion, the closed-form equations of motion are obtained. No simplifying assumptions are made on the relative dynamics. [less ▲] Detailed reference viewed: 25 (6 ULg)Complex dynamics of a nonlinear aerospace structure: numerical continuation and normal modes Renson, Ludovic ; Noël, Jean-Philippe ; Kerschen, Gaëtan in Nonlinear Dynamics (2015), 79(2), 1293-1309 This paper investigates the dynamics of a real-life aerospace structure possessing a strongly nonlinear component with multiple mechanical stops. A full-scale finite element model is built for gaining ... [more ▼] This paper investigates the dynamics of a real-life aerospace structure possessing a strongly nonlinear component with multiple mechanical stops. A full-scale finite element model is built for gaining additional insight into the nonlinear dynamics that was observed experimentally, but also for uncovering additional nonlinear phenomena, such as quasiperiodic regimes of motion. Forced/unforced, damped/undamped numerical simulations are carried out using advanced techniques and theoretical concepts such as numerical continuation and nonlinear normal modes. [less ▲] Detailed reference viewed: 46 (7 ULg)Grey-box identification of a non-linear solar array structure using cubic splines Noël, Jean-Philippe ; Kerschen, Gaëtan ; et al in International Journal of Non-Linear Mechanics (2014), 67 Most identification methods in non-linear structural dynamics assume in advance a mathematical model of the non-linearities. This is however possible in specific situations only, since non-linear effects ... [more ▼] Most identification methods in non-linear structural dynamics assume in advance a mathematical model of the non-linearities. This is however possible in specific situations only, since non-linear effects may be caused by numerous phenomena and a priori knowledge is generally limited. The present paper investigates the usefulness of piecewise third-order polynomials, termed cubic splines, to identify the complex non-linear dynamics of solar arrays in their stowed configuration. The estimation of the model parameters is achieved using the frequency-domain non-linear subspace identification (FNSI) method. A distinct advantage of the FNSI approach is its capability to calculate accurately a large number of parameters, while maintaining an acceptable computational burden. This makes tractable the use of cubic splines to represent non-linearity in real-life mechanical systems, as the dimensionality of the inverse problem is known to increase dramatically in this case. The experimental structure of interest consists of two parallel aluminium plates assembled with bolted connections. This application is challenging because of the existence of impacts between the two plates at high excitation amplitude, and of the activation of complicated stiffness and damping mechanisms within the bolted connections. [less ▲] Detailed reference viewed: 63 (4 ULg)Piezoelectric vibration damping using resonant shunt circuits: an exact solution Soltani, Payam ; Kerschen, Gaëtan ; et al in Smart Materials & Structures (2014), 23 Detailed reference viewed: 13 (2 ULg)Probabilistic Assessment of Lifetime of Low-Earth-Orbit Spacecraft: Uncertainty Propagation and Sensitivity Analysis Dell'Elce, Lamberto ; Kerschen, Gaëtan in Journal of Guidance Control & Dynamics (2014) This paper is devoted to the probabilistic uncertainty quantification of orbital lifetime estimation of low-altitude satellites. Specifically, given a detailed characterization of the dominant sources of ... [more ▼] This paper is devoted to the probabilistic uncertainty quantification of orbital lifetime estimation of low-altitude satellites. Specifically, given a detailed characterization of the dominant sources of uncertainty, we map this input into a probabilistic characterization of the orbital lifetime through orbital propagation. Standard Monte Carlo propagation is first considered. The concept of drag correction is then introduced to facilitate the use of polynomial chaos expansions and to make uncertainty propagation computationally effective. Finally, the obtained probabilistic model is exploited to carry out stochastic sensitivity analyses, which in turn allow gaining insight into the impact uncertainties have on orbital lifetime. The proposed developments are illustrated using one CubeSat of the QB50 constellation. [less ▲] Detailed reference viewed: 24 (7 ULg)Finite element model reduction for the determination of accurate conductive links and application to MTG IRS BTA Jacques, Lionel ; Thibert, Tanguy ; Jamotton, Pierre et al Conference (2014, October 15) Detailed reference viewed: 37 (11 ULg)Electrical tuned vibration absorber: application of the equal-peak method to linear and non-linear RL piezoelectric shunts ; ; Soltani, Payam et al Scientific conference (2014, October) Detailed reference viewed: 28 (4 ULg)Linear and nonlinear piezoelectric shunting strategies for vibration mitigation Soltani, Payam ; ; et al Scientific conference (2014, September 01) Detailed reference viewed: 6 (0 ULg)Practical design of a nonlinear tuned vibration absorber Grappasonni, Chiara ; Habib, Giuseppe ; Detroux, Thibaut et al in Proceedings of the ISMA 2014 conference (2014, September) The aim of the paper is to develop a new nonlinear tuned vibration absorber (NLTVA) capable of mitigating the vibrations of nonlinear systems which are known to exhibit frequency-energy-dependent ... [more ▼] The aim of the paper is to develop a new nonlinear tuned vibration absorber (NLTVA) capable of mitigating the vibrations of nonlinear systems which are known to exhibit frequency-energy-dependent oscillations. A nonlinear generalization of Den Hartog’s equal-peak method is proposed to ensure equal peaks in the nonlinear frequency response for a large range of forcing amplitudes. An analytical tuning procedure is developed and provides the load-deflection characteristic of the NLTVA. Based on this prescribed relation, the NLTVA design is performed by two different approaches, namely thanks to (i) analytical formulas of uniform cantilever and doubly-clamped beams and (ii) numerical shape optimization of beams with varying width and thickness. A primary system composed of a cantilever beam with a geometrically nonlinear component at its free end serves to illustrate the proposed methodology. [less ▲] Detailed reference viewed: 110 (18 ULg)A rigorous phase separation method for testing nonlinear structures Noël, Jean-Philippe ; Renson, Ludovic ; Grappasonni, Chiara et al in Proceedings of ISMA 2014 - International Conference on Noise and Vibration Engineering (2014, September) The objective of the present paper is to develop a rigorous identification methodology of nonlinear normal modes (NNMs) of engineering structures. This is achieved by processing experimental measurements ... [more ▼] The objective of the present paper is to develop a rigorous identification methodology of nonlinear normal modes (NNMs) of engineering structures. This is achieved by processing experimental measurements collected under broadband forcing. The use of such a type of forcing signal allows to excite multiple NNMs simultaneously and, in turn, to save testing time. A two-step methodology integrating nonlinear system identification and numerical continuation of periodic solutions is proposed for the extraction of the individual NNMs from broadband input and output data. It is demonstrated using a numerical cantilever beam possessing a cubic nonlinearity at its free end. The proposed methodology can be viewed as a nonlinear generalization of the phase separation techniques routinely utilized for experimental modal analysis of linear structures. [less ▲] Detailed reference viewed: 49 (5 ULg)Experimental evidence and numerical prediction of nonlinear modal interactions in a real-life aerospace structure Renson, Ludovic ; Noël, Jean-Philippe ; Kerschen, Gaëtan in Proceedings of the ISMA 2014 conference (2014, September) During the last decade, the existence of nonlinear behaviour in spacecraft dynamic testing was frequently attested. However, current practice in industry is still to ignore nonlinearities, arguably ... [more ▼] During the last decade, the existence of nonlinear behaviour in spacecraft dynamic testing was frequently attested. However, current practice in industry is still to ignore nonlinearities, arguably because their analysis is regarded as impractical. The objective of the present contribution is to show that there now exists experimental and numerical methodologies which can deal with nonlinear phenomena in real-life structures. Specifically, this study investigates nonlinear modal interactions evidenced during the qualification campaign of the SmallSat spacecraft developed by EADS-Astrium. The ability to understand and reliably predict such interactions is of utmost importance as they may involve energy transfer between modes and, in turn, jeopardise the structural integrity. The paper proceeds in two steps, leading to great-fidelity reproductions of the experimental observations. In the first step, sine-sweep data collected during the qualification campaign are exploited to build a nonlinear computational model of the SmallSat with good predictive capabilities. To this end, the complete progression through nonlinearity detection, characterisation and parameter estimation is carried out by means of several techniques, such as the wavelet transform and the restoring force surface method. In the second step, the computational model is exploited through continuation algorithms to compute the nonlinear normal modes of the spacecraft and predict potential interactions. A very good agreement between experimental and numerical results is obtained for 2:1 interactions between modes with non-commensurate linear frequencies. [less ▲] Detailed reference viewed: 34 (9 ULg)Enhancement of ray tracing method for radiative heat transfer: application to EUI space instrument Jacques, Lionel ; Masset, Luc ; Kerschen, Gaëtan in Proceedings of the 15th International Heat Transfer Conference, IHTC-15 (2014, August) The finite element method (FEM) is widely used in mechanical engineering, in particular for space structure design. However, FEM is not yet often used for thermal engineering of space structures where the ... [more ▼] The finite element method (FEM) is widely used in mechanical engineering, in particular for space structure design. However, FEM is not yet often used for thermal engineering of space structures where the lumped parameter method is still dominant. Radiative exchange factors (REFs), used to calculate radiative thermal exchanges in space, are usually computed through Monte Carlo ray tracing. Due to the large number of elements composing a FE model, the computation of the REFs is prohibitively expensive. The isocell method aims at reducing the computational effort of the REFs with FEM, by decreasing the number of rays required to achieve a given accuracy. Based on Nusselt’s analogy, the ray direction sampling is carried out by sampling the unit disc to derive the ray directions. The isocell method is a special case of stratified sampling. It divides the unit disc into cells of almost same area and shape from which random points are generated. This enhances the uniformity of the ray directions and leads to faster convergence. This isocell method is associated with different surface sampling to derive the REFs. The method is benchmarked against ESARAD, the standard thermal analysis ray tracing engine used in the European aerospace industry. One entrance baffle of the Extreme Ultraviolet Imager (EUI) instrument developedat the Centre Spatial de Liège in Belgium is used as benchmarking case. Solar Orbiter is an European Space Agency mission to be launched in a Sun-centered 0.28 perihelion orbit. [less ▲] Detailed reference viewed: 61 (14 ULg)Continuation of bifurcations of periodic solutions based on the harmonic balance method Detroux, Thibaut ; Kerschen, Gaëtan Conference (2014, July 08) This paper proposes to extend the harmonic balance method to perform the continuation of bifurcations of periodic solutions in a codimension-2 parameter space. Based on the framework of bordering ... [more ▼] This paper proposes to extend the harmonic balance method to perform the continuation of bifurcations of periodic solutions in a codimension-2 parameter space. Based on the framework of bordering techniques, the procedure utilizes Hill’s method to augment the system of equations in order to track bifurcations. As an application to validate the procedure, the design of a nonlinear vibration absorber attached to a Duffing oscillator is studied. [less ▲] Detailed reference viewed: 25 (4 ULg)The nonlinear tuned vibration absorber, part I: Design and performance analysis Habib, Giuseppe ; Detroux, Thibaut ; Kerschen, Gaëtan in Proceedings of the 5th Conference on Nonlinear Vibrations, Localization and Energy Transfer (NV 2014) (2014, July 03) Detailed reference viewed: 21 (1 ULg)The nonlinear tuned vibration absorber, part II: Robustness and sensitivity analysis Detroux, Thibaut ; Habib, Giuseppe ; Masset, Luc et al in Proceedings of the 5th Conference on Nonlinear Vibrations, Localization and Energy Transfer (NV 2014) (2014, July 03) Detailed reference viewed: 35 (9 ULg)Experimental analysis of 2:1 modal interactions with noncommensurate linear frequencies in an aerospace structure Noël, Jean-Philippe ; Renson, Ludovic ; Kerschen, Gaëtan in Proceedings of the 8th European Nonlinear Dynamics Conference (ENOC) (2014, July) Nonlinear interactions between modes with noncommensurate linear frequencies are studied. It is experimentally evidenced that a strongly nonlinear, full-scale aerospace structure may exhibit such 2:1 ... [more ▼] Nonlinear interactions between modes with noncommensurate linear frequencies are studied. It is experimentally evidenced that a strongly nonlinear, full-scale aerospace structure may exhibit such 2:1 interactions in typical testing conditions. The experimental observations are compared with numerical predictions. [less ▲] Detailed reference viewed: 39 (4 ULg)Stability and bifurcation analysis of a Van der Pol–Duffing oscillator with a nonlinear tuned vibration absorber Habib, Giuseppe ; Kerschen, Gaëtan Conference (2014, July) The Van der Pol (VdP) oscillator is a paradigmatic model for description of self-excited oscillations, which are of practical interest in many engineering applications. In this paper the dynamics of a VdP ... [more ▼] The Van der Pol (VdP) oscillator is a paradigmatic model for description of self-excited oscillations, which are of practical interest in many engineering applications. In this paper the dynamics of a VdP-Duffing (VdPD) oscillator with an attached nonlinear tuned vibration absorber (NLTVA) is considered; the NLTVA has both linear and nonlinear restoring force terms. In the first part of this work, the stability of the trivial solution of the system is investigated, following results of previous works. The analysis allows to define an optimal tuning rule for the linear parameters of the absorber, which substantially enlarges the domain of safe operation of the primary system. In this case, the system loses stability through a double Hopf bifurcation. In the second part of this work, the bifurcations occurring at the loss of stability are analytically investigated, using the technique of the center manifold reduction and transformation to normal form. The obtained results show the effects of the nonlinear parameter of the absorber, which, in turn, allows to define its optimal value in order to avoid subcriticality and reduce the amplitude of self-excited oscillations. [less ▲] Detailed reference viewed: 107 (12 ULg) |
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