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The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems Detroux, Thibaut ; Renson, Ludovic ; Masset, Luc et al in Computer Methods in Applied Mechanics and Engineering (2015), 296 The harmonic balance (HB) method is widely used in the literature for analyzing the periodic solutions of nonlinear mechanical systems. The objective of this paper is to exploit the method for bifurcation ... [more ▼] The harmonic balance (HB) method is widely used in the literature for analyzing the periodic solutions of nonlinear mechanical systems. The objective of this paper is to exploit the method for bifurcation analysis, i.e., for the detection and tracking of bifurcations of nonlinear systems. To this end, an algorithm that combines the computation of the Floquet exponents with bordering techniques is developed. A new procedure for the tracking of Neimark–Sacker bifurcations that exploits the properties of eigenvalue derivatives is also proposed. The HB method is demonstrated using numerical experiments of a spacecraft structure that possesses a nonlinear vibration isolation device. [less ▲] Detailed reference viewed: 38 (10 ULg)The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems Detroux, Thibaut ; Renson, Ludovic ; Masset, Luc et al Conference (2015, August 26) The harmonic balance (HB) method is widely used in the literature for analyzing the periodic solutions of nonlinear mechanical systems. The objective of this paper is to extend the method for bifurcation ... [more ▼] The harmonic balance (HB) method is widely used in the literature for analyzing the periodic solutions of nonlinear mechanical systems. The objective of this paper is to extend the method for bifurcation analysis, i.e., for the detection and tracking of bifurcations of nonlinear systems. To this end, an algorithm that combines the computation of the Floquet exponents with bordering techniques is developed. A new procedure for the tracking of Neimark-Sacker bifurcations that exploits the properties of eigenvalue derivatives is also proposed. As an application, the frequency response of a structure 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: 17 (1 ULg)Bifurcation analysis of a spacecraft structure using the harmonic balance method Detroux, Thibaut ; Renson, Ludovic ; Masset, Luc et al in Proceedings of the ASME 2015 International Design Engineering Technical Conferences (2015, August) The harmonic balance (HB) method has been widely used in the past few years, as a numerical tool for the study of nonlinear models. However, in its classical formulation the HB method is limited to the ... [more ▼] The harmonic balance (HB) method has been widely used in the past few years, as a numerical tool for the study of nonlinear models. However, in its classical formulation the HB method is limited to the approximation of periodic solutions. The present paper proposes to extend the method to the detection and tracking of bifurcations in the codimension-2 system parameters space. To validate the methodology, the forced response of a real spacecraft is examined. The paper first provides some numerical evidence of the presence of quasiperiodic oscillations and isolated solutions. It then demonstrates how the tracking of Neimark-Sacker and fold bifurcations can help get a deeper understanding of these attractors. [less ▲] Detailed reference viewed: 33 (5 ULg)Performance, robustness and sensitivity analysis of the nonlinear tuned vibration absorber Detroux, Thibaut ; Habib, Giuseppe ; Masset, Luc et al in Mechanical Systems & Signal Processing (2015), 60-61 The nonlinear tuned vibration absorber (NLTVA) is a recently developed nonlinear absorber which generalizes Den Hartog׳s equal peak method to nonlinear systems. If the purposeful introduction of ... [more ▼] The nonlinear tuned vibration absorber (NLTVA) is a recently developed nonlinear absorber which generalizes Den Hartog׳s equal peak method to nonlinear systems. If the purposeful introduction of nonlinearity can enhance system performance, it can also give rise to adverse dynamical phenomena, including detached resonance curves and quasiperiodic regimes of motion. Through the combination of numerical continuation of periodic solutions, bifurcation detection and tracking, and global analysis, the present study identifies boundaries in the NLTVA parameter space delimiting safe, unsafe and unacceptable operations. The sensitivity of these boundaries to uncertainty in the NLTVA parameters is also investigated. [less ▲] Detailed reference viewed: 34 (16 ULg)Numerical study of intrinsic features of isolas in a 2-dof nonlinear system Detroux, Thibaut ; Noël, Jean-Philippe ; Masset, Luc et al in Proceedings of the ICEDyn conference (2015, June) In the present paper, isolated response curves in a nonlinear system consisting of two masses sliding on a horizontal guide are examined. Transverse springs are attached to one mass to provide the ... [more ▼] In the present paper, isolated response curves in a nonlinear system consisting of two masses sliding on a horizontal guide are examined. Transverse springs are attached to one mass to provide the nonlinear restoring force, and a harmonic motion of the complete system is imposed by prescribing the displacement of their supports. Numerical simulations are carried out to study the conditions of existence of isolated solutions, their bifurcations, their merging with the main response branch and their basins of attraction. This is achieved using tools including nonlinear normal modes, energy balance, harmonic balance-based continuation and bifurcation tracking, and global analysis. [less ▲] Detailed reference viewed: 53 (6 ULg)Bifurcation analysis of large-scale dynamical systems using the harmonic balance method Detroux, Thibaut ; Renson, Ludovic ; Masset, Luc et al in Proceedings of the 12th Colloque National en Calcul des Structures (CSMA) (2015, May 22) The harmonic balance (HB) method has been widely used in the past few years, as a numerical tool for the study of nonlinear industrial models. However, in its classical formulation the HB method is ... [more ▼] The harmonic balance (HB) method has been widely used in the past few years, as a numerical tool for the study of nonlinear industrial models. However, in its classical formulation the HB method is limited to the approximation of periodic solutions. 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 and its bifurcations are studied, together with two nonlinear phenomena, namely quasiperiodic oscillations and detached resonance curves. [less ▲] Detailed reference viewed: 31 (7 ULg)Finite Element Model Reduction of Thermal Systems with Conductive and Radiative Heat Transfers Jacques, Lionel ; Masset, Luc ; Kerschen, Gaëtan Scientific conference (2015, March 24) The Lumped parameter method (LPM) is the main method used for space structures thermal design. It is very versatile and allows easy integration of user-defined components but the computation of the ... [more ▼] The Lumped parameter method (LPM) is the main method used for space structures thermal design. It is very versatile and allows easy integration of user-defined components but the computation of the conductive links is error-prone and still too often computed by hand. Widely used in structural design, the finite element method (FEM) is however not yet often used for thermal analysis. One of the main reasons is that the radiative exchange factors, usually computed through Monte Carlo ray tracing, are extremely expensive to compute due to the large number of elements composing a FE model. A new global approach for FE model reduction of thermal systems is presented. The method is based on an automated FE mesh partitioning leading to super-faces and super-nodes. It is tailored for radiative exchange factors computation, taking into account selected quadric recognition and material constraints. The method also provides accurate conductive links computation and enables a direct mapping of the reduced temperatures back onto the detailed FE mesh (for e.g. thermo-elastic analyses). The application to two instruments developed at the Centre Spatial de Liège in Belgium will be presented, namely the Extreme Ultraviolet Imager (EUI) onboard Solar Orbiter and the Back Telescope Assembly (BTA) onboard Meteosat Third Generation. [less ▲] Detailed reference viewed: 33 (4 ULg)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: 163 (35 ULg)Direction and surface sampling in ray tracing for spacecraft radiative heat transfer Jacques, Lionel ; Masset, Luc ; Kerschen, Gaëtan in Aerospace Science and Technology (2015), 47 This paper addresses the computation of radiative exchange factors through Monte Carlo ray tracing with the aim of reducing their computation time when dealing with the finite element method. Both ... [more ▼] This paper addresses the computation of radiative exchange factors through Monte Carlo ray tracing with the aim of reducing their computation time when dealing with the finite element method. Both direction and surface samplings are studied. The recently-introduced isocell method for partitioning the unit disk is applied to the direction sampling and compared to other direction sampling methods. It is then combined to different surface sampling schemes with either one or multiple rays traced per surface sampling point. Two promising approaches present better performances than standard spacecraft thermal analysis software. The first approach combines a Gauss surface sampling strategy with a local isocell direction sampling, whereas the second approach fires one ray per surface points using a global isocell direction sampling scheme. The advantages and limitations of the two methods are discussed, and they are benchmarked against a standard thermal analysis software using the entrance baffle of the Extreme Ultraviolet Imager instrument of the Solar Orbiter mission. [less ▲] Detailed reference viewed: 38 (13 ULg)Isolated response curves in a base-excited, two-degree-of-freedom, nonlinear system Noël, Jean-Philippe ; Detroux, Thibaut ; Masset, Luc et al in Proceedings of the ASME 2015 International Design Engineering Technical Conferences (2015) In the present paper, isolated response curves in a nonlinear system consisting of two masses sliding on a horizontal guide are examined. Transverse springs are attached to one mass to provide the ... [more ▼] In the present paper, isolated response curves in a nonlinear system consisting of two masses sliding on a horizontal guide are examined. Transverse springs are attached to one mass to provide the nonlinear restoring force, and a harmonic motion of the complete system is imposed by prescribing the displacement of their supports. Numerical simulations are carried out to study the conditions of existence of isolated solutions, their bifurcations, their merging with the main response branch and their basins of attraction. This is achieved using tools including nonlinear normal modes, energy balance, harmonic balance-based continuation and bifurcation tracking, and global analysis. [less ▲] Detailed reference viewed: 44 (8 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: 36 (10 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)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)Enhancement of ray tracing method for radiative heat transfer with new isocell quasi-monte carlo technique and application to EUI space instrument Jacques, Lionel ; Masset, Luc ; Kerschen, Gaëtan in Proceedings of the 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, HEFAT2014 (2014, July) Monte Carlo ray tracing method for thermal analysis. The rationale for this research is the speed-up of radiative heat transfer computation with the Finite Element Method, widely used in mechanical ... [more ▼] Monte Carlo ray tracing method for thermal analysis. The rationale for this research is the speed-up of radiative heat transfer computation with the Finite Element Method, widely used in mechanical engineering especially for space structure design but not yet often for thermal analysis of these structures. Based on Nusselt’s analogy, the ray direction sampling is done by sampling the unit disc to derive the ray directions. Stratified sampling is applied to the unit disc that is divided into cells or strata into which random points are generated. The isocell method relies on cells that have the particularity of presenting almost the same area and shape. This enhances the uniformity of the generated quasi-random sequence of ray directions and leads to faster convergence. The isocell method is associated with different surface sampling to derive REFs. The method is benchmarked against ESARAD, the standard ray tracing engine of the thermal analysis software used in the European aerospace industry. Various geometries are used. In particular, one entrance baffle of the Extreme Ultraviolet Imager (EUI) instrument developed at the Centre Spatial de Liège in Belgium is presented. The EUI instrument of the Solar Orbiter European Space Agency mission and will be launched in a 0.28 perihelion orbit around the Sun in 2018. [less ▲] Detailed reference viewed: 47 (4 ULg)Ray tracing enhancement for space thermal analysis: isocell method Jacques, Lionel ; Masset, Luc ; Kerschen, Gaëtan in Sarler, Bozidar; Massaroti, Nicola; Nithiarasu, Perumal (Eds.) Third International Conference on Computational Methods for Thermal Problems (2014, June 02) The finite element method (FEM) is widely used in mechanical engineering, especially 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, especially 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) 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 developments of the new Isocell quasi-Monte Carlo ray tracing method are presented. The Isocell method enhances the uniformity of the generated quasi-random sequence of ray directions and leads to faster convergence. It is associated with different surface sampling to derive the REFs. The method is benchmarked against ESARAD, the standard ray-tracing engine for thermal analysis used in the European aerospace industry. Various geometries are used. In particular, one entrance baffle of the Extreme Ultraviolet Imager (EUI) instrument developed at the Centre Spatial de Liège in Belgium is used. The EUI instrument of the Solar Orbiter European Space Agency mission and will be launched in a Sun-centered 0.28 perihelion orbit in 2018. [less ▲] Detailed reference viewed: 31 (7 ULg)Ray tracing enhancement for space thermal analysis: isocell method Jacques, Lionel ; Masset, Luc ; Kerschen, Gaëtan Conference (2013, December 04) The finite element method (FEM) is widely used in mechanical engineering, especially 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, especially 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. In the frame of a global approach, several research axes will be investigated to reduce the computational effort of the REFs with FEM. The first one focuses on accelerating the convergence and enhancing the accuracy of the ray-tracing process to decrease the number of rays required to achieve a given accuracy. The developments of the new Isocell quasi-Monte Carlo ray tracing method are presented. Based on Nusselt’s analogy, the ray direction sampling is carried out by sampling the unit disc to derive the ray directions. The unit disc is divided into cells into which random points are then generated. The cells have the particularity of presenting almost the same area and shape. This enhances the uniformity of the generated quasi-random sequence of ray directions and leads to faster convergence. This Isocell method has been associated with different surface sampling to derive the REFs. The method is benchmarked against ESARAD, the standard thermal analysis software used in the European aerospace industry. Various geometries have been used. In particular, one entrance baffle of the Extreme Ultraviolet Imager (EUI) instrument developed at the Centre Spatial de Liège in Belgium is used. The EUI instrument of the Solar Orbiter European Space Agency mission and will be launched in a Sun-centered (0.28 perihelion) orbit in 2018. [less ▲] Detailed reference viewed: 30 (3 ULg)Performance and Robustness of the Nonlinear Tuned Vibration Absorber Detroux, Thibaut ; Masset, Luc ; Kerschen, Gaëtan in Proceedings of the GDR DYNOLIN 3437 (2015) (2013, October 17) Detailed reference viewed: 14 (2 ULg)Partition of the circle in cells of equal area and shape Masset, Luc Report (2011) In the present paper, a new method for partitioning a circle in cells is presented. Cells have equal areas and shapes, so the method is termed the Isocell method. Its most interesting property is that ... [more ▼] In the present paper, a new method for partitioning a circle in cells is presented. Cells have equal areas and shapes, so the method is termed the Isocell method. Its most interesting property is that cell centres are uniformly distributed inside the circle. Among possible applications of the Isocell method, the calculation of view factors by ray-tracing (image rendering, radiative heat transfer modelling) is presented. [less ▲] Detailed reference viewed: 97 (14 ULg)Thermal model reduction using the super-face concept Masset, Luc ; Bruls, Olivier ; Kerschen, Gaëtan Conference (2011) The objective of this presentation is to carry out thermal model reduction in the context of the finite element method. The finite element model is decomposed in several sets of adjacent faces called ... [more ▼] The objective of this presentation is to carry out thermal model reduction in the context of the finite element method. The finite element model is decomposed in several sets of adjacent faces called super-faces. Specialized algorithms such as the METIS partitioning algorithm are used to automatically generate the super-faces. Several constraints may be imposed, e.g., the size of the super-face, its aspect ratio or its aperture angle. Once the model is decomposed, view factors between super-faces are calculated with direct numerical integration or ray-tracing methods. This method offers a very substantial reduction of the computational burden compared to the full model, which is particularly interesting for pre-design studies or specific applications such as deployable structures. [less ▲] Detailed reference viewed: 40 (13 ULg)Proper Orthogonal Decomposition for Nonlinear Radiative Heat Transfer Problems ; Masset, Luc ; Kerschen, Gaëtan et al in Proceedings of the ASME International Design Engineering Technical Conferences (2011) Analysing large scale, nonlinear, multiphysical, dynamical structures, by using mathematical modelling and simulation, e.g. Finite Element Modelling (FEM), can be computationally very expensive ... [more ▼] Analysing large scale, nonlinear, multiphysical, dynamical structures, by using mathematical modelling and simulation, e.g. Finite Element Modelling (FEM), can be computationally very expensive, especially if the number of degrees-of-freedom is high. This paper develops modal reduction techniques for such nonlinear multiphysical systems. The paper focuses on Proper Orthogonal Decomposition (POD), a multivariate statistical method that obtains a compact representation of a data set by reducing a large number of interdependent variables to a much smaller number of uncorrelated variables. A fully coupled, thermomechanical model consisting of a multilayered, cantilever beam is described and analysed. This linear benchmark is then extended by adding nonlinear radiative heat exchanges between the beam and an enclosing box. The radiative view factors, present in the equations governing the heat fluxes between beam and box elements, are obtained with a raytracing method. A reduction procedure is proposed for this fully coupled nonlinear, multiphysical, thermomechanical system. Two alternative approaches to the reduction are investigated, a monolithic approach incorporating a scaling factor to the equations, and a partitioned approach that treats the individual physical modes separately. The paper builds on previous work presented previously by the authors. The results are given for the RMS error between either approach and the original, full solution. [less ▲] Detailed reference viewed: 27 (7 ULg) |
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