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See detailComplex dynamics of a nonlinear aerospace structure: numerical continuation and normal modes
Renson, Ludovic ULg; Noël, Jean-Philippe ULg; Kerschen, Gaëtan ULg

in Nonlinear Dynamics (in press)

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 ▲]

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See detailA rigorous phase separation method for testing nonlinear structures
Noël, Jean-Philippe ULg; Renson, Ludovic ULg; Grappasonni, Chiara ULg 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 ▲]

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See detailExperimental evidence and numerical prediction of nonlinear modal interactions in a real-life aerospace structure
Renson, Ludovic ULg; Noël, Jean-Philippe ULg; Kerschen, Gaëtan ULg

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 ▲]

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See detailExperimental analysis of 2:1 modal interactions with noncommensurate linear frequencies in an aerospace structure
Noël, Jean-Philippe ULg; Renson, Ludovic ULg; Kerschen, Gaëtan ULg

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 ▲]

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See detailComputation of damped nonlinear normal modes with internal resonances: a boundary value approach
Renson, Ludovic ULg; Touzé, Cyril; Kerschen, Gaëtan ULg

in Proceedings of the 8th European Nonlinear Dynamics Conference (ENOC 2014) (2014, July)

This paper considers the computation of nonlinear normal modes (NNMs) defined as two-dimensional manifolds in phase space. Because existing methods use explicit manifold parameterization, NNM computation ... [more ▼]

This paper considers the computation of nonlinear normal modes (NNMs) defined as two-dimensional manifolds in phase space. Because existing methods use explicit manifold parameterization, NNM computation in the presence of internal resonances requires multiple pairs of constraint coordinates. This paper investigates an alternative method for which the manifold is computed using successive boundary value problems. [less ▲]

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See detailComplex dynamics of a nonlinear aerospace structure: experimental identification and modal interactions
Noël, Jean-Philippe ULg; Renson, Ludovic ULg; Kerschen, Gaëtan ULg

in Journal of Sound & Vibration (2014), 333

Nonlinear system identification is a challenging task in view of the complexity and wide variety of nonlinear phenomena. The present paper addresses the identification of a real-life aerospace structure ... [more ▼]

Nonlinear system identification is a challenging task in view of the complexity and wide variety of nonlinear phenomena. The present paper addresses the identification of a real-life aerospace structure possessing a strongly nonlinear component with multiple mechanical stops. The complete identification procedure, from nonlinearity detection and characterization to parameter estimation, is carried out based upon experimental data. The combined use of various analysis techniques, such as the wavelet transform and the restoring force surface method, brings different perspectives to the dynamics. Specifically, the structure is shown to exhibit particularly interesting nonlinear behaviors, including jumps, modal interactions, force relaxation and chattering during impacts on the mechanical stops. [less ▲]

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See detailDynamics of a Strongly Nonlinear Spacecraft Structure Part I: Experimental Identification
Noël, Jean-Philippe ULg; Renson, Ludovic ULg; Kerschen, Gaëtan ULg

in Proceedings of the 13th European Conference on Spacecraft Structures, Materials and Environmental Testing (2014, April)

The present paper addresses the identification of a real-life spacecraft structure possessing a strongly nonlinear component with multiple mechanical stops. The complete identification procedure, from ... [more ▼]

The present paper addresses the identification of a real-life spacecraft structure possessing a strongly nonlinear component with multiple mechanical stops. The complete identification procedure, from nonlinearity detection and characterization to parameter estimation, is carried out based upon experimental sine-sweep data collected during a classical spacecraft qualification campaign. [less ▲]

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See detailDynamics of a Strongly Nonlinear Spacecraft Structure Part II: Modal Analysis
Renson, Ludovic ULg; Noël, Jean-Philippe ULg; Kerschen, Gaëtan ULg

in Proceedings of the 13th European Conference on Spacecraft Structures, Materials & Environmental Testing (2014, April)

The present paper investigates the dynamics of a real-life spacecraft structure possessing a strongly nonlinear component with multiple mechanical stops. A full-scale finite element model is built for ... [more ▼]

The present paper investigates the dynamics of a real-life spacecraft 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 in a companion paper (Part I). To this end, advanced techniques and theoretical concepts such as numerical continuation and nonlinear normal modes are exploited. [less ▲]

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See detailNonlinear Modal Analysis of Conservative and Nonconservative Aerospace Structures
Renson, Ludovic ULg

Doctoral thesis (2014)

The concept of nonlinear normal modes (NNMs) provides a solid and rigorous theoretical framework for the analysis of the nonlinear oscillations of mechanical systems. If NNMs have been studied since more ... [more ▼]

The concept of nonlinear normal modes (NNMs) provides a solid and rigorous theoretical framework for the analysis of the nonlinear oscillations of mechanical systems. If NNMs have been studied since more than fifty years, it is only very recently that contributions dealing with their numerical calculation have been reported in the literature. Although these methods pave the way for the application of NNMs to more complex systems, they have not yet reached the necessary maturity. In this context, the purpose of this research is (i) to further investigate the performance of an existing method for computing the NNMs of conservative systems and (ii) to propose two new methods for the computation of NNMs of nonconservative systems. The first contribution of this thesis is to calculate the NNMs of a real-life aerospace structure, the SmallSat spacecraft developed by EADS Astrium. An algorithm that combines an advanced shooting method with the pseudo-arclength continuation technique is utilized. We show that the NNMs provide a very useful interpretation of the strongly nonlinear dynamics of the spacecraft. One specific contribution is to numerically reproduce with great fidelity several interactions between modes with noncommensurate linear frequencies that were observed experimentally. The second original contribution of this thesis is to develop two new methods for computing the NNMs of damped systems. The first method solves the partial differential equations (PDEs) governing the geometry of the NNM. The PDEs are recognized as hyperbolic, and it is shown that they require appropriate numerical treatments including specific boundary conditions. The proposed method combines a streamline upwind Petrov-Galerkin finite-element formulation with a resolution strategy based on annular domains to grow sequentially the manifold. The algorithm is demonstrated using a wide variety of systems ranging from two-degree-of-freedom to multi-degree-of-freedom nonlinear systems with linear and nonlinear damping. The applicability of the algorithm to complex real-life structures is demonstrated using a full-scale aircraft. The second method presented in this work computes a NNM as a collection of trajectories defined with boundary value problems (BVPs). The method has the distinctive advantage that it does not rely on a parameterization of the NNM. It is demonstrated on two-degree-of-freedom examples featuring linear and nonlinear damping. [less ▲]

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See detailThe harmonic balance method for advanced analysis and design of nonlinear mechanical systems
Detroux, Thibaut ULg; Renson, Ludovic ULg; Kerschen, Gaëtan ULg

in Proceedings of the SEM IMAC XXXII (2014, February)

As a tool for analyzing nonlinear large-scale structures, the harmonic balance (HB) method has recently received increasing attention in the structural dynamics community. However, its use was so far ... [more ▼]

As a tool for analyzing nonlinear large-scale structures, the harmonic balance (HB) method has recently received increasing attention in the structural dynamics community. However, its use was so far limited to the approximation and study of periodic solutions, and other methods as the shooting and orthogonal collocation techniques were usually preferred to further analyze these solutions and to study their bifurcations. This is why the present paper intends to demonstrate how one can take advantage of the HB method as an efficient alternative to the cited techniques. Two different applications are studied, namely the normal modes of a spacecraft and the optimization of the design of a vibration absorber. The interesting filtering feature of the HB method and the implementation of an efficient bifurcation tracking extension are illustrated. [less ▲]

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See detailAn effective finite-element-based method for the computation of nonlinear normal modes of nonconservative systems
Renson, Ludovic ULg; Deliège, Geoffrey ULg; Kerschen, Gaëtan ULg

in Meccanica (2014), 49(8), 1901-1916

This paper addresses the numerical computation of nonlinear normal modes defined as two-dimensional invariant manifolds in phase space. A novel finite-element-based algorithm, combining the streamline ... [more ▼]

This paper addresses the numerical computation of nonlinear normal modes defined as two-dimensional invariant manifolds in phase space. A novel finite-element-based algorithm, combining the streamline upwind Petrov-Galerkin method with mesh moving and domain prediction-correction techniques, is proposed to solve the manifold-governing partial differential equations. It is first validated using conservative examples through the comparison with a reference solution given by numerical continuation. The algorithm is then demonstrated on nonconservative examples. [less ▲]

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See detailNumerical computation of nonlinear normal modes of nonconservative systems
Renson, Ludovic ULg; Kerschen, Gaëtan ULg

in Proceedings of the ASME IDETC/CIE 2013 (2013, August)

Since linear modal analysis fails in the presence of nonlinear dynamical phenomena, the concept of nonlinear normal modes (NNMs) was introduced with the aim of providing a rigorous generalization of ... [more ▼]

Since linear modal analysis fails in the presence of nonlinear dynamical phenomena, the concept of nonlinear normal modes (NNMs) was introduced with the aim of providing a rigorous generalization of linear normal modes to nonlinear systems. Initially defined as periodic solutions, numerical techniques such as the continuation of periodic solutions were used to compute NNMs. Because these methods are limited to conservative systems, the present study targets the computation of NNMs for nonconservative systems. Their definition as invariant manifolds in phase space is considered. Specifically, the partial differential equations governing the manifold geometry are considered as transport equations and an adequate finite element technique is proposed to solve them. The method is first demonstrated on a conservative nonlinear beam and the results are compared to standard continuation techniques. Then, linear damping is introduced in the system and the applicability of the method is demonstrated. [less ▲]

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See detailExperimental identification of the complex dynamics of a strongly nonlinear spacecraft structure
Noël, Jean-Philippe ULg; Renson, Ludovic ULg; Kerschen, Gaëtan ULg

in Proceedings of the ASME IDETC/CIE 2013 (2013, August)

The present paper addresses the identification of a real-life spacecraft structure possessing an impact-type nonlinear component. The complete identification procedure, i.e. from nonlinearity detection to ... [more ▼]

The present paper addresses the identification of a real-life spacecraft structure possessing an impact-type nonlinear component. The complete identification procedure, i.e. from nonlinearity detection to parameter estimation, is carried out using experimental data collected during a typical spacecraft qualification test campaign. The complementary use of several techniques reveals particularly interesting and complex phenomena such as nonlinear jumps, nonlinear modal interactions, internal force relaxation and chattering during impacts. [less ▲]

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See detailA new computational method for nonlinear normal modes of nonconservative systems
Renson, Ludovic ULg; Kerschen, Gaëtan ULg

in Proceedings of the Euromech Colloquium n. 541 - New Advances in the Nonlinear Dynamics and Control of Composites for Smart Engineering Design (2013, June)

The concept of nonlinear normal modes (NNMs) was introduced with the aim of providing a rigorous generalization of normal modes to nonlinear systems. Initially, NNMs were defined as periodic solutions of ... [more ▼]

The concept of nonlinear normal modes (NNMs) was introduced with the aim of providing a rigorous generalization of normal modes to nonlinear systems. Initially, NNMs were defined as periodic solutions of the underlying conservative system, and continuation algorithms were recently exploited to compute them. To extend the concept of NNMs to nonconservative systems, Shaw and Pierre defined an NNM as a two-dimensional invariant manifold in the system’s phase space. This contribution presents a novel algorithm for solving the set of partial differential equations governing the manifold geometry numerically. The resolution strategy takes advantage of the hyperbolic nature of the equations to progressively solve them in annular regions. Each region is defined by two different iso-energy curves and equations are discretized using a specific finite element technique. The proposed strategy also offers the opportunity to estimate the frequency-energy dependence of the mode without using time integration. The algorithm is applied to both conservative and nonconservative systems. [less ▲]

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See detailNonlinear dynamic analysis of an F-16 aircraft using GVT data
Noël, Jean-Philippe ULg; Renson, Ludovic ULg; Kerschen, Gaëtan ULg et al

in Proceedings of the International Forum on Aeroelasticity and Structural Dynamics (2013, June)

This paper aims at investigating the nonlinear dynamics of an F-16 aircraft, based upon sine-sweep data collected during a ground vibration test (GVT) campaign. Various analysis techniques, including the ... [more ▼]

This paper aims at investigating the nonlinear dynamics of an F-16 aircraft, based upon sine-sweep data collected during a ground vibration test (GVT) campaign. Various analysis techniques, including the mere visual inspection of the time series, the wavelet transform and the restoring force surface method, are utilised and reveal that the F-16 wing-to-payload mounting interfaces exhibit both softening and hardening nonlinearities. [less ▲]

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See detailComputation of nonlinear normal modes through continuation methods
Renson, Ludovic ULg; Kerschen, Gaëtan ULg

Conference (2013, May)

In mechanical engineering, performance enhancement usually results in lighter and more flexible structures and pushes the limits of the system operating envelope. Nonlinearity is therefore becoming a ... [more ▼]

In mechanical engineering, performance enhancement usually results in lighter and more flexible structures and pushes the limits of the system operating envelope. Nonlinearity is therefore becoming a frequent occurrence and linear design tools show their limitations. To overcome these issues, nonlinear normal modes (NNMs) were introduced in structural dynamics as a direct extension of linear normal modes to nonlinear systems. Our contribution reviews the history and the new trends for the computation of NNMs in mechanical engineering. Specifically, algorithms for the continuation of periodic solutions were first developed. Such algorithms are now well-established and applicable to large-scale systems such as real-life aerospace structures. To further extend the concept of NNMs to nonconservative systems, the definition of an NNM as an invariant manifold in the system’s phase space was introduced. Again, continuation techniques are particularly well suited for computing these invariant manifolds. The geodesic level set method developed by Krauskopf and Osinga [1] as well as the “PDE formulation” method of Guckenheimer and Vladimirsky [2] are both considered. [1] Krauskopf, B. and H. Osinga (2003). "Computing Geodesic Level Sets on Global (Un)stable Manifolds of Vector Fields." SIAM Journal on Applied Dynamical Systems 2(4): 546-569. [2] Guckenheimer, J. and A. Vladimirsky (2004). "A Fast Method for Approximating Invariant Manifolds." SIAM Journal on Applied Dynamical Systems 3(3): 232-260. [less ▲]

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See detailNonlinear Normal Modes of Nonconservative Systems
Renson, Ludovic ULg; Kerschen, Gaëtan ULg

in Proceedings of the SEM IMAC XXXI Conference (2013)

Linear modal analysis is a mature tool enjoying various applications ranging from bridges to satellites. Nevertheless, modal analysis fails in the presence of nonlinear dynamical phenomena and the ... [more ▼]

Linear modal analysis is a mature tool enjoying various applications ranging from bridges to satellites. Nevertheless, modal analysis fails in the presence of nonlinear dynamical phenomena and the development of a practical nonlinear analog of modal analysis is a current research topic. Recently, numerical techniques (e.g., harmonic balance, continuation of periodic solutions) were developed for the computation of nonlinear normal modes (NNMs). Because these methods are limited to conservative systems, the present study targets the computation of NNMs for nonconservative systems. Their definition as invariant manifolds in phase space is considered. Specifically, a new finite element technique is proposed to solve the set of partial differential equations governing the manifold geometry. [less ▲]

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See detailNonlinear Dynamic Analysis of Aerospace Structures
Kerschen, Gaëtan ULg; Noël, Jean-Philippe ULg; Renson, Ludovic ULg et al

Conference (2012, October)

Current practice in industry is to rely on linear finite element simulations. However, nonlinearity is a frequent occurrence in engineering structures. It is at the origin of rich and complex dynamical ... [more ▼]

Current practice in industry is to rely on linear finite element simulations. However, nonlinearity is a frequent occurrence in engineering structures. It is at the origin of rich and complex dynamical phenomena that cannot be observed in linear structures. Solving both the direct and inverse problems in nonlinear structural dynamics therefore warrants the development of appropriate methodologies. The focus of the presentation will first be on the inverse problem. We will describe the different steps of the nonlinear system identification process and discuss the current capabilities of existing methods. The presentation will then address the direct problem during which the identified model is used for accurately predicting the structure’s dynamic characteristics. A rigorous nonlinear extension of modal analysis will be presented, and we will show that it represents a very useful framework for understanding nonlinear dynamical phenomena and supporting design decisions. Two real-life aerospace structures will be considered for illustrating the proposed developments. [less ▲]

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See detailFinite element computation of nonlinear normal modes of nonconservative systems
Renson, Ludovic ULg; Deliège, Geoffrey ULg; Kerschen, Gaëtan ULg

in Proceedings of the ISMA 2012 conference (2012, September)

Modal analysis, i.e., the computation of vibration modes of linear systems, is really quite sophisticated and advanced. Even though modal analysis served, and is still serving, the structural dynamics ... [more ▼]

Modal analysis, i.e., the computation of vibration modes of linear systems, is really quite sophisticated and advanced. Even though 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 modal analysis fails in the presence of nonlinear dynamical phenomena, the development of a practical nonlinear analog of modal analysis is the objective of this research. Progress in this direction has been made recently with the development of numerical techniques (harmonic balance, continuation of periodic solutions) for the computation of nonlinear normal modes (NNMs). Because these methods consider the conservative system, this study targets the computation of NNMs for nonconservative systems, i.e. defined as invariant manifolds in phase space. Specifically, a new finite element technique is proposed to solve the set of partial differential equations governing the manifold geometry. The algorithm is demonstrated using different two-degree-of-freedom systems. [less ▲]

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See detailTransport Methods for the Numerical Computation of Nonlinear Normal Modes
Renson, Ludovic ULg; Blanc, François; Touzé, Cyril et al

Conference (2012, July)

Detailed reference viewed: 17 (5 ULg)