References of "Kerschen, Gaëtan"
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See detailGrey-box identification of a non-linear solar array structure using cubic splines
Noël, Jean-Philippe ULg; Kerschen, Gaëtan ULg; Emmanuel, Foltête 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 ▲]

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See detailProbabilistic Assessment of Lifetime of Low-Earth-Orbit Spacecraft: Uncertainty Propagation and Sensitivity Analysis
Dell'Elce, Lamberto ULg; Kerschen, Gaëtan ULg

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 ▲]

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See detailPractical design of a nonlinear tuned vibration absorber
Grappasonni, Chiara ULg; Habib, Giuseppe ULg; Detroux, Thibaut ULg 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 ▲]

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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 detailEnhancement of ray tracing method for radiative heat transfer: application to EUI space instrument
Jacques, Lionel ULg; Masset, Luc ULg; Kerschen, Gaëtan ULg

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 ▲]

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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 detailStability and bifurcation analysis of a Van der Pol–Duffing oscillator with a nonlinear tuned vibration absorber
Habib, Giuseppe ULg; Kerschen, Gaëtan ULg

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 ▲]

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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 detailEnhancement of ray tracing method for radiative heat transfer with new isocell quasi-monte carlo technique and application to EUI space instrument
Jacques, Lionel ULg; Masset, Luc ULg; Kerschen, Gaëtan ULg

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 ▲]

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See detailRay tracing enhancement for space thermal analysis: isocell method
Jacques, Lionel ULg; Masset, Luc ULg; Kerschen, Gaëtan ULg

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 ▲]

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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 detailProbabilistic Assessment of the Lifetime of Low-Earth-Orbit Spacecraft: Uncertainty Characterization
Dell'Elce, Lamberto ULg; Arnst, Maarten ULg; Kerschen, Gaëtan ULg

in Journal of Guidance Control & Dynamics (2014)

Orbital lifetime estimation is a problem of great timeliness and importance in astrodynamics. In view of the stochastic nature of the thermosphere and of the complexity of drag modeling, any deterministic ... [more ▼]

Orbital lifetime estimation is a problem of great timeliness and importance in astrodynamics. In view of the stochastic nature of the thermosphere and of the complexity of drag modeling, any deterministic assessment of orbital lifetime is likely to be bound to failure. This is why the present paper performs uncertainty quantification of satellite orbital lifetime estimation. Specifically, this paper focuses on the probabilistic characterization of the dominant sources of uncertainty inherent to low-altitude satellites. Uncertainties in the initial state of the satellite and in the atmospheric drag force, as well as uncertainties introduced by modeling limitations associated with atmospheric density models, are considered. Mathematical statistics methods, in conjunction with mechanical modeling considerations, are used to infer the probabilistic characterization of these uncertainties from experimental data and atmospheric density models. This characterization step facilitates the application of uncertainty propagation and sensitivity analysis methods, which in turn allows gaining insight into the impact that these uncertainties have on the orbital lifetime. The proposed developments are illustrated using one CubeSat of the QB50 constellation. [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 detailSubspace and maximum likelihood identification of nonlinear mechanical systems
Noël, Jean-Philippe ULg; Schoukens, Johan; Kerschen, Gaëtan ULg

Conference (2014, March)

The present work focuses on a recent nonlinear generalisation of the existing (linear) frequency-domain, discrete-time subspace methods applicable to mechanical systems. The proposed estimator, termed ... [more ▼]

The present work focuses on a recent nonlinear generalisation of the existing (linear) frequency-domain, discrete-time subspace methods applicable to mechanical systems. The proposed estimator, termed FNSI method, is interesting because it benefits from the numerical robustness and efficacy of subspace algorithms, while maintaining an acceptable computational burden. However, it derives estimates of the model parameters, namely the modal properties of the underlying linear system and the coefficients of the nonlinearities, based on deterministic arguments and one has thus no guarantee that the estimates still behave well in the presence of disturbing noise. A possible alternative is to embed the identification problem in a stochastic framework through the minimisation of a well-chosen cost function incorporating noise information. In particular, the maximum likelihood cost function is attractive because it yields estimates of the model parameters with optimal stochastic properties, and simplifies to a weighted least-squares expression in the frequency domain. However, the maximum likelihood suffers from issues typically encountered in optimisation problems, especially related to initialisation. The contribution of this work lies in the utilisation of the model parameter estimates provided by the FNSI method to serve as starting values for the minimisation of the maximum likelihood cost function. This initialisation strategy possesses the important advantage that the FNSI method generates a fully nonlinear model of the system under test, while classical approaches commonly use a linear model of the nonlinear system as starting point. This ensures that the resulting maximum likelihood model performs at least as good as the nonlinear subspace model. The complete methodology is demonstrated using experimental data measured on the Silverbox benchmark, an electronic circuit emulating the behaviour of a mechanical system with cubic nonlinearity. [less ▲]

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See detailSubspace-based identification of a nonlinear spacecraft in the time and frequency domains
Noël, Jean-Philippe ULg; Marchesiello, Stefano; Kerschen, Gaëtan ULg

in Mechanical Systems & Signal Processing (2014), 43(1-2), 217-236

The objective of the present paper is to address the identification of a strongly nonlinear satellite structure. To this end, two nonlinear subspace identification methods formulated in the time and ... [more ▼]

The objective of the present paper is to address the identification of a strongly nonlinear satellite structure. To this end, two nonlinear subspace identification methods formulated in the time and frequency domains are exploited, referred to as the TNSI and FNSI methods, respectively. The modal parameters of the underlying linear structure and the coefficients of the nonlinearities will be estimated by these two approaches based on periodic random measurements. Their respective merits will also be discussed in terms of both accuracy and computational efficiency and the use of stabilisation diagrams in nonlinear system identification will be introduced. The application of interest is the SmallSat spacecraft developed by EADS-Astrium, which possesses an impact-type nonlinear device consisting of eight mechanical stops limiting the motion of an inertia wheel mounted on an elastomeric interface. This application is challenging for several reasons including the non-smooth nature of the nonlinearities, high modal density and high non-proportional damping. [less ▲]

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See detailA stochastic framework for subspace identification of a strongly nonlinear aerospace structure
Noël, Jean-Philippe ULg; Schoukens, Johan; Kerschen, Gaëtan ULg

in Proceedings of the International Modal Analysis Conference (IMAC) XXXII (2014, February)

The present study exploits the maximum likelihood identification framework for deriving statistically-optimal models of nonlinear mechanical systems. The identification problem is formulated in the ... [more ▼]

The present study exploits the maximum likelihood identification framework for deriving statistically-optimal models of nonlinear mechanical systems. The identification problem is formulated in the frequency domain, and model parameters are calculated by minimising a weighted least-squares cost function. Initial values of the model parameters are obtained by means of a nonlinear subspace algorithm. The complete identification methodology is first demonstrated on a Duffing oscillator, prior to being applied to a full-scale aerospace structure. [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 detailSubspace and nonlinear-normal-modes-based identification of a beam with softening-hardening behaviour
Grappasonni, Chiara ULg; Noël, Jean-Philippe ULg; Kerschen, Gaëtan ULg

in Proceedings of the International Modal Analysis Conference (IMAC) XXXII (2014, February)

The capability to reproduce and predict with high accuracy the behaviour of a real system is a fundamental task of numerical models. In nonlinear structural dynamics, additional parameters compared to ... [more ▼]

The capability to reproduce and predict with high accuracy the behaviour of a real system is a fundamental task of numerical models. In nonlinear structural dynamics, additional parameters compared to classical linear modelling, which include the nonlinear coefficient and the mathematical form of the nonlinearity, need to be identified to bring the numerical predictions in good agreement with the experimental observations. In this context, the present paper presents a method for the identification of an experimental cantilever beam with a geometrically nonlinear thin beam clamped with a prestress, hence giving rise to a softening-hardening nonlinearity. A novel nonlinear subspace identification method formulated in the frequency domain is first exploited to estimate the nonlinear parameters of the real structure together with the underlying linear system directly from the experimental tests. Then a finite element model, built from the estimated parameters, is used to compute the backbone of the first nonlinear normal mode motion. These numerical evaluations are compared to a nonlinear normal modes-based identification of the structure using system responses to stepped sine excitation at different forcing levels. [less ▲]

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See detailClassification of periodic orbits of two-dimensional homogeneous granular crystals with no pre-compression
Detroux, Thibaut ULg; Starosvetsky, Yuli; Kerschen, Gaëtan ULg et al

in Nonlinear Dynamics (2014), 76(April 2014), 673-696

In the present study we classify the periodic orbits of a squarely packed, uncompressed and undamped, homogeneous granular crystal, assuming that all elastic granules oscillate with the same frequency (i ... [more ▼]

In the present study we classify the periodic orbits of a squarely packed, uncompressed and undamped, homogeneous granular crystal, assuming that all elastic granules oscillate with the same frequency (i.e., under condition of 1:1 resonance); this type of Hamiltonian periodic orbits have been labeled as nonlinear normal modes. To this end we formulate an auxiliary system which consists of a two-dimensional, vibro-impact lattice composed of non-uniform “effective particles” oscillating in an anti-phase fashion. The analysis is based on the idea of balancing linear momentum in both horizontal and vertical directions for separate, groups of particles, whereby each such a group is represented by the single effective particle of the auxiliary system. It is important to emphasize that the auxiliary model can be defined for general finite, squarely packed granular crystals composed of n rows and m columns. The auxiliary model is successful in predicting the total number of such periodic orbits, as well as the amplitude ratios for different periodic regimes including strongly localized ones. In fact this methodology enables one to systematically study the generation of mode localization in these strongly nonlinear, highly degenerate dynamical systems. Good correspondence between the results of the theoretical model and direct numerical simulations is observed. The results presented herein can be further extended to study the intrinsic dynamics of the more complex granular materials, such as heterogeneous two-dimensional and three-dimensional granular crystals and multi-layered structures. [less ▲]

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