Tuning methodology of nonlinear vibration absorbers coupled to nonlinear mechanical systems

in Proceedings of the ASME International Design Engineering Technical Conferences (2011)

A large body of literature exists regarding linear and nonlinear dynamic absorbers, but the vast majority of it deals with linear primary structures. However, nonlinearity is a frequent occurrence in ... [more ▼]

A large body of literature exists regarding linear and nonlinear dynamic absorbers, but the vast majority of it deals with linear primary structures. However, nonlinearity is a frequent occurrence in engineering applications. Therefore, the present paper focuses on the mitigation of vibrations of nonlinear primary systems using nonlinear dynamic absorbers. Because most existing contributions about their design rely on extensive parametric studies, which are computationally demanding, or on analytic methods, which may be limited to small-amplitude motions, this study proposes a tuning procedure which is computationally tractable and can treat strongly nonlinear regimes of motion. The proposed methodology relies on a frequency-energy based approach followed by bifurcation analysis. The results are illustrated using a one-degree-of-freedom primary system, which can, for instance, represent the vibrations of a specific mode of a multi-degree-of-freedom structure. [less ▲]

Modal Analysis of Nonlinear Vibrating Systems: Recent Progress and Challenges, KEYNOTE LECTURE

in Proceeedings of the Eighth European Conference on Structural Dynamics (2011)

Theoretical and experimental modal analysis, i.e., the computation of vibration modes from a mathematical model and from experimental data, respectively, is quite sophisticated and advanced in linear ... [more ▼]

Theoretical and experimental modal analysis, i.e., the computation of vibration modes from a mathematical model and from experimental data, respectively, is quite sophisticated and advanced in linear structural dynamics. However, nonlinearity is a frequent occurrence in real-world engineering structures, and the existing linear methodologies can no longer be used in this context. Therefore, the development of a nonlinear analog of modal analysis would be a timely contribution. Because nonlinear normal modes (NNMs) provide solid mathematical foundations for a rigorous analysis of nonlinear dynamical behaviors, a framework which includes both their computation from finite element models and their identification from experimental data is proposed in this paper. In view of the still limited use of NNMs in structural dynamics, special attention is devoted to develop tools that have the potential to deal with large-scale structures. [less ▲]

Nonlinear normal modes and band zones in granular chains with no precompression

in Nonlinear Dynamics (2011), 63

We study standing waves (nonlinear normal modes—NNMs) and band zones in finite granular chains composed of spherical granular beads in Hertzian contact, with fixed boundary conditions. Although these are ... [more ▼]

We study standing waves (nonlinear normal modes—NNMs) and band zones in finite granular chains composed of spherical granular beads in Hertzian contact, with fixed boundary conditions. Although these are homogeneous dynamical systems in the notation of Rosenberg, we show that the discontinuous nature of the dynamics leads to interesting effects such as separation between beads, NNMs that appear as traveling waves (these are characterized as pseudo-waves), and localization phenomena. In the limit of infinite extent, we study band zones, i.e., pass and stop bands in the frequency–energy plane of these dynamical systems, and classify the essentially nonlinear responses that occur in these bands. Moreover, we show how the topologies of these bands significantly affect the forced dynamics of these granular media subject to narrowband excitations. This work provides a classification of the coherent (regular) intrinsic dynamics of one-dimensional homogeneous granular chains with no pre-compression, and provides a rigorous theoretical foundation for further systematic study of the dynamics of granular systems, e.g., the effects of disorders or clearances, discrete breathers, nonlinear localized modes, and high-frequency scattering by local disorders. Moreover, it contributes toward the design of granular media as shock protectors, and in the passive mitigation of transmission of unwanted disturbances. [less ▲]

CubeSat Activities at the University of Liège

Conference (2011)

Computation of nonlinear normal modes of large structures: application to a full-scale aircraft

in Proceedings of the 7th European Nonlinear Dynamics Conference (ENOC 2011) (2011)

The objective of this paper is to demonstrate that the numerical computation of the nonlinear normal modes (NNMs) of complex real-world structures is now within reach. The application considered in this ... [more ▼]

The objective of this paper is to demonstrate that the numerical computation of the nonlinear normal modes (NNMs) of complex real-world structures is now within reach. The application considered in this study is the airframe of the Morane-Saulnier Paris aircraft, whose ground vibration tests exhibited some nonlinear structural behaviors. The NNMs are computed using a numerical algorithm combining shooting and pseudo-arclength continuation. [less ▲]

Detection and quantification of non-linear structural behavior using principal component analysis

in Mechanical Systems & Signal Processing (2011), 26

The detection of non-linear behavior in structural dynamics is a very important step to the extent that the presence of non-linearities, even local, can affect the global dynamic behavior of a structure ... [more ▼]

The detection of non-linear behavior in structural dynamics is a very important step to the extent that the presence of non-linearities, even local, can affect the global dynamic behavior of a structure. A large number of techniques that enable engineers to detect non-linear behavior can be found in the literature but most of these methods exploit frequency domain data and give better results with a stepped-sine excitation. The goal of this paper is to propose an alternative methodology that is based on the principal component analysis and uses time responses obtained with a random excitation. Two criteria will be used to quantify the difference between two response subspaces, based on the angle between them and the residual error resulting from the projection of one on the other. The concept of limit of linearity and design decision margins is also addressed in this paper. The methodology is demonstrated using an academic simulated system and then using measured data of a simplified solar array system. [less ▲]

Modal testing of nonlinear vibrating structures based on nonlinear normal modes: Experimental demonstration

in Mechanical Systems & Signal Processing (2011), 25

Nonlinear Normal Modes of a Full-Scale Aircraft

in 29th International Modal Analysis Conference, Jacksonville, 2011 (2011)

Model order reduction techniques for thermomechanical systems with nonlinear radiative heat transfer using proper orthogonal decomposition

in Proceedings of ISMA 2010 (2010, September)

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 beam is then extended to incorporate an external box. The nonlinear radiative exchanges between the beam and the external box are analysed and a reduction procedure is proposed for this fully coupled, nonlinear, multiphysical, thermomechanical system. Two alternative approaches to the reduction are investigated, a monolithic scaled approach and a partitioned approach that treats the individual physical modes separately. [less ▲]

Orbital dynamics characteristics of a QB50 CubeSat performing atmospheric reentry

in Proceedings of the AIAA Atmospheric Flight Mechanics Conference (2010)

The QB50 mission has the scientific objective to study the temporal and spatial variations of a number of key parameters in the lower thermosphere with a network of 50 CubeSats, each performing identical ... [more ▼]

The QB50 mission has the scientific objective to study the temporal and spatial variations of a number of key parameters in the lower thermosphere with a network of 50 CubeSats, each performing identical in-situ measurements. One of these 50 CubeSats, the von Karman Institute Atmospheric Re-Entry CubeSat, will further be equipped by a thermal protection system and a dedicated sensor pack to study the atmospheric re-entry. This paper is devoted to the orbital dynamics analysis performed for the QB50 mission and the atmospheric re-entry trajectory analysis for a double unit CubeSat. The main focus is on the sensitivity of the results on atmospheric models, drag coefficient and the launch date. Typical atmospheric re-entry trajectories, including the stagnation point heat flux values are calculated using three different methods for three different scenarios. The predicted heat flux values will be used in the preliminary design of the thermal protection system of the VKI atmospheric re-entry CubeSat, which is to be the first CubeSat to be used as an atmospheric re-entry demonstrator. [less ▲]