Nonlinear Normal Modes of Nonconservative Systems

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 ▲]

Finite element computation of nonlinear normal modes of nonconservative systems

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 ▲]

Nonlinear Modal Analysis of the SmallSat Spacecraft

in Proceedings of the European Conference on Spacecraft Structures, Materials & Environmental Testing (2012, March)

Non-linear elements are present in practically all spacecraft structures. When such non-linear effects are important linear modal analysis can no longer be applied. The development of a non-linear ... [more ▼]

Non-linear elements are present in practically all spacecraft structures. When such non-linear effects are important linear modal analysis can no longer be applied. The development of a non-linear analogue of linear modal analysis is therefore an important endeavor. The objective of this paper is to show that nonlinear normal modes (NNMs) represent a useful and practical tool in this context. A full-scale spacecraft structure is considered and is modeled using the finite element method. Its NNMs are computed using advanced numerical algorithms, and the resulting dynamics is then carefully analyzed. Nonlinear phenomena with no linear counterpart including nonlinear modal interactions are also highlighted. [less ▲]

Identifying and computing nonlinear normal modes

in Proceedings of the SEM IMAC XXX Conference (2012, February)

Non linear normal modes offer a rigorous framework, both mathematical and physical, for theoretical and experimental dynamical analysis. Albeit still in its infancy, the concept of non linear normal modes ... [more ▼]

Non linear normal modes offer a rigorous framework, both mathematical and physical, for theoretical and experimental dynamical analysis. Albeit still in its infancy, the concept of non linear normal modes has the potential of providing to both the academic and the industrial establishment a powerful tool for the analysis of non linear dynamical systems. However, in order to exploit the full potential of this theory (and its associated simulation capability), there is need to integrate it with other branches of non linear structural dynamics: namely, in order for the non linear normal modes of a real - physical - structure to be computed, there is need to identify and quantify its non linearity. In this paper, an identification method based on the measured Frequency Response Function (FRF) is employed to identify and quantify the system's non linearity before computing the system's non linear normal modes. [less ▲]

Contract 21539/08/NL/SFe - Advancement of mechanical verification methods for non-linear spacecraft: Modal analysis using nonlinear normal modes.

Report (2012)

The objective of this technical note is to explore the applicability of nonlinear modal analysis to spacecraft structures. To this end, algorithms for the continuation of periodic solutions are applied to ... [more ▼]

The objective of this technical note is to explore the applicability of nonlinear modal analysis to spacecraft structures. To this end, algorithms for the continuation of periodic solutions are applied to the finite element model of the SmallSat spacecraft. Nonlinear normal modes and their corresponding frequencies of oscillation are computed, and the results are discussed. [less ▲]

Nonlinear modal analysis of the SmallSat spacecraft

in Proceedings of the SEM IMAC XXX Conference (2012)

Non-linear elements are present in practically all spacecraft structures. The assumption of a (quasi-)linear structure is nevertheless adequate for structural analyses and design verification purposes in ... [more ▼]

Non-linear elements are present in practically all spacecraft structures. The assumption of a (quasi-)linear structure is nevertheless adequate for structural analyses and design verification purposes in those cases where these structural non-linearities are relatively weak or not substantially activated by the mechanical environments encountered during the launch or during ground testing. However, when significant non-linear effects in spacecraft structures are no longer negligible then linear modal analysis will not be able to handle non-linear dynamical phenomena in an adequate manner: the development of a non-linear analogue of linear modal analysis becomes an urgent and important issue. The objective of this paper is to show that nonlinear normal modes (NNMs) represent a useful and practical tool in this context. A full-scale spacecraft structure is considered and is modeled using the finite element method. Its NNMs are computed using advanced numerical algorithms, and the resulting dynamics is then carefully analyzed. Nonlinear phenomena with no linear counterpart including nonlinear modal interactions are also highlighted. [less ▲]

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 ▲]