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 fail dramatically in the presence of nonlinear dynamical phenomena. Therefore, the present thesis focuses on the development of a practical nonlinear analog of modal analysis for properly accounting for nonlinearity in mechanical systems. The concept of nonlinear normal mode (NNM) provides solid mathematical and theoretical foundations for a rigorous, yet understandable by the practicing engineer, analysis of nonlinear dynamical behaviors. In this context, a useful framework for nonlinear modal analysis of vibrating structures, which includes the computation of NNMs from finite element models and their identification from experimental data, is proposed in this dissertation. In view of the still limited use of NNMs in structural dynamics, special attention is devoted to progress toward a practical tool that has the potential to deal with large-scale, real-world structures. Targeting an effective and exact computation of NNMs, even in strongly nonlinear regimes of motion, one original contribution of this work is to resort to numerical methods. An algorithm combining a shooting procedure and the so-called pseudo-arclength continuation method is developed. On the other hand, a nonlinear extension of phase resonance testing (also known as force appropriation) is introduced for the experimental identification of NNMs, which is another innovative aspect of the doctoral thesis. In particular, the phase lag quadrature criterion, which is used for linear experimental modal analysis, is generalized in the presence of nonlinear dynamical behavior. Academic examples are first considered to illustrate, in a simple manner, that the proposed methods form an effective and adequate framework for nonlinear modal analysis. Furthermore, more realistic structures, including a full-scale aircraft, are studied to demonstrate the potential applicability of the approach to large-scale, real-life applications.

This dissertation deals with dynamics of engineering structures and principally discusses the identification of the modal parameters (i.e., natural frequencies, damping ratios and vibration modes) using output-only information, the excitation sources being considered as unknown and unmeasurable. To solve these kind of problems, a quite large selection of techniques is available in the scientific literature, each of them possessing its own features, advantages and limitations. One common limitation of most of the methods concerns the post-processing procedures that have proved to be delicate and time consuming in some cases, and usually require good users expertise. The constant concern of this work is thus the simplification of the result interpretation in order to minimize the influence of this ungovernable parameter. A new modal parameter estimation approach is developed in this work. The proposed methodology is based on the so-called Blind Source Separation techniques, that aim at reducing large data set to reveal its essential structure. The theoretical developments demonstrate a one-to-one relationship between the so-called mixing matrix and the vibration modes. Two separation algorithms, namely the Independent Component Analysis and the Second-Order Blind Identification, are considered. Their performances are compared, and, due to intrinsic features, one of them is finally identified as more suitable for modal identification problems. For the purpose of comparison, numerous academic case studies are considered to evaluate the influence of parameters such as damping, noise and nondeterministic excitations. Finally, realistic examples dealing with a large number of active modes, typical impact hammer modal testing and operational testing conditions, are studied to demonstrate the applicability of the proposed methodology for practical applications.