Nonlinear modal analysis of aerospace structures

The dynamic systems theory is well-established for linear systems and can rely on mature tools such as the theories of linear operators and linear integral transforms. This is why
theoretical and experimental modal analysis, i.e., the computation of vibration modes from a
mathematical model and from experimental data, respectively, is really quite sophisticated and
advanced. Even though linear 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 linear modal analysis fails in the presence of nonlinear dynamical phenomena, the development of a practical nonlinear analog of modal analysis would be an extremely timely contribution; it is clearly missing in the structural dynamics literature. A new framework for nonlinear modal analysis of real-world structures, which includes the computation of nonlinear modes from finite element models, is introduced in this paper. This framework will permit a rigorous, yet understandable by the practicing engineer, analysis of nonlinear dynamical phenomena. It will also provide solid theoretical foundations for extending finite element model validation to nonlinear aerospace structures.