Finite element computation of nonlinear normal modes of nonconservative systems

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.