Since linear modal analysis fails in the presence of nonlinear dynamical phenomena, the concept of nonlinear normal modes (NNMs) was introduced with the aim of providing a rigorous generalization of linear normal modes to nonlinear systems. Initially defined as periodic solutions, numerical techniques such as the continuation of periodic solutions were used to compute 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, the partial differential equations governing the manifold geometry are considered as transport equations and an adequate finite element technique is proposed to solve them. The method is first demonstrated on a conservative nonlinear beam and the results are compared to standard continuation techniques. Then, linear damping is introduced in the system and the applicability of the method is demonstrated.
|Title of host publication||9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control|
|Publisher||American Society of Mechanical Engineers (ASME)|
|Publication status||Published - 2013|
|Event||ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2013 - Portland, OR, United States|
Duration: 4 Aug 2013 → 7 Aug 2013
|Conference||ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2013|
|Period||4/08/13 → 7/08/13|