Bridging the Gap Between Nonlinear Normal Modes and Modal Derivatives [chapter]

Cees Sombroek, Ludovic Renson, Paolo Tiso, Gaetan Kerschen
2016 Nonlinear Dynamics, Volume 1  
General rights This document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: Abstract Nonlinear Normal Modes (NNMs) have a clear conceptual relation to the classical linear normal modes (LNMs), yet they offer a solid theoretical framework for interpreting a wide class of non-linear dynamical phenomena with no linear counterpart. The main difficulty associated with NNMs is that their
more » ... is that their calculation for largescale models is expensive, particularly for distributed nonlinearities. Repeated direct time integrations need to be carried out together with extensive sensitivity analysis to reproduce the frequency-energy dependence of the modes of interest. In the present paper, NNMs are computed from a reduced model obtained using a quadratic transformation comprising LNMs and Modal Derivatives (MDs). Previous studies have shown that MDs can capture the essential dynamics of geometrically nonlinear structures and can greatly reduce the computational cost of time integration. A direct comparison with the NNMs computed from another standard reduction technique highlights the capability of the proposed reduction method to capture the essential nonlinear phenomena. The methodology is demonstrated using simple examples with 2 and 4 degrees of freedom.
doi:10.1007/978-3-319-15221-9_32 fatcat:z5sxxayeyjc5rhueawxo3w7ou4