Nonlinear normal modes (NNMs) offer a solid theoretical framework for interpreting a wide class of nonlinear dynamic phenomena. However, the computation of NNMs for large-scale models can be time consuming, particularly when nonlinearities are distributed across the degrees of freedom. In this paper, the NNMs of systems featuring distributed geometric nonlinearities are computed from reduced-order models comprising linear normal modes and modal derivatives. Modal derivatives stem from the differentiation of the eigenvalue problem associated with the underlying linearised vibrations and can therefore account for some of the distortions introduced by nonlinearity. The cases of the Roorda's frame model, a doubly-clamped beam, and a shallow arch discretised with planar beam finite elements are investigated. A comparison between the NNMs computed from the full and reduced-order models highlights the capability of the reduction method to capture the essential nonlinear phenomena, including low-order modal interactions.

General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. AbstractNonlinear 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 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.