The effect of nonlinear cross-coupling on reduced-order modelling

The use of reduced-order models (ROMs) for nonlinear systems has received significant attention due to their potential to greatly reduce computational cost, compared to full nonlinear finite-element models. Here, we consider and compare two indirect methods; the applied modal force and enforced modal displacement techniques, paying particular attention to the effect of nonlinear cross-coupling terms. The analysis we present shows that the applied modal force technique is able to account for some effects arising from modes that are not retained in the ROMs, but the resulting accuracy of the ROM depends on the amplitudes selected for the set of forces used to estimate the coefficients of the ROMs. This analysis also shows that the enforced modal displacement technique does not compensate for the effect of modal interactions with modes that are not included in the ROM, but its accuracy is independent of the amplitude of the forces used to estimate the coefficients. The mechanisms that lead to the differences between these techniques is firstly demonstrated using a two conceptually-simple, discrete systems, before a nonlinear beam model is considered