Discussion on “A non-intrusive model-order reduction of geometrically nonlinear structural dynamics using modal derivatives”

This note is a short discussion of the paper “A Non-Intrusive Model-Order Reduction of Geometrically Nonlinear Structural Dynamics Using Modal Derivatives” in which reduced order models (ROMs) of the dynamic response of structures in the nonlinear geometric regime are constructed. The paper proposes modal derivatives to complement the linear modes for the representation of the structural displacements and compares the corresponding predictions obtained for 3 simple structures to those obtained with the linear modes + dual modes basis initially published about a decade ago. The predictions obtained with the latter bases are shown in the paper to be rather poor in contradiction with the many successful applications of this methodology in the literature. It is shown here that the issue stems in the paper from truncating too early the proper orthogonal decomposition (POD), i.e., taking too few eigenvectors in the dual mode construction. When the POD approximation is conducted normally to convergence, it is found that the ROMs with linear modes + dual modes bases lead to very good predictions of the dynamic response. In fact, this good accuracy is seen to be maintained even when the response level is much larger than the examples shown in the paper.