Abstract
This note is a short discussion of the paper “A NonIntrusive ModelOrder 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.
Original language  English (US) 

Article number  107638 
Journal  Mechanical Systems and Signal Processing 
Volume  159 
DOIs 

State  Published  Oct 2021 
Keywords
 Basis construction
 Dual modes
 Nonlinear geometric response
 Reduced order modeling
 Structural dynamics
ASJC Scopus subject areas
 Control and Systems Engineering
 Signal Processing
 Civil and Structural Engineering
 Aerospace Engineering
 Mechanical Engineering
 Computer Science Applications