Component-Centric Reduced Order Modeling of the Dynamic Response of Linear Multibay Structures

Abstract

Component-centric reduced order models (ROMs) are introduced here as small-size ROMs providing an accurate prediction of the linear response of part of a structure (the β component) without focusing on the rest of it (the α component). Craig–Bampton (CB) substructuring methods are first considered. In one method, the β component response is modeled with its fixed interface modes while the other adopts singular value eigenvectors of the β component deflections of the linear modes of the entire structure. The deflections in the α component induced by harmonic motions of these β component modes are processed by a proper orthogonal decomposition (POD) to model the α component response. A third approach starts from the linear modes of the entire structure which are dominant in the β component response. Then, the contributions of other modes in this part of the structure are approximated in terms of those of the dominant modes with close natural frequencies and similar mode shapes in the β component, i.e., these nondominant modal contributions are “lumped” onto dominant ones. This lumping permits to increase the accuracy in the β component at a fixed number of modes. The three approaches are assessed on a structural finite element model of a nine-bay panel with the modal lumping-based method yielding the most “compact” ROMs. Finally, good robustness of the ROM to changes in the β component properties (e.g., for design optimization) is demonstrated and a similar sensitivity analysis is carried out with respect to the loading under which the ROM is constructed.