Reduction and coupling of substructures via Gram–Schmidt Interface modes

Abstract

The paper presents a novel reduction method in the class of component mode synthesis techniques. The method is here called Gram–Schmidt Interface (GSI), since it is based on the Gram–Schmidt algorithm. The GSI reduction method addresses problems where the Craig–Bampton reduced order model of a substructure has still a large number of interface degrees of freedom that should be further reduced. Starting from the pre-existing reduction method based on the Characteristic Constraint Modes, the GSI technique goes further, being suitable to reduce a Craig–Bampton model that retains as a master a wide variety of boundary DoFs (interface, active, etc.). The GSI method is here proved to be effective when assembling adjacent substructures having non-compatible meshes at the interfaces. This is possible by performing the interfaces coupling in the modal space of the GSI modes instead in the space of physical degrees of freedom. The technique is here applied to a turbomachinery test case consisting of a blade coupled with a disk’s sector treated in cyclic symmetry conditions. It is also demonstrated how the GSI method appears useful in the reduction of cyclic symmetric structures, representing a valid alternative of the method developed by Tran.