Geometrically non-linear structural modal model for aeroelastic applications

The paper reviews a novel methodology for analysis of geometrically non-linear structures by substructuring that was recently presented by Bern-hammer at al. [13]. In this methodology, the structure is divided into a few substructures. The deformations of each substructure are composed of rigid body and elastic deformations, where the latter are described by modes. Modes of the substructures are computed using the fictitious mass method. The method is appealing, both because of its computational efficiency when compared to a nonlinear finite-element analysis (due to the use of few substructures, and the modal representation), and because it only requires knowledge of the modes of the substructures. That is, it over-comes the need of a nonlinear finite element software. The current study examines the intricacy related to the use of modal representation in cases of finite rigid body rotations, and proposes mathematical formulation of two approaches that overcome the related issues. The first approach uses modes to represent the whole displacement, while in the second approach modes are used to represent the displacements about a co-rotated system attached to the substructure. The two approaches are examined using a test case of a beam subjected to a large follower and non-follower tip forces. Both approaches yield excellent results compared with a solution by a nonlin-ear finite-element software, by using a very small number of segments and modes.