Nonlinear structural modal model for aeroelastic applications

The paper revisits a novel methodology for analysis of geometrically nonlinear structures by substructuring. In this methodology, the structure is divided into a few substructures. The deformation of each substructure is written in terms of a corotated system that is attached to the substructure, and is expressed through modes computed using the fictitious mass method. 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 corotated 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 nonlinear finite-element software, by using a very small number of segments and modes. These methods are appealing, both because of their computational efficiency when compared to a nonlinear finite-element analysis (due to the use of few substructures, and the modal representation). Moreover, for the second approach, only the knowledge of the modes of the substructures is needed. That is, it overcomes the need of a nonlinear finite element software.