Risks of Linear Design of Joined Wings: a Nonlinear Dynamic Perspective in the Presence of Follower Forces

TL;DR: In this article, a post-critical analysis of a joined-wing system is presented, showing that even if the design is well below the critical point (snapbuckling state) and the response appears to be quasi linear, there is a potential risk that a dynamic disturbance (perturbation) may move the system to a relatively far equilibrium state on a postcritical branch.

Abstract: Past work on Joined Wings pointed out the importance of including structural geometric nonlinearities since the early stages of the design. However, the attention was mainly focused on conservative loadings and several open questions needed an answer. In a effort to simulate aerodynamic-pressure-like loads, this effort focuses on non-conservative follower forces. Several numerical evaluations demonstrated that follower loadings exacerbate the risks of snap-instability in Joined Wings. Dynamic response analysis of vanishing perturbations showed that for certain combination of geometry and stiffness distributions, the phenomenon of branch-jumping is possible. This is directly linked to the existence of a bi-stable region. The presence of follower loads increases these risks with respect to conservative forces. For some configurations, a small change of a parameter (e.g. the lower-to-upper-wing bending stiffness ratio) can produce a sudden appearance of a bi-stable region and the risk of branch jumping becomes serious. This paper demonstrates that even if the design of a joined-wing system is well below the critical point (snap-buckling state) and the response appears to be quasi linear, there is a potential risk that a dynamic disturbance (perturbation) may move the system to a relatively far equilibrium state on a post-critical branch. Thus, a post-critical analysis need to be included even if a linear design point for the Joined Wing is sought. Results of this effort suggest that preliminary multidisciplinary optimizations technique can not confidently rely on linear analyses augmented with eigenvalue instability investigations. On the contrary, a post-critical study is strongly recommended for a safe design of innovative wing configurations based on the joined-wing concept.