Analytical criterion of a multimodal snap-through flutter of thin-walled panels with initial imperfections

Abstract

This work deals with snap-through flutter dynamics of thin-walled shallow panels accompanied by flexural mode transitions assuming cylindrical bending conditions. The problem is therefore multimodal and, in addition, essentially non-local due to the presence of multiple equilibrium positions. The corresponding analysis is based on the asymptotic of a perfectly flexible panel with a continuous manifold of equilibrium configurations. It is assumed that trajectories of the snap-through dynamics are close to such a manifold, which is interpreted as a family of generating solutions. It is shown that the two-mode approximation depicts major physical specifics of the snap-through process, whereas higher modes can be reasonably treated as a perturbation. As a main result of the analysis, the analytical estimate for the critical speed of airflow leading to the cyclical snap-through flutter is derived.