Static instability analysis for travelling membranes and plates interacting with axially moving ideal fluid
Banichuk, N., Jeronen, J., Neittaanmäki, P., & Tuovinen, T. (2009). Static instability analysis for travelling membranes and plates interacting with axially moving ideal fluid. Journal of Fluids and Structures, 26 (2), 274-291. doi:10.1016/j.jfluidstructs.2009.09.006
Published inJournal of Fluids and Structures
© Elsevier. This is an author's final draft version of an article whose final and definitive version has been published by Elsevier.
The out-of-plane instability of a moving plate, travelling between two rollers with constant velocity, is studied, taking into account the mutual interaction between the buckled plate and the surrounding, axially flowing ideal fluid. Transverse displacement of the buckled plate (assumed cylindrical) is described by an integro-differential equation that includes the centrifugal force, the aerodynamic reaction of the external medium, the vertical projection of membrane tension, and the bending force. The aerodynamic reaction is found analytically as a functional of the displacement. To find the critical divergence velocity of the moving plate and its corresponding buckling mode, an eigenvalue problem and variational principle are derived. Plate divergence, both within a vacuum and when submerged in an external medium, is investigated with the application of analytical and numerical techniques.