On the mechanical stability and out-of-plane dynamics of a travelling panel submerged in axially flowing ideal fluid : a study into paper production in mathematical terms

Jeronen, Juha On the mechanical stability and out-of-plane dynamics of a travelling panel submerged in axially flowing ideal fluid: a study into paper production in mathematical terms Jyväskylä: University of Jyväskylä, 2011, 243 p. (Jyväskylä Studies in Computing ISSN 1456-5390; 148) ISBN 978-951-39-4595-4 (nid.) ISBN 978-951-39-4596-1 (PDF) Finnish summary Diss. In this study, we consider the dynamical behaviour and stability of a moving panel submerged in two-dimensional potential flow in a papermaking context. The steady-state critical velocity of the system is determined in terms of problem parameters. Dynamical response is predicted via direct temporal simulations, and the eigenfrequency spectrum is analyzed, obtaining both the subcritical free vibration behaviour and the initial postbuckling response. By using an analytical functional solution for the reaction force of the surrounding air, the fluidstructure interaction model is reduced to one integro-differential equation. This makes it possible to work with this fluid-structure interaction problem efficiently with modest computational resources, while improving on the accuracy when compared to the classical technique of added-mass approximation. Discretization is performed by the Fourier–Galerkin method, and results from the numerical computations are visualized. The predictions of the model are successfully validated against existing results. It is found that the model works especially well for long, narrow web spans. To accomodate readers from various technical backgrounds, the topics are reported in a detailed, ground-up manner. After a general introduction, the elastic stability properties of the classical moving string and those of the damped moving string are analyzed in detail as an introduction to this class of problems. Finally, to facilitate eigenfrequency spectrum analysis for the main problem, techniques are developed for overcoming the two main practical challenges: producing continuous curves out of randomly ordered eigenvalue data, and classifying physically meaningful solutions versus numerical artifacts.