Abstract
The paper considers the analysis of a traveling panel, submerged in axially flowing fluid. In order to accurately model the dynamics and stability of a lightweight moving material, the interaction between the material and the surrounding air must be taken into account. The lightweight material leads to the inertial contribution of the surrounding air to the acceleration of the panel becoming significant. This formulation is novel and the case complements our previous studies on the field. The approach described in this paper allows for an efficient semi-analytical solution, where the reaction pressure of the fluid flow is analytically represented by an added-mass model in terms of the panel displacement. Then, the panel displacement, accounting also for the fluid–structure interaction, is analyzed with the help of the weak form of the governing partial differential equation, using a Galerkin method. In the first part of this paper, we represent the traveling panel by a single partial differential equation in weak form, using an added-mass approximation of the exact fluid reaction. In the second part, we apply a Galerkin method for dynamic stability analysis of the panel, and present an analytical investigation of static stability loss (divergence, buckling) based on the added-mass model.
Highlights
In this study, we develop a mathematical model representing the behavior of an open draw in the paper making process, taking into account the effects of fluid–structure interaction and of thermal expansion of the material
In order to accurately model the dynamics and stability of a lightweight moving material, the interaction between the material and the surrounding air must be taken into account
The approach described in this paper allows for an efficient semi-analytical solution, where the reaction pressure of the fluid flow is analytically represented by an added-mass model in terms of the panel displacement
Summary
We develop a mathematical model representing the behavior of an open draw in the paper making process, taking into account the effects of fluid–structure interaction and of thermal expansion of the material. We formulate the dynamic aerothermomechanical problem for an axially moving panel, interacting with potential flow and subject to thermal expansion. This formulation is novel and the case complements our previous studies on the field. The travelling panel is interacting with a two-dimensional model of fluid moving in axial and normal (transverse) directions These assumptions give us the possibilities to apply complex variable techniques for finding analytical solutions of a two-dimensional hydrodynamical (plane) problem with arbitrary distribution of elastic deflections w(x, t). Even if the bending rigidity slightly varies due to the temperature dependence of the Young’s modulus, it will not have a major effect on the critical velocity predicted by the model
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