Development of an Efficient Stability Analysis Method for a Plate in Uniform Flow by Using Differential Algebraic Equations

This paper addresses an instability problem of a plate in a uniform incompressible and irrotational flow. In particular, this study is aimed at developing a stability analysis method with low computational cost. An analytical dynamics framework for constraint systems is applied to derivation of the fluid force acting on the plate surface. This formulation gives an algebraic relation between the plate displacement and the generalized momentum regarding the velocity potential as a constraint, that is, this relation plays the role of the fluid-structure interaction in the present formulation. Then, the algebraic equation for calculating the fluid force is obtained by a second order time derivative of the constraint. Specifically, the fluid force is given as the Lagrange multiplier, which is introduced for imposing the constraint regarding the fluid-structure interaction mentioned above. The resulting equations are comprised of differential equations regarding the plate displacement and the algebraic equation giving the fluid force. This kind of equations are referred to as the differential algebraic equations. Moreover, derived equations for the fluid-structure interaction are reduced to the eigenvalue problem by employing the generalized Fourier series expansion technique. Then, the stability of this system is evaluated by the eigenvalue analysis. After that, the results are verified by comparing with the results by the previous method.