Finite element analysis of aero-hydroelastic stability of arbitrary shape panels

Abstract

A fluid-structure model based on Mindlin-Reissner plate theory and linearized incompressible potential flow theory is used to study the aero-hydroelastic stability of panels of arbitrary planforms. A finite-element procedure is developed to reduce the continuous system to a finite flow-structure system, which is solved in the frequency domain. The finite element method is crucial for the study of panels of arbitrary geometry and circumvents difficulties with the assumed mode shape approach. This paper is the first finite-element formulation of a fully coupled fluid-structure model of the aero-hydroelastic panel stability problem for incompressible flow. Circular, square, and triangular panels surrounded by a rigid baffle with different boundary conditions are studied. Eigenvalues of the system are surveyed as a function of the hydrodynamic loading at high and low density ratios. Critical flow velocity at divergence-onset and modal coalescence divergence or flutter are determined and compared for the three planforms. For simply supported or clamped panels of equal area and flexural rigidity, as the fluid velocity increases from zero the circular panel diverges first then the square and equilateral triangle, the later is the most stable. In order to compare the relative stability of the three geometries considered, a velocity ratio that consolidates divergence and flutter conditions for the three panels is introduced. Such a parameter offers a simple formula for the divergence velocity in terms of the panel geometry and flow and material properties, and is very useful to the designer in a wide range of engineering applications.