A THEORETICAL AND EXPERIMENTAL STUDY ON THE STATIC AERO-ELASTIC INSTABILITY OF AN INVERTED CANTILEVERED PLATE IN A CONFINED SUBSONIC FLOW

The plate and shell structures have been widely used in many engineering areas such as aerospace, high-speed trains and energy harvesting. An inverted cantilever plate in an axial airflow confined by a rigid wall has the adjustable critical airflow velocity and is one of the most important ways for the optimization of energy harvesters. However, the mechanism of instability of inverted cantilever plates in rigid wall effect still needs further studies. This paper aims at the static aero-elastic instability of an inverted cantilevered plate in a confined subsonic flow, and such problem is studied by both the theoretical and the experiment analysis. In theory, first the effect of rigid wall is modelled by using the mirror image function and the fluid force on the plate is presented as a Possio integral equation within the frame work of differential operators, and the wall effect is featured by a composite operator involving the shifted Tricomi operator; then the solution of the instability equation is changed into the problem of approximation of function at a given interval; and finally the optimal solution is obtained by using the least square method with the help of the Wererstrass theorem. In experimental analysis, a test method for the static instability of the plate developed from the theory of column is applied for the wind tunnel test. The theoretical results show that the plate experiences the static aero-elastic instability; the critical dynamic pressure increases with the the increasing spacing between the wall and the plate but finally becomes steady (the case without rigid wall). A comparison of the present theoretical results with other existing theory and the experiment shows that the present theory is reliable and accurate. In this paper, the instability problem, which is not solved with the discretization of partial differential equation and by the eigenvalue analysis, has been transformed into the problem of approximation of function, and this can serve as another new thinking way to the problem of static aero-elastic instability of plates.