Instability and its prediction of an inverted inhomogeneous plate loaded by a subsonic airflow: Theory and experiment

Abstract

This paper presents a study on the instability of an inverted cantilevered plate with an inhomogeneous cross-section in axial flow from both theory and experiment. The plate is free at the leading edge and clamped at the trailing one. It has a cross-section with discontinuity, bringing difficulty in solving the fluid–structure interaction equation by the traditional methods. We study this problem in state space and transfer its solution into a function approximation problem. We bring no approximation at the first equation level, and the derived instability equation is on the continuum. A numerical scheme is proposed to solve the instability equation. Series expansion and least square method apply to the numerical solutions. The convergence and reliability of the present method are entirely tested. This present modeling method preserves the original information of the problem and facilitates the exploration of the effects of inhomogeneity. Based on the present continuum instability equation, prediction formulas for critical dynamic pressure and instability slope of an inhomogeneous plate are first given and verified. They can apply to the stability prediction of arbitrary cross-sectional plates and have application potential for the plate design. In addition, we report an optimized stiffness distribution of the plate for the maximum critical dynamic pressure. Finally, a wind tunnel test is designed and implemented. A comparative study shows that the present method and prediction formula agree well with the experiment. The present modeling method for a fluid–structure interaction problem in a continuous sense, avoiding approximation at the beginning level, can serve as another new way to address the static instability problem of plates.