Aeroelastic instability of an inverted cantilevered plate with cracks in axial subsonic airflow

Abstract

This paper reports a mathematical modeling and theoretical instability analysis of an inverted cantilevered plate in the effect of both cracks and subsonic axial flow. The plate model is clamped at the trailing edge but free at the other and contains an arbitrary number of all-over part-through cracks. It focuses on an analysis methodology of such a plate aeroelastic instability problem and its convergent numerical solutions. We apply the Possio integral equation for fluids and the fracture mechanics for cracks’ modeling, respectively. We transfer the instability problem into a mathematical function approximation problem in the state-space formulation, avoiding the difficulty of solving the plate slope function directly because of the discontinuities caused by cracks. According to the Stone-Weierstrass theorem, the slope function of the cracked plate is expanded as a linear combination of polynomial functions, including the cracks’ effect. The numerical solution of the plate slope function is finally solved by the least square method. The numerical analysis shows that the critical flow speed significantly decreases as the crack flexible coefficient increases. The change of critical dynamic pressure and instability modes of the cracked plates has been theoretically analyzed and analytically expressed in terms of the crack parameters. The present modeling and analysis strategy has potential applications for investigations of other engineering problems, which can naturally exhibit plate-like systems with inverted configurations and discontinuity.