Static aeroelastic instability analysis of an inverted plate in ground effect and comparison with a wind-tunnel test. (January 2023) - Li, Peng; Zhang, Dechun; Peng, Wei; Cui, Junzhe; Yang, Yiren
Abstract: This paper visits the static instability of an inverted cantilevered plate in axial flow with the ground effect. This plate model is clamped at the trailing edge, and its leading-edge is allowed to move freely. A theoretical analysis strategy and corresponding convergent numerical solutions are reported and compared with a wind-tunnel experiment. In theory, we try a new way to study such an instability problem. We derive the instability equation by operator theory in state-space formulation and model such an instability problem as a mathematical function approximation problem. Glauert's expansion and the least square method are applied for the numerical solutions of vorticity in ground effect using the mirror image method. The unknown function of the plate slope is expanded as a series of essential polynomial functions based on the Weierstrass theorem, and the least square method is applied for its numerical solutions. The experimental study develops a multi-point contact method using a control rod to preload the tested plate with a slight static deformation close to its natural modal shape. The contact state change between the initially deformed tested plate and the control rod is reflected by the evolution of the voltage output of a designed circuit. A criterion for determining the critical condition of plate instability is established based on such voltage change, and it has a better anti-interference ability to the flow. Results show that the present theoretical analysis agrees well with the experiment and other archived theories. The critical plate slopes (i.e., the plate instability modes) are not dependent on the ground confinement. This conclusion allows us to establish an analytical approximation between the critical dynamic pressure and the ground confinement. The present study and results can successfully predict the plate instability in the ground effect. Highlights: An instability analysis strategy and its convergent numerical solution is proposed. Least square method applies for instability solution, a function approximation problem. An improved test method is developed for plate instability test in a wind tunnel. A five-second scaling law of the plate instability boundary is explored.