Static aeroelastic instability of an inverted cantilevered plate in inviscid channel flow

Abstract

The static aeroelastic instability of an inverted cantilevered plate confined inside a two-dimensional channel is examined in this paper. In our present study, the inverted plate, in contrast to the typical one with a fixed leading edge and a free trailing edge, is clamped at the trailing edge but free at the leading edge. The airflow in the channel is assumed inviscid, low-speed, and potential. A theoretical analysis strategy for instability within differential operators and convergent numerical solutions is proposed. The fluid solution has been presented as a Possio integral equation, a composite operator involving the Hilbert and Tricomi operators. We derive the instability equation by operator theory in state–space formulation and model such an instability problem as a mathematical function approximation problem. The least-square method assesses its numerical solutions with the help of the Weierstrass theorem. Compared with the other results, the present way successfully predicts the divergence instability of the inverted cantilevered plate in a confined channel flow. Numerical results show that the channel confinement plays a destabilizing effect, and the critical flow velocity significantly decreases as it is increased. Asymmetric plate placement in the channel also leads to a significant decrease in the critical flow velocity. The critical plate slopes, i.e., the plate instability modes, are not dependent on the channel parameters, and their values at the leading edge remain constant. Further theoretical exploration allows a semi-analytical approximation of the instability boundary.