Hydroelastic stability of an inhomogeneous flexible panel in a uniform mean flow

Abstract

A state-space model, based upon computational modelling, is used to investigate the aero-/hydro-elastic stability of a flexible panel. The system studied is two-dimensional although the concepts presented can readily be extended to three dimensions. We solve the boundary-value problem to determine the long-time response and investigate the effects of adding localised structural inhomogeneity on linear stability. We also study the system response to an initial applied excitation. The Laplace equation for the perturbation-velocity potential is solved using a boundary-element method fully coupled to a finite-difference representation of classical thin-plate mechanics. Thus, the modelling omits viscous effects in the fluid but remains appropriate to the high-Reynolds flows typical in engineering applications. A single system equation is derived in terms of the interfacial deflection and its time derivatives that is then cast in time-invariant state-space form. The FSI system eigenmodes are then extracted to predict the behaviour of the system. In particular we identify the critical flow speed at which the panel becomes unstable. We then modify the structural side of the equation to permit the incorporation of structural inhomogeneity.Results presented in this paper show how localised inhomogeneity can be used to postpone the instability-onset flow speeds of simple flexible panels with its focus on the combination of location and magnitude of the stiffening that best achieves these gains.