A New Method for Determining the Eigenmodes of Finite Flow-Structure Systems

Abstract

A new method for directly determining the eigenmodes of finite flow-structure systems is presented, using the classical problem of the interaction of a uniform flow with a flexible panel, held at both ends, as an exemplar. The method is a hybrid of theoretical analysis and computational modelling. This new approach is contrasted with the standard Galerkin method that is most often used to study the hydro-elasticity of finite systems. Unlike the Galerkin method, the new method does not require an a priori approximation of perturbations via a finite sum of modes. Instead, the coupled equations for the wall-flow system are cast, using computational methods that, in this exemplar, combine boundary-element and finite-element methods, to yield a single matrix equation for the system that is a second-order differential equation for the panel-displacement variable. Standard state-space methods are then used to extract the eigenmodes of the system directly. We present definitive results for the stability of the case of an unsupported flexible plate, elucidating its divergence and flutter characteristics, and the effect of energy dissipation in the structure. Finally, we present some results for the case of a spring-backed flexible plate that illustrate the complicated dynamics of this type of wall; these dynamics would be poorly modelled by a traditional Galerkin method.

The cascade structure of linear instability in collapsible channel flows

“…And then at a slightly higher flow velocity, the system loses stability to second-mode flutter; this is followed by third-mode flutter at a still higher velocity. A similar finding is discovered in a one-dimensional softpalate model of snoring (Lucey & Pitman 2006;Tetlow, Lucey & Balint 2006), and for a tensioned-riser in the sea (Bearman & Huarte 2006), although in the latter, mode switching in vortex-induced vibration is related to a Strouhal frequency in the excitation, and the mechanism may be very different from what is discussed here.…”