An improvement to the quasi-steady model with application to cross-flow-induced vibration of tube arrays

A generalization of the quasi-steady theory is proposed, the aim of which is to model the most important unsteady effects neglected by the conventional quasi-steady assumption. Although this generalized model, referred to as the quasi-unsteady model, can be applied in a vast range of flow-induced vibration problems, including classical aeroelasticity, it was primarily developed to improve the theoretical prediction of the fluidelastic behaviour of a single flexible cylinder positioned in the midst of an array of rigid cylinders. In this context, it is shown that the previous improvement to the quasi-steady theory proposed by Price & Païdoussis can be considered as a particular case of the quasi-unsteady model. Results obtained with the quasi-unsteady model are compared to experimental data and to solutions from the Price & Païdoussis model; both modal parameter variation with flow velocity and stability diagrams are considered. This comparison shows that the quasi-unsteady model is a clear improvement on Price & Païdoussis’ approach, leading to a more reasonable agreement with experimental results and providing refined insights into the physical mechanisms responsible for fluidelastic instability.