A theoretical investigation of flow-induced instabilities in compliant coatings

The flow-induced instabilities of a fairly general class of compliant coatings are investigated theoretically. The coatings are of finite length and consist of elastic plates or membranes stretched over a fluid substrate having a density which may be different from the main flow. Provision is also made for the plate to be backed by an elastic foundation of arbitrary spring stiffness. Fairly standard aeroelastic methods are followed. The aerodynamic forces generated by the main flow are calculated by using thin aerofoil theory with a correction factor to allow for the presence of a boundary layer. The pressure induced in the substrate fluid is calculated by assuming potential flow and applying the method of images. A single-mode analysis shows that coatings with laminar boundary layers suffer a divergence-type instability in contrast to turbulent boundary layers which always give rise to a flutter-type instability with a higher critical velocity. The order of the most dangerous mode is calculated and found to rise with an increase in equivalent spring stiffness for fixed tension or flexural rigidity. Results are presented for plates and membrane coatings with an air stream over air and water substrates. Taking account of the substrate fluid dynamics reduces the growth rate of the instability by an order of magnitude and completely suppresses flutter with water substrates. Single-, double- and triple-mode analyses are carried out and the results compared. The critical velocity is adequately predicted by single-mode analysis but a coupling of odd and even modes can lead to flutter even with a laminar boundary layer.