Transient Growth Before Coupled-Mode Flutter

Transient growth of energy is known to occur even in stable dynamical systems due to thenon-normality of the underlying linear operator. This has been the object of growingattention in the field of hydrodynamic stability, where linearly stable flows may be foundto be strongly nonlinearly unstable as a consequence of transient growth. We apply theseconcepts to the generic case of coupled-mode flutter, which is a mechanism with importantapplications in the field of fluid-structure interactions. Using numerical and analyticalapproaches on a simple system with two degrees-of-freedom and antisymmetric couplingwe show that the energy of such a system may grow by a factor of more than 10, beforethe threshold of coupled-mode flutter is crossed. This growth is a simple consequence ofthe nonorthogonality of modes arising from the nonconservative forces. These generalresults are then applied to three cases in the field of flow-induced vibrations: (a) panelflutter (two-degrees-of-freedom model, as used by Dowell) (b) follower force (two-degrees-of-freedom model, as used by Bamberger) and (c) fluid-conveying pipes (two-degree-of-freedom model, as used by Benjamin and Pai¨doussis) for different mass ratios.For these three cases we show that the magnitude of transient growth of mechanicalenergy before the onset of coupled-mode flutter is substantial enough to cause a signifi-cant discrepancy between the apparent threshold of instability and the one predicted bylinear stability theory. @DOI: 10.1115/1.1631591#