We present a unified theory of flutter in inviscid and viscous flows interacting with flexible
structures based on the phenomenon of 1 : 1 resonance. We show this by treating four
extreme cases corresponding to viscous and inviscid flows in confined and unconfined
flows. To see the common mechanism clearly, we consider the limit when the frequencies
of the first few elastic modes are closely clustered and small relative to the convective
fluid time scale. This separation of time scales slaves the hydrodynamic force to the
instantaneous elastic displacement and allows us to calculate explicitly the dependence
of the critical flow speed for flutter on the various problem parameters. We show that
the origin of the instability lies in the coincidence of the real frequencies of the first
two modes at a critical flow speed beyond which the frequencies become complex,
thus making the system unstable to oscillations. This critical flow speed depends on
the difference between the frequencies of the first few modes and the nature of the
hydrodynamic coupling between them. Our generalized framework applies to a range
of elastohydrodynamic systems and further extends the Benjamin–Landahl classification
of fluid–elastic instabilities.