  A variety of models describing the interaction between flows and oscillating
structures are discussed. The main aim is to analyze conditions under which
structural instability (flutter) induced by a fluid flow can be suppressed or
eliminated. The analysis provided focuses on effects brought about by: (i)
different plate and fluid boundary conditions, (ii) various regimes for flow
velocities: subsonic, transonic, or supersonic, (iii) different modeling of the
structure which may or may not account for in-plane accelerations (full von
Karman system), (iv) viscous effects, (v) an assortment of models related to
piston-theoretic model reductions, and (iv) considerations of axial flows (in
contrast to so called normal flows). The discussion below is based on
conclusions reached via a combination of rigorous PDE analysis, numerical
computations, and experimental trials.
