A Conceptual Flutter Analysis of a Packet of Vanes Using a Mass-Spring Model

The linear aeroelastic stability of a simplified mass-spring model representing the basic dynamics of a packet of $Na$ airfoils has been used to uncover a new type of coupled mode flutter. This simple model retains an essential dynamical feature of the vane packet: the presence of a cluster of $Na−1$ nearly identical purely structural natural frequencies due to the much larger stiffness of the lower platform as compared to that of the airfoil. Using this model it may be seen that this degeneracy makes the $Na−1$ associated mode shapes extremely sensible to the addition of small perturbations such as the aerodynamic forces. Since the determination of the aerodynamic vibrational correction (damping and frequency) requires knowing the mode shape, the aerodynamic corrections of the $Na−1$ cluster modes are now unavoidably coupled together. Moreover, the computation of the aerodynamic correction independently for each structural mode shape leads typically to dangerously overpredicting the stabilizing effect of vane packing. It is shown that the expected stabilizing effect due to the packets may be negligible, depending on the relative frequency split associated with the strength of the aerodynamic forces and realistic structural effects such as the finite stiffness of the lower platform. It is also shown that in these cases, the most unstable mode may be, in a first approximation, very similar to that obtained modeling the stator as a continuous ring.