Cascade Flutter Analysis of Cantilevered Blades

Abstract

An analysis has been developed to treat the aeroelastic behavior of a cascade of cantilevered blades. The unique features of the formulation include consideration of (a) coupling between bending and torsion in each of the blade modes, (b) coupling among blade modes, (c) spanwise variation of blade mode shapes, (d) mechanical damping in each mode, (e) aerodynamic coupling among all blades of the assembly, and (f) mistuning. The methodology leads to a complex eigenvalue problem of the form [A (λ)] {x} = λ {x} the solution of which establishes the nature of stability and determines the flutter modes of vibration. A parametric study is made to examine the influence on flutter of (a) the strength of coupling between bending and torsion, (b) proximity of modal frequencies, (c) mass ratio, and (d) mistuning. Numerical results presented here are restricted to a twelve bladed system coupled aerodynamically. The flow conditions are assumed to be subsonic but the formulation of the problem and the organization of the computer program are such that other conditions can easily be considered in computation. The extension of the analysis to include mechanical coupling between the blades (through either shrouds or disk) is shown to be straightforward.