Optimization of cascade blade mistuning. I — Equations of motion andbasic inherent properties

The present work is divided into two main parts. Part I deals with the derivation of the equations of motion of mistuned compressor blades, where the aerodynamic coefficients are interpolated using quadratic expressions in the reduced frequency. It is shown that if the coefficients of the quadratic expressions are permitted to assume complex values, excellent accuracy is obtained, so that Fade rational expressions are not required (thus avoiding augmented states). Based on the resulting equations, it is analytically shown that the sum of all the real parts of the eigenvalues is independent of the mistuning introduced into the system. The problem of blade mistuning is further tackled using the aerodynamic energy approach, and the limiting vibration modes associated with purely alternate mistunings are identified. In Part II the aerodynamic energy approach is used to identify analytically the optimum mistunings together with their associated vibration modes. Numerical optimization of mistuning is employed and the existence of multiple optimum mistuning vectors is shown to exist. Part II also shows that any bending-torsion compressor blade system can be reduced to an equivalent purely torsional system of blades.