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An investigation of the fundamental aspects of flutter in mistuned turbomachinery rotors is presented. Perturbation methods are used to obtain asymptotic solutions to arbitrary order in the mistuning parameter. These solutions require only the knowledge of the eigensolution of the tuned system, and thus provide efficient formulas for calculating the effect of mistuning without solving a new eigenvalue problem. Numerical results presented for design parameters representative of fan rotors indicate that a critical reduced frequency exists, below which mistuning alone cannot stabilize the rotor. The sensitivity of the stability boundaries to mistuning was found to depend fundamentally on relations between the left and right eigenvectors. For systems where the left and right eigenvectors form complex conjugate pairs, mistuning cannot destabilize the system unless the reduced frequency of the least stable mode is decreased by the perturbation. In general, only cascades and rotors with a single degree-of-freedom per blade belong to this class.

In the present paper, we introduce a novel computational method for aeroelastic stability and structural response calculations. The entire fluid-structure system is treated as one continuum dynamics problem, by using a mixed Eulerian-Lagrangian formulation and switching from an Eulerian to a Lagrangian description at the fluidstructure boundary. This method has two important advantages. First, it effectively eliminates the phase integration errors associated with previous methods, where the fluid and the structure are integrated sequentially by different schemes. Second, it provides a systematic method for coupling finite element structural codes to finite volume fluid dynamics codes, in a manner that leads to highly vectorizable overall codes. The method is applied to transonic flutter calculations for wings and cascades, using simple finite element models. These results suggest that the method is capable of reproducing the energy exchange between the fluid and the structure with much less error that existing methods. U -= mesh velocity vector U = U , / b w , U = strain energy U , = freestream velocity at upstream infinity a = angle of attack; also torsional deflection p =m 0 = stagger angle; also node rotation p = m/7tpb2= mass ratio p = air density o = interblade phase angle w = circular frequency, rad/s w,, = uncoupled frequency in bending w, = uncoupled frequency in torsion Superscripts and Subscripts s =structure f =fluid w = conditions at upstream infinity 1.0 Introduction Nomenclature a = speed of sound; also location of elastic axis c = 2b = blade chord e = total energy f = body force h = bending deflection, positive down k = wb/U= reduced frequency Kh = typical section bending stiffness K , = typical section torsional stiffness m = mass per unit span of blade M = Mach number p = pressure qi = generalized coordinates r = position vector r , = nondimensional radius of gyration about EA t =time T = stress vector T = kinetic energy x , = nondimensional CG-EA offset u,v = velocities in x,y directions * Associate Professor. Member AIAA. Copyright O 1991 by Bendiksen. Published by the AIAA with permission.Recent advances in supercomputer technology and computational methods are revolutionizing the fields of fluid and solid mechanics. Problems that only a few years ago were considered beyond the scope of theoretical calculations are now yielding to supercomputer simulations. The increased use of supercomputers to simulate the behavior of physical systems has also encouraged a reexamination of the existing classical approaches to certain problems. Indeed, shortcomings in computational procedures are often amplified in a parallel processing environment, because they typically prevent the generation of highly vectorized codes.The difficulty in formulating efficient computational schemes for solving fluid-structure interaction problems arises from basic differences in the method of description and numerical schemes presently favored in fluid dynamics and in structural dynamics. In fluid dynamics, finite difference ...