Fluid-Structural Coupling Effects on the Dynamics of Mistuned Bladed Disks

Mistuning changes the vibration of bladed disks dramatically. Various aeroelastic models have been used to investigate the free vibration and forced response problems of mistuned bladed disks. Most of these models used simplified structural and/or aerodynamic models. The traditional way to incorporate the aerodynamic coupling in the high-fidelity structuralmodels is to use the cantilever-blade normalmodes to calculate the unsteady aerodynamic forces. In this paper, a new reduced-order modeling approach is developed by using the tuned system modes to calculate the unsteady aerodynamic forces directly. This new approach is applied to an industrial rotor. The results show that aerodynamic coupling has significant effects on the vibration of bladed disks for the case studied. Also, constraint modes are needed to yield accurate results if cantilever-blade normal modes are used to calculate the unsteady aerodynamic forces. However, using the tuned systemmodes to calculate the unsteady aerodynamic forces saves a significant amount of computation time compared to the method using both cantilever-blade normal modes and constraint modes. Nomenclature A = aerodynamic stiffness matrix C = speed of sound E = complex Fourier matrix f, F = physical and modal forces h = height of stream tube j = imaginary unit K,M = stiffness and mass matrices NB = number of blades P, Q = modal transformation matrices p = flow pressure Q = flow mass flux at the boundary q = generalized (modal) coordinate s = distance along the boundary T = period of flow unsteadiness U = blade normal and constraint modes K, M = physical mistuned stiffness and mass matrices = structural damping c = ratio of specific heats = flow density = interblade phase angle = system and blade mode shapes = velocity potential of the flow = blade constraint mode shape! = complex frequency Subscripts T = total flow density and pressure = blade part of mode shape Superscripts a = aerodynamic quantity CB, S = cantilevered-blade modes and system modes M, T = mistuned and tuned n = steps of iterative calculations syn = in the synthetic modal space 0 = structural-only quantities = Hermitian of a complex matrix