Modified Modal Domain Analysis (MMDA), a reduced order modeling technique, is applied to a geometrically mistuned integrally bladed rotor to obtain its natural frequencies, mode shapes and forced response. The geometric mistuning of blades is described in terms of proper orthogonal decomposition (POD) of the coordinate measurement machine (CMM) data. Results from MMDA are compared to those from the full (360 degrees) rotor ANSYS model. It is found that the MMDA can accurately predict natural frequencies, mode shapes, and forced response. The effects of the number of POD features and the number of tuned modes used as bases for model reduction are examined. Results from frequency mistuning approaches, fundamental mistuning model (FMM) and subset of nominal modes (SNM), are also generated and compared to those from full (360 degree) rotor ANSYS model. It is clearly seen that FMM and SNM are unable to yield accurate results whereas MMDA yields highly accurate results.

Modified modal domain analysis (MMDA) is a method to generate an accurate reduced-order model (ROM) of a bladed disk with geometric mistuning. An algorithm based on the MMDA ROM and a state observer is developed to estimate forcing functions for synchronous (including integer multiples) conditions from the dynamic responses obtained at few nodal locations of blades. The method is tested on a simple spring-mass model, finite element model (FEM) of a geometrically mistuned academic rotor, and FEM of a bladed rotor of an industrial-scale transonic research compressor. The accuracy of the forcing function estimation algorithm is examined by varying the order of ROM and the number of vibration output signals.

Modified modal domain analysis (MMDA), a reduced order modeling technique, is applied to a geometrically mistimed integrally bladed rotor to obtain its natural frequen cies. mode shapes, and forced response. The geometric mistuning of blades is described in terms of proper orthogonal decomposition (POD) of the coordinate measurement machine (CMM) data. Results from MMDA are compared to those from the full (360 deg) rotor ansys model. It is found that the MMDA can accurately predict natural frequencies, mode shapes, and forced response. The effects of the number of POD features and the number of tuned modes used as bases for model reduction are examined. Results from fre quency mistuning approaches, fundamental mistuning model (FMM) and subset of nomi nal modes (SNM), are also generated and compared to those from full (360deg) rotor ansys model. It is clearly seen that FMM and SNM are unable to yield accurate results whereas MMDA yields highly accurate results.

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This paper deals with efficient computation of the statistics of the normalized peak maximum amplitude (npma) for a bladed rotor with geometric mistuning. The method is based on the high-fidelity reduced-order model, Modified Modal Domain Analysis (MMDA). It is shown that the statistical distributions of npma from random permutations of blades, which do not require any additional finite element sector analysis, are close to those from conventional Monte Carlo simulations in which coefficients of proper orthogonal decomposition features of geometric mistuning are randomly selected. Nomenclature C = damping matrix of full rotor r C = reduced order model damping matrix ) (t f = forcing function vector for full rotor j = imaginary number, 1  K = stiffness matrix of full mistuned rotor t K = stiffness matrix of full tuned rotor r K = stiffness matrix of reduced order model M = mass matrix of full mistuned rotor t M = mass matrix of full tuned rotor r M = mass matrix of reduced order model n = number of blades used for POD analysis of CMM data nb = number of blades or sectors in a rotor nd = number of degrees of freedom for full rotor np = number of POD features used for model reduction s n = number of sample blades for random permutations x = nodal co-ordinates of full rotor model y = modal coordinates of reduced order model K  = deviation in stiffness matrix due to mistuning M  = deviation in mass matrix due to mistuning  = transformation matrix for model reduction H  = complex conjugate transpose of 