A method for determining the eigenvalues of a synthesized system from the Frequency Response Function (FRF) for noise contaminated subsystems is presented. This method first uses matrix Auto-Regressive Moving-Average (ARMA) model in the Laplace domain to describe each subsystem. Then a modal force method by ARMA model can be established. Only the FRF at the connecting joints is needed in the analysis to form a matrix named Modal Force Matrix. From this matrix, both synthesized system modes and substructure modes can be extracted simultaneously. Since the inverse operation is not required to form Modal Force Matrix, the computation is reduced drastically. The eigensolution of the system in any frequency range can be determined independently. Numerical study suggests that good results can be achieved by this method.

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