Modal parameters of a rotating multiple-disk-shaft system from simulated frequency response data

Abstract

Modal parameters of a rotating multiple disk-shaft system are estimated in Multiple Input/Multiple Output (MIMO) scheme. The response at multiple output degrees of freedom (dofs) and excitations at multiple input (reference) dofs are related through the Frequency Response Function (FRF) matrix. The corresponding Impulse Response Function (IRF) matrix is obtained by Inverse Fast Fourier Transform (IFFT) of the FRF matrix. The resulting FRF matrix is not symmetric due to the gyroscopic effects introduced by rotation. The Eigensystem Realization Algorithm (ERA) and its equivalent low order time domain algorithm, based on the Unified Matrix Polynomial Approach (UMPA) are employed to estimate the desired modal parameters, i.e., system eigenvalues and the asso- ciated right hand and left hand eigenvectors. The right hand vectors are estimated from multiple columns of the FRF matrix with the structure rotating in one direction, and the left hand vectors are estimated from the multiple rows of the FRF matrix, which are calculated as the transpose of the same multiple columns of the FRF matrix, estimated with rotation in the opposite direction. The obtained results are found to be in excellent agreement with results obtained from Theoretical Modal Analysis (TMA).