Dynamic condensation in a damped system through rational selection of primary degrees of freedom

Various system reduction methods have been proposed to calculate eigenvalues and eigenvectors with computational efficiency. In the case of system condensation, the method of selecting proper primary degrees of freedom (PDOFs) is crucial because they are closely related to the accuracy and reliability of eigensystem prediction in a reduced system. Although reasonable selection methods for PDOFs have been proposed for undamped systems, these methods cannot be directly extended to damped systems. We propose a PDOF selection method for a damped system. The proposed method is based on the ratio of DOF-wise energy distributions. In order to estimate the energy distribution of the structure, Ritz vectors are obtained using a two-sided Lanczos algorithm. Energy distribution matrices are calculated from the obtained Ritz vectors. Then, degrees of freedom (DOFs) corresponding to the lowest Rayleigh quotients are selected as the PDOFs. The efficiency and reliability of the proposed method are demonstrated using numerical examples.