Two-level scheme for selection of primary degrees of freedom and semi-analytic sensitivity based on the reduced system

A number of approximate techniques have been developed to calculate the eigenvalues in a reduced manner. These schemes approximate the lower eigenvalues that represent the global behavior of the structures. The present study proposes a two-level condensation scheme (TLCS). This scheme consists of two-steps. In the first step, the candidate elements are selected for constructing the reduced system by energy estimation. In the second step, primary degrees of freedom are selected by sequential elimination from the candidate degrees of freedom linked to the selected elements through the first step. The proposed method saves computational cost effectively and recovers eigenvalues of the full system with high accuracy from the lowest to the truncated range of frequency. Moreover, besides the accuracies of the eigenvalue, well-constructed reduced system assures the accuracy of sensitivity of the eigenvalue compared to full system. In this paper, the semi-analytic design sensitivity of eigenvalues is obtained by the rigid body separation technique in reduced system. For the sensitivity calculation, the eigenvectors obtained from the reduced system are transformed into global system field. Numerical examples demonstrate the reliability of the eigenvalue and its sensitivity obtained by the reduced system through the comparison with conventional sensitivity schemes.