The Effective Dynamic Response Prediction Through Condensation in Damped System

Abstract

Selection of the primary degrees of freedom (PDOFs) is a matter of great importance because it is very closely related to accuracy of the eigenpairs in dynamic condensation. In case of undamped systems, reasonable selection method of the PDOFs have been proposed; however, it cannot be extended to damped systems. Therefore, new approach is needed in selection of the PDOFs analytically. The proposed method is based on the degrees of freedom – level energy distribution. Ritz vectors to estimate energy distribution of structures are obtained by using two-side Lanczos algorithm. From them, energy distribution are calculated and then degrees of freedom corresponding to the lowest Rayleigh quotients are selected as the PDOFs. In numerical examples, results are presented for the verification of the proposed method. I. Introduction he eigenproblems of large and complex structural systems through the finite element method (FEM) require too much computation resource and time. Enormous advance in computer capability enables to compute more large scale problems. However, the effort to overcome the limitation of computational resource and shorten computational time is still under way. From this point of view, many researchers have developed efficient model reduction methods. The need for the model reduction increase more and more at various fields such as inverse problem, multi-scale, multi-physics problem. In structural dynamics, one field related to model reduction is the reduced order method (ROM). While accurate solutions in ROM can be obtained by saving the computational resource and time, it loses information related to physical coordinates after constructing the reduced system. The other research is about system condensation. The advantage of system condensation compared with ROM is to keep up the relationship between origin and reduced system. This fact means to be closely related to sensor positioning in experiments. Condensation technique in undamped systems was proposed by Guyan 1 at first. However, Guyan‟s method could not produce accurate eigenvalues because the effect of mass associated with the secondary degrees of freedom (SDOFs) is not rationally considered when constructing the reduced system matrices. Leung 2