An Improved Dynamic Condensation Approach

Abstract

It is difficult to determine natural frequencies and modal shapes of a Dynamic system having large number of degrees of freedom (DOF) and, in addition, expensive. It is always desirable to reduce the DOF of the system. Of various methods Guyan’s condensation and Component modal analysis are quite popular for reducing the problem size. The present work deals with Guyan’s approach and improvements in its basic form to suit for dynamic problems. The Guyan’s Reduction method ignores the mass in calculating the transformation matrix, hence for dynamic problems its accuracy is usually low. This problem is overcome, by adopting an iterative technique in which the inertia terms are improved by a linearization process. Another important aspect in the implementation of a condensation procedure is the selection of the primary and slave DOF. In the present work, a two step approach is attempted wherein, first, a primary DOF set is selected on the basis of energy method or Ritz vectors and later, the inertial contribution of the transformation matrix is improved through an iterative procedure. The effectiveness of the proposed method is illustrated with two examples.