An Improved MDOF Model Simulating some System with Distributed Mass

Abstract

The paper proposed and examined a MDOF model whose mass properties are determined on the hypothesis that at an arbitrary time in the course of the system’s motion, the kinetic energy as well as the nodal displacements of the actual system (system with distributed mass) are the same as those of the simulating MDOF model. The solution of this formulation for any MDOF system with n degrees of freedom leads to n distance mass vectors, each satisfying this condition of dynamic equivalence for a particular vibrational mode. Further more, for the conditions of dynamic equivalence to be satisfied the lumped masses of the simulating MDOF model must not be constant but are dependent upon the excitation frequencies. All the natural frequencies evaluated on the basis of this present formulation are almost identical with those of the actual system proving the high accuracy of the proposed model.