A Modal Synthesis Technique for Determining Dynamic Properties for a Structure for Mass and Stiffness Changes

The assembly and particularly the reduction of the mass and stiffness matrix for a large system can be a significant portion of the computational cost of finding the mode shapes and natural frequencies. Therefore, parameter studies for design purposes can be prohibitive if these matrices are reassembled and reduced for each change. The purpose of this paper is to outline the procedure for using the modes of the original system to determine the dynamic characteristics of the changed system. The method also results in computational savings for boundary condition changes and for large systems that are nearly-symmetric except for a few mass and stiffness changes.

To illustrate the method several changes are made to a ladder frame. The results from an analysis using the reconstructed mass and stiffness matrices and the modal synthesis technique are compared to show the accuracy and freedom requirements.