Modal Synthesis Method for General Dynamic Systems

Abstract

A modal synthesis method is presented to calculate the lower eigenproperties of a general dynamic system divided into subsystems. The left and right eigenproperties of the subsystems associated with their equations of motion expressed in the state form are used. To account for the truncated higher eigenproperties of a subsystem, the force derivative approach formulated for general dynamic systems is used. The reduced order equations of the subsystems are coupled by enforcing displacement and force compatibility conditions at the interface. The approach is quite general, so it can be used with nonclassical damped systems as well as with systems with asymmetric matrices, such as gyroscopic and other circulatory systems. The numerical examples of: (1) A piping system carrying rotating parts and provided with discrete dampers; and (2) a large rotor‐disk‐bearing system are presented to demonstrate the effectiveness of the proposed approach. It is shown that lower eigenproperties of a system can be accurately calculated by using only the first few eigenproperties of its subsystems.