Modal Truncation of Substructures Used in Free Vibration Analysis

Abstract

A unified approach to a group of structural dynamics analyses using the substructures technique and a consistent basis for the selection of substructure principal modes as required by this method are provided. Substructure frequency roots and strain energy in the principal modes are two criteria evaluated for the selection of substructure principal modes. Based on a simple example of a cantilever beam, it is noted that the substructure principal mode strain energy criterion provides slightly better results in terms of system eigenvalues and system strain energy in the principal modes. Errors in system eigenvalues and principal mode strain energy converge nonmonotonically as the number of substructure modes retained is increased. Since in actuality, these errors are not known, expressions for their estimates are presented. It is seen that modal truncation errors in system strain energy can be better estimated in comparison to the system eigenvalue errors. The substructure approach applied to solve an initial conditions problem indicates that the process of modal truncation depends to some extent on the type of initial conditions prescribed for the structure.