Abstract: The Branch Mode Analysis developed by G. M. L. Gladwell is a dynamic computational procedure in which the vibration modes of a complete structure are synthesized from modes of branch systems into which the structure is divided. The inverse problem of the Branch Mode Synthesis presented herein is how to identify the modal behavior of a branch system from modes of the complete structure and the other branch systems. In the paper, for simplicity, a Ritz analysis of the inverse problem only for a structure divided into two branches is discussed, and the inverse problem for a structure into more branches is then solved by using both the Branch Mode Synthesis and the in -verse analysis for a structure into two branches. The presented results of the two computational examples have verified the correctness of the above inverse analysis. The inverse analysis of the Branch Mode Synthesis is applicable for the problems of dynamic design and analytical model updating of structures.

Key words: mode synthesis, dynamic inverse problem, Ritz analysis, dynamic design, model updating