The Frequency Based Substructuring (FBS) method reformulated according to the dual Domain Decomposition method

In this article the Lagrange Multiplier Frequency Based Substructuring method (LM FBS) is introduced. This method is an evolution of the classical Frequency Based Substructuring (FBS) method where substructures characterized by their dynamic admittance can be assembled. In this paper we place the FBS method in the framework of dual Domain Decomposition methods in order to introduce in the problem the interface forces explicitly and in a general manner. In the LM FBS method Lagrange Multipliers are defined, which function as coupling forces between the substructure interfaces when they are coupled. With this formulation only boolean constraint matrices need to be defined. The resulting equations are easy to interpret and they are easy to implement in a computational environment. The proposed formulation of the FBS assembly opens new perspective for future improvement of experimental substructuring. In this article, the LM FBS method is compared to other FBS methods. Here the similarity between the methods are illustrated and the advantages of the LM FBS method are outlined. We also indicate how the LM FBS Method can be reformulated to extract substructure data when the dynamics of the total structure is known.