Direct response and force transmissibilities in the characterization of coupled structures

A description of coupled structures, and structures with blocked degrees of freedom, is presented in terms of direct transmissibility functions (DTFs) as an alternative to the standard mobility approach. The notion of DTFs between degrees of freedom is extended to DTFs between groups of subsystems for that purpose. The relation between DTFs and mobilities is clearly established and the concept of direct force transmissibility, which offers a different description of signal transmission within a structure, is also introduced. Moreover, a physical interpretation for the decomposition of the mobility matrix of the coupled substructures in terms of Schur complements is given. This highlights the transmission process from input forces to substructure responses. Finally, two numerical examples are included to elucidate all concepts and outline their potential for practical applications. The first one deals with predicting vibrations of a plate after blocking some of its degrees of freedom. The second one addresses signal transmission between two plates with elastic coupling.