Direct Hybrid Formulation for Substructure Decoupling

Abstract

The paper considers the decoupling problem or subsystem subtraction, i.e. the identification of the dynamic behaviour of a structural subsystem, starting from the known dynamic behaviour of both the coupled system and the remaining part of the structural system (residual subsystem). Often it is necessary to combine numerical models (e.g. FEM) and test models (e.g. FRFs). In such cases, one speaks of experimental dynamic substructuring. Substructure decoupling techniques can be classified as inverse coupling or direct decoupling techniques. In inverse coupling, the equations describing the coupling problem are rearranged to isolate the unknown substructure instead of the coupled structure. Direct decoupling consists in adding to the coupled system a fictitious subsystem that is the negative of the residual subsystem. In this paper, starting from the 3-field formulation (dynamic balance, interface compatibility and equilibrium), a direct hybrid approach is developed by requiring that both compatibility and equilibrium conditions are satisfied exactly, either at coupling DoFs only, or at additional internal DoFs of the residual subsystem. Equilibrium and compatibility DoFs might not be the same: this generates the so-called non-collocated approach. The technique is applied using simulated data from a discrete system.