On the physically consistent characterisation of a system for FRF-based substructuring

Substructuring approaches have been extensively used since long time to predict the vibroacoustic behaviour of built-up mechanical systems. In the frequency domain, these methods build on the dynamic characterisation of the subsystems via frequency response functions at the coupling interfaces. Intensively used for subsystems connected by points, dynamic substructuring still constitutes an open area of research for systems comprising continuous interfaces. Within this framework, a method which allows to characterise subsystems connected along lines is presented. The approach is based on a discretisation of the continuous interfaces into a small set of points, where the information of the subsystems is condensed. For this purpose, an inverse approach is used, which allows to characterise the dynamics of the passive subsystem using data of the assembled system. A straightforward inversion, however, does not assure the physical consistency of the characterized subsystem. In other words, the subsystem extraction procedure must not only guarantee correct dynamic behaviour of the assembled system, but the obtained subsystem must also be reciprocal and passive. The central theme of this paper is the formulation of a constrained optimisation procedure for the enforcement of reciprocity and passivity on the inversely obtained subsystem characteristics. The method is validated on a structure made of two plates connected along a common edge through a beam.