ESTIMATION OF SEA COUPLING LOSS FACTORS USING A DUAL FORMULATION AND FEM MODAL INFORMATION, PART I: THEORY

The theoretical approach presented in this paper allows SEA coupling loss factors for subsystems to be modelled with FEM. It is then possible to take into account the complicated substructure that can be encountered in practical industrial application. The technique relies on the basic SEA relation for coupled oscillators and the use of dual modal formulation to describe vibration of coupled subsystems. With this approach, the boundary conditions of uncoupled subsystems are clearly defined and, as assumed in SEA, no modal coupling exists in a subsystem. Modes of two different subsystems are coupled together by gyroscopic elements and the coupling strength is related to eigenfrequencies of the uncoupled subsystems and mode shapes through the interaction modal works. A general expression for CLF has been obtained, and it allows CLF to be determined only from the knowledge of the modes of the uncoupled subsystems and the modal damping. Finite element model can be used to calculate the modal information in the case of complex substructures. It is possible to treat the case of heterogeneous subsystems having three-dimensional vibration motions without difficulty. Contrary to the classical approach which is based on SEA inverse matrix and numerical experiments which necessitate calculations of subsystem energies for the coupled structures for many excitation points, this technique calculates CLF directly from the governing equations without solving them. In a companion paper, the present approach is applied to a simple example to illustrate and validate the approach.