Estimation of Sea Coupling Loss Factors Using a Dual Formulation and Fem Modal Information, Part I: Theory

Abstract

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 de"ned and, as assumed in SEA, no modal coupling exists in a subsystem. Modes of two di!erent 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 di$culty. 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.

Extension of SEA model to subsystems with non-uniform modal energy distribution

“…Of course, the use of SmEdA necessitate to calculate the uncoupled subsystem modes, but is only required for these particular subsystems for which SmEdA is useful. =0.001 ( [1,7]). Table 1.…”

“…The dual modal formulation described in [1] for the general case of coupled continuous elastic systems is based on a dual displacement-stress formulation and two kinds of subsystem modes :…”

“…where  c is the central angular frequency of the band of interest, and, pq  is called the modal coupling loss factor (see [1] …”

“…The application of this model is not limited to academic structures, but can be apply to complex structures by using finite element method (FEM). As described in [1,31] to evaluate CLFs, FEM can be used to calculate the uncoupled subsystems modes which permit to determine the modal coupling loss factors.…”

“…The approach, based on the dual modal formulation proposed in [1,2] take into account the modal energies distribution of each subsystem. The present model is called SmEdA (Statistical modal Energy distribution Analysis) and can be seen as a refinement of traditional SEA.…”