Calculation of coupling loss factors using a hybrid finite element/wave and finite element approach

The vibration of built-up structures at higher frequencies can be analysed using energy based methods such as the Statistical Energy Analysis (SEA). Central to SEA is the calculation of the coupling loss factors (CLFs) between the subsystems. This can be difficult, for example when complex joints connect wave-bearing substructures of complicated constructions (laminates, truss cored or sandwiched panels, etc.). In this paper, we present a hybrid finite element/ wave and finite element approach for predicting these CLFs. Each substructure is modelled using the wave and finite element (WFE) method where a small segment of the structure is modelled using standard finite element (FE) techniques and then periodic structure theory is used to predict the wave characteristics of the substructure. The propagating waves in the substructure are treated as SEA subsystems. The joint is modelled using standard FEs, and the joint FE model is coupled with the WFE models of the substructures to yield the scattering properties of the joint. These can then be used to predict the diffuse field transmission efficiency and CLFs between the various subsystems. The strength of the approach is two-fold. First, the substructures and joints can be arbitrarily complicated. Second, the full power of existing FE libraries/packages can be used to obtain the WFE models of the substructures and the FE model of the joint. Numerical examples are presented to illustrate the approach.