Coupling loss factor calculation through Lorentzian-weighted frequency averaging of the direct field dynamic stiffness.

Coupling loss factors (CLFs) between components of a structure play an important role in high frequency simulation techniques, such as the Statistical Energy Analysis and hybrid deterministic/statistical approaches, to describe how energy is transferred between the components. They are usually obtained from experiments or from analytical models, based on a modal or wave formulation. However, when the connections between components become more complex, deterministic methods such as the Finite Element Method (FEM) or the Boundary Element Method (BEM) are used. By using the diffuse field reciprocity relation, CLFs can be expressed in terms of the direct field dynamic stiffness matrices. Assuming equivalence between the ensemble and frequency average, this direct field dynamic stiffness can be calculated through frequency averaging of the dynamic stiffness at the junction. The presented method proposes the use of the Lorentzian function as weighting function for the frequency averaging procedure. By applying the complex residue theorem, the Lorentzian weighted frequency integral can be calculated by a single evaluation of the dynamic stiffness at a complex frequency. This method allows for great flexibility since the CLFs can be computed by simple manipulation of matrices from a FEM model that is evaluated at a complex frequency instead of a real one. The introduction of an imaginary part to the evaluation frequency can also be interpreted as the addition of artificial damping to the system. Since the damped waves require a smaller number of elements to capture its behaviour, this opens up the possibility of coarsening the mesh to further improve the computational efficiency. The developed approach is applied to a number of cases and CLF results are compared to those of classical analytical models. The tuning of the width of the Lorentzian function and mesh coarsening are also investigated.