Calculation of the Coupling Loss Factors for a Hybrid FEM/SEA Line Junction

In the present thesis a hybrid theory [Shorter and Langley 2005] for calculation of Coupling Loss Factors (CLFs) in hybrid Finite Element Method (FEM) / Statistical Energy Analysis (SEA) modelling is applied to a hybrid line junction, with the aim of providing a derivation example. The case study is chosen to be a hybrid line junction composed by a rigid beam modelled with FEM, which couples two incident SEA plates coincident to the beam along one of their edges. The theory allows to obtain the Coupling Loss Factors from the Stiffness Matrix of the deterministic subsystems and the Direct Field Dynamic Stiffness Matrix of the statistical subsystems. Most of this work is focused on the derivation of the plate's Direct Field Dynamic Stiffness under the assumption of semi-infinite plate, explaining in detail the reason why such a hypothesis can be reliable when computing the CLFs, and its resulting benefits. Three possible methods for the derivation of the direct field stiffness in modal coordinates are proposed using Green's Functions, wavenumber modal transformation and defining complex-valued shape functions in the wavenumber domain for a Galerkin method, which has consequences on the symmetry of the stiffness. Results for the CLFs are shown and compared between the different derivations of the direct field stiffness.