Statistical Energy Analysis and the Individual Case

Doctoral thesis, 1995

For many years, one of the most used methods for vibro-acoustic analysis of transmission of Structure-Borne Sound in complex built up structures has been the method of Statistical Energy Analysis (SEA). SEA has many advantages that makes it attractive for engineering use. Notable among these is the ease with which an analysis can be carried out and the close understanding of the significance of design variables given to the analyst when using the method. However, the difficulty to find input data to the model and the necessity for the analyst to be experienced in the use of method often is mentioned as disadvantages in SEA. The reliability of the method is vital in the case analysis takes place at early stage of product development. A SEA-like method for derivation of coupling data with the FE method has therefore been examined and shows that coupling data can be derived at any frequency and coupling strength. A fundamental difference between SEA and the SEA-like procedure is that the former applies for the ensemble, while the latter addresses the individual case. Conventional SEA theory has repeatedly been shown to apply for the case of two-subsystems. Less attention has been given to theoretical verification of cases where more than two subsystems participate. The case of a U-shaped assembly of thin rectangular plates has therefore been examined. The energy-flow and power balances are derived without making a priori assumptions about their form or content. The investigated three-subsystem case shows that six couplings, as opposed to the conventional four couplings in SEA, should be included in the model. The SEA approach to the assembly of subsystem data can thus be seen as a substructuring technique which is an ad hoc extension of the two-subsystem case and applicable for weakly coupled systems. A technique for the derivation of coupling data that applies for any coupling strength is therefore derived. This SEA-like technique can be used when computed or measured subsystem energies and power inputs are available, as it is found to yield a uniquely defined set of coupling and loss factor data. However, the suggested approach does not solve the issue of how indirect couplings can be introduced into SEA. An awareness of the conditions that lead to weak and strong coupling can serve to increase the reliability of results from SEA and SEA-like methods. Features that influence the validity of the energy flow model have therefore been examined for various conditions of weak and strong coupling. The investigation identifies situations in which the SEA approach to substructuring lead to results of satisfactory quality and situations in which the extended energy flow model with its six couplings should be used.