Hybrid and Dynamic Substructuring Methods for Energy Flow Analysis

Modeling techniques and solution tools to analyze the dynamic and vibro-acoustic behavior of complex built-up structures are matters of increasing interest, especially for thin walled structures as in transportation vehicles, such as automobiles, trucks, trains and aircraft. In structures like these, the reduction of cost, weight, sound and vibration levels are primary issues for research and development. However, reducing the weight of a vehicle may lead to an increase in cost, as well as higher noise and vibration levels, and the desired reduction of sound levels may lead to unwanted increase in mass and cost. These conflicting objectives underline the need for new tools with sufficient predictive capacity in the early design stages. In the present thesis a rigorous study and a solid mechanics formulation of complex valued mechanical intensity, by use of ordinary harmonic response finite element analysis, are presented to serve as one part in such an analysis tool. The potential use of mechanical energy flow in built-up structures by use of substructured finite element models to identify transmission paths for energy is demonstrated. As a part of the study, dynamic substructuring is applied to viscoelastic structures with constitutive relations containing fractional derivatives. Also methods for combining statistical energy analysis (SEA) and the finite element method (FEM) or modal approaches suitable for the vibro-acoustic analysis of realistic built-up structures are studied. Using the two methods simultaneously is not entirely straightforward due to the nature of the different methods. In the present study means to extend a primarily low frequency method, the finite element method, and a high frequency method, statistical energy analysis, to the mid frequency region are addressed. Two approaches are studied. Firstly, an iterative approach is taken where the finite element method and statistical energy analysis are used simultaneously. This approach is intended to extend the frequency range for a FEM based vibration analysis, and is in this thesis applied to a combined truck cabin/frame structure. Here dynamic model reduction is employed to the finite element model and suitable parts of the structure are modeled with SEA. Forces in cross sections connecting the FEM and SEA parts are determined iteratively to ensure that energy balance for the structure is fulfilled. Secondly, parts of a more complete approach to extend the frequency range where SEA is applicable is studied in detail. The focus is on the spatial correlation between different sets of the modes used to describe the energy state of the system, with application to coupled beams and plates