Last modified: 2016-06-10
Abstract
Complex dynamical systems such as car body, aircraft fuselage or train coach are conveniently modeled with Finite Element Method (FEM) in the Low Frequency range (LF). Increasing the frequency range to Mid-Frequencies (MF), typically up to 1000-2000 Hz, requires larger and larger FEM mesh. Presently, MF fluid/structure interaction problems on large structures cannot be solved in decent time at engineering level. Reduction of model size is required especially under random distributed loads. Energy methods like Statistical Energy Analysis (SEA) provide a theoretical framework for building small models based on power-balanced- equations they can be run in High Frequency range (HF). Nevertheless, SEA parameters are derived from analytical solutions of differential operators and submitted to many assumptions and simplifications. They cannot provide robust enough prediction in MF range due to inherent complexity of industrial systems.
To improve predictability of energy models, the relevant parameters are then identified by inverse method from the “statistical” dynamic information contained in side FEM model. The FEM-derived SEA models are called Virtual SEA models (VSEA). They use the same parameters than the classical “analytical” SEA models. VSEA parameters can then be directly compared to their analytical counterparts. VSEA models may be understood as compressed FEM models in which the narrow-band frequency and spaced-varying FEM dynamic is replaced by band-integrated frequency and spaced averaged dynamic applied to a partition of FEM domain into subsystems. This compression leads to very small models while minimizing the information depredation. For example car body-in-white dynamic described by 6 million DoF’s in FEM is encapsulated as a real-valued 50x50 matrix relating injected power from impressed forces to energy in each of the subsystems. Problems involving random loads can then be solved by using VSEA models rather than original FEM’s. VSEA models can also be complemented by analytical other subsystems such as fluid cavities to solve full vibroacoustic response involving airborne and structure-borne propagation paths. Outputs from VSEA models are also more easily interpreted and provide description of propagation paths in the system.