Virtual SEA for noise prediction and structure borne sound modeling

Introduction In the mid-frequency range (200-2000 Hz), the difficulties encountered when modeling the car body structural interactions as well as the related acoustic radiation properties are mainly due to the complexity of automotive structures. Previous work [1, 2] has proven the predictive efficiency of an energy-based representation of these interactions within the SEA framework (Statistical Energy Analysis). Nevertheless, classical SEA modeling [3] is submitted to some drawback. Before any SEA modeling, it is required to separate the system domain into mechanically weakly coupled regions. It is only at this stage, that a region can be considered as a SEA subsystem. This first modeling step is critical for several reasons: • There is presently no reliable theory that mathematically defines the notion of “weakly coupled systems”. • The illicit partition a single-piece homogeneous subsystem -such as a beam, a plate or an acoustic cavityinto separate SEA subsystems may lead to some physical inconsistency. • The gathering of subsystems may lead to errors in the vibration level prediction. Moreover, the practice shows that the discontinuities able to generate an energy gap (condition for the existence of a power flow between subsystems) are more numerous at high frequencies. Consequently, the number of subsystems should increase with frequency. In the case of a complex structure such as a car body, a well-suited system decomposition is especially difficult to find, due to the variety of structural components and assembly details. It is only up to 2000-4000 Hz that a car body degenerates into a set of weakly-coupled homogeneous plates or shells, easy to identify as separate regions. At lower frequencies, creating relevant SEA models -independent of user's choice-, is a real challenge. Sub-structuring is not the only difficulty when modeling an automotive structure with SEA: the isolated subsystems often differ from “known” SEA kind of subsystems. Classical SEA components modeling rely on wave-based models; such models only apply for regular topologies when a car body is polymorphic. Virtual SEA (VSEA) was introduced in order to overcome these limitations by using a Finite Element Method to describe the dynamical behavior of any structure [1, 2]. Then, the proposed method applies to any structural problem that can be addressed using a FE modeling. VSEA provides an automatic sub-structuring of the studied structure, as well as SEA parameters of subsystems, adjusted to the FE model dynamical behavior. VSEA is shortly described in the first part of the paper. Nevertheless, up to this stage, VSEA was restricted to structural vibrations of the system associated to the FE model. No sound radiation -i.e. coupling with a cavitynor system extension –adding new subsystemswas possible. The modeling of insulating treatments, that slightly interact with the structure but change the acoustic radiation, could not be achieved too, since the only practicable modeling at mid-high frequencies relies on a wave modeling of the structural vibrations [4, 5]. To above features are mandatory when one wish to get involved into