Virtual SEA - FEA-Based Modeling of Mid-Frequency Structure-Borne Noise

Virtual SEA (statistical energy analysis) is similar to experimental SEA, but based on frequency response functions computed using a FE model of the studied structure. The knowledge of the internal loss factors (defined by the user) as well as numerous observation and excitation points leads to a consistent data set that may be used to properly identify a SEA model. This process has been improved by developing an original automatic sub-structuring technique that guarantees optimized model construction and consequently a robust identification. This last feature supports SEA users with a lower level of expertise. As an example, virtual SEA is applied to the floor of a minivan. Convincing results are obtained when compared to experimental methods.

Improvement in vehicle acoustic performance at low frequencies (booming noise) and high frequencies (insulation) has left perceived medium frequencies (200-1000 Hz) as the critical hand in passenger comfort vs. power-train or road excitations. Simultaneously, new design processes (e.g. systems engineering), development time reduction and prototype availability are pushing computational methods, which can predict vehicle performances in any technical field - CFD and thermal comfort, durability, crash analysis, CEM, vehicle dynamics and NVH. Sound transmission at medium frequencies (especially structure-borne transmission) is one of the last vibroacoustic subdomains not covered by any computational method.

This frequency range is part of the physical medium frequencies, where the response of the structure involves global as well as local behaviors. Neither the 'modal' behavior, dominant at low frequencies, nor the 'statistical' behavior, dominant at high frequencies, can alone represent the medium frequency behavior. Numerous dedicated computational techniques for addressing this issue are in progress and have remained at a research stage until now.1-5

Thus, the industrial design process led us to develop a method whose main features include adaptability to the current design process, reducing operating time, and lowering the required user level of expertise. The proposed method, called Virtual SEA, allows car body modeling that surpasses traditional SEA limitations by an extensive use of numerical simulation.6,7

This article covers the Virtual SEA method and includes an example application using the floor of a minivan (Peugeot 806). First, a brief background of the method is presented.

Extension of the FEA Process to Medium Frequencies

With crash analysis, refined meshes such as the one shown in Figure 1 are available, at least for the body in white (BIW), from the early design stage of any vehicle project.

The mesh size of a few centimeters allows computations up to 1 kHz with no major difficulty. Because of insufficient memory size problems, a direct solver is used instead of the common modal solution. The resulting increase of the CPU time has not been seen as an obstacle, considering a number of recent improvements in numerical solvers for dynamic problems.8-10

If FE computations are available at rather high frequencies, why not use FEA directly?

* Increasing frequency makes the structures hyper-sensitive to small uncertainties in material properties and geometrical details. Such sensitivity, inherent to mass production objects such as cars, cannot be ignored in the medium frequency range. In this case only space- and frequency-averaged responses (i.e., energetic responses) can be predicted with adequate precision.

* FE modeling in itself does not provide the understanding necessary for project improvement. The modal understanding of the structure, used at low frequencies, is no longer relevant due to the high number of modes overlapping to produce the observed responses. Modal behavior provides clear design information through the locations of kinetic and elastic energies, respectively, indicating where mass and stiffness or damping modification are sensitive. At higher frequencies, when modes start overlapping, such information is no longer available. In the asymptotic case of high frequencies, the kinetic and elastic energies are considered equal at any point of the structure.

This quantity is preferred to the squared transfer of mobility function because its variance among input points is much smaller, meaning it provides more information about the dynamics of the system. Its use in the Virtual SEA Process is shown explicitly in the appendix.

Noto that, although observation as well as excitation points do not have the same location in both cases, measurements and computations lead to very similar results in terms of spectral shape and spread among excitation points - except for part 1, where calculations show an overestimated value that was later related to a reinforcing plate, unfortunately welded to the prototype. This problem is purposely highlighted in order to emphasize the difficulties inherent in a design process. With the possibility of local changes in the body design, any modeling, even the most accurate, remains uncertain regarding the design process. Work is in progress in order to account for such modeling uncertainties.