Shape optimization of a vehicle hat-shelf: Improving acoustic properties for different load cases by maximizing first eigenfrequency

This paper presents design optimization of the geometry of a vehicle hat-shelf. At first two existing finite element discretizations are investigated for two different element types. The structural model is then parameterized. Only four design variables have been chosen to control the shape modification of the hat-shelf. The aim of this paper is to decrease the vehicle interior noise due to three different excitations for two cases of fluid damping. With respect to the support conditions of the hat-shelf these three load cases and the two cases of different damping are considered simultaneously by maximizing the lowest eigenfrequency of the structural model. Although remarkable differences in the natural frequencies are discovered for the four discretizations, a similar dependence of the objective function in terms of the design variables is observed. Thus, a multigrid strategy can be applied. The coarsest mesh is used to obtain suitable initial sets of optimization variables, one of the finer meshes serves for a pre-optimization and the finest mesh is optimized to find the final set of parameters. While the lowest eigenfrequency of the original model is found at about 31 Hz, the corresponding value in the optimized variant exceeds 100 Hz being the upper bound of the frequency range under consideration. Evaluation of the noise transfer function proves that this strategy decreases its average between 4.4 and 13.9 dB.