Shape optimization under vibroacoustic criteria in the mid-high frequency range using gradient-based approach

Shape optimization issues under vibroacoustic criteria within the specific mid high frequency range are under consideration in the present paper. The main objective of this research is to develop an adjoint formulation for the shape optimization using Simplified Energy Method (MES). This will allow to implement the method into numerical modeling of engineering applications, such as noise reduction, aeronautic domain, etc., with large number of variables and reasonable computational cost. The adjoint method was developed to minimize the energy density in the cavity by changing its geometry parameters. We use the Simplified Energy Method (MES), which gives a solution that only depends on the cavity shape, not on the material properties and doesn’t need fine meshes. Firstly, the proposed shape optimization method aims at avoiding the remeshing during the optimization process and it has to model the acoustic cavity surface exactly. To achieve this goal, we rely on a transformation function which maps a 3D cavity surface on a 2D domain. Hence, the optimization is conducted on this function directly. Secondly, as for realistic applications the number of design variables is very high, so the gradient based methods are in demand. In the present contribution the optimization process is based on adjoint calculation of the gradient that leads to an analytical expression of the directional derivatives without additional computational cost. To prove the versatility of the method, we apply it on a rectangular cavity shape modeled with patches of Bezier surfaces. The results of shape optimization are presented and the robustness of the method is shown.