Optimal Design of an Asymmetrical Sandwich Panel for Acoustical and Mechanical Properties

The aim of the present study is to develop specific tools to design optimal panels for multi-objective applications. The objectives considered are stiffness, strength and acoustic insulation at minimum weight. A genetic algorithm is used to design optimal sandwich structures with a good balance of mechanical and acoustical properties. The bending stiffness and mechanical strength of the panel are calculated using beam theory. This analysis is focused on a 3-point bending test, giving the stiffness as the ratio between the concentrated force and the deflection at the center of the sandwich panel. The strength is calculated as the critical force at the onset of plastic deformation. A vibro-acoustical model based on Lagrange’s equations is used to give access to the sound transmission loss of the sandwich panel with anisotropic elastic layers. The main interest is on the mean transmission loss for a diffused incident acoustic field over the frequency range 500–10000Hz. First of all, the optimal design for mechanical properties is assessed at a minimal weight. Quite expectedly, the best solutions are composite-skin with high specific stiffness and soft cores with high shear modulus for a minimum weight. The geometry depends on the required stiffness and strength. The design/properties relationship is discussed by monitoring the evolution of both the material properties and the geometry of the panel. Similarly, a parametric study is performed for acoustical design at minimal weight. In order to maximize the mean transmission loss, it is preferable to lower the critical frequency for which acoustic radiating is maximal. Then, the best solutions for the panel are those who maximize the square root of the density over Young’s modulus. The trade-off between mass and loss transmission is then explored. A comparison between all these solutions provides significant differences in the design with respect to the objectives. In the next step, a multi-objective genetic algorithm is used to find an optimized panel with a good compromise between acoustical and mechanical properties. The optimization is considered with several approaches depending on whether the mass is regarded as the cost function or as a constraint. This study thus provides a preview of the capabilities of multi-objective optimization in design of sandwich panel.