On Decoupled Shape-Parameterization of Damping Layers using Polygons

In order to reduce noise in a cabin, the radiated power of a surrounding structure is to be minimized by positioning damping layers on the panels that make up the structure. One aspect in every optimization task, the importance of which is not to be underestimated, is how to parameterize the system. By parameterization, the space of possible designs is chosen, and the efficiency and effectiveness of the optimization are greatly influenced. Parameters should be of minimum number, the parameter space should be orthogonal, and parameterization should be least restrictive to aspects of the design which are not directly relevant for the functional optimization goal. Since every panel surface can be described by a two-dimensional coordinate system, the shape of respective damping layers is also a 2-D form with added thickness. A lot of work on the description, movement and deformation of 2-D shapes has already been done in the field of computer graphics and 2-D animations. Shapes are approximated by polygons, which are fully defined by the coordinates of their vertices and edges. When moving and deforming these polygons, care has to be taken to prevent self-intersecting polygons and other implausible shapes. Shape and position of the considered damping layers can easily be decoupled by choosing local coordinate systems for each damping layer. Thereby, the position of the local coordinate system respective to the global coordinates describes the position of the damping layer, while the coordinates of the polygon's vertices in the local coordinate system describe its shape. Additionally, methods exist to preserve the area of a polygon in deformation. This in combination with an area scaling factor is employed to decouple shape, position and area of the damping layers which are to be optimized. Furthermore, the control of damping layer areas can conveniently be used to incorporate constraints on the overall damping layer area. Through advanced parameterization, the use of an evolutionary optimization algorithm is made viable, because the number of design variables it has to handle is greatly reduced. Evolutionary Optimization bears the advantage of not getting stuck so easily in local optima, which is especially important for a multimodal problem like the one considered here. An additional advantage is the possibility to extend the optimization to a multi-modal evolutionary algorithm in future work, which can in a next step be evaluated in a coupled structural-acoustic simulation with respect to acoustic objectives.