Optimal distribution of holes in a partition interfacing two cavities for controlling the eigenfrequencies by acoustical topology optimization

When two acoustic cavities are connected through an opening, the acoustical characteristics of the resulting double cavity can be considerably affected by the opening. Typical examples include a passenger vehicle where a passenger compartment cavity is acoustically coupled with the trunk compartment cavity through small holes in the package tray. Although the locations and cross-sectional areas of these holes are known to significantly affect the acoustical characteristics, there is no systematic design method available to determine an optimal multi-hole distribution. Since the hole distribution problem can be formulated as a topology optimization problem, the eigenfrequencies of the double cavity system having a partition with holes can be controlled by an optimal multi-hole distribution solved in the topology optimization setting. After demonstrating that it is difficult to find satisfactory results by using only a single initial guess, significant efforts are made to develop a systematic procedure to generate a suitable set of initial guesses. The proposed method uses the so-called cross-modes that appear due to the presence of a hole. The obtained results are compared with those obtained by using randomly-generated initial guesses. In addition, the physics behind the optimized results, obtained by using the developed method, is explained by the concept of the added length associated with the cross-modes of evanescent waves. The effectiveness of the developed approach is tested with a three-dimensional simplified half-scaled car cavity connected to the car trunk cavity by a package tray with holes.