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

Jin W. Lee, Purdue University - Main Campus
Yoon Young Kim, Seoul National University

Date of this Version



Comput. Methods Appl. Mech. Engrg. 198 (2009) 2175–2189

This document has been peer-reviewed.



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.


Nanoscience and Nanotechnology