Acoustic topology optimization of fibrous material with Delany–Bazley empirical material formulation

This research details a new acoustic topology optimization (ATO) framework with an empirical material formulation for fibrous material. Despite the importance of considering pressure attenuation not only by internal solid structures but also by fibrous (porous) structures in acoustic design, a systematic ATO approach with an empirical material formulation has not yet been proposed. Thus, in this paper, an empirical material formulation called the Delany–Bazley model is implemented for the development of an ATO framework for fibrous material with porosity close to 1. By means of the SIMP (solid isotropic material with penalization) interpolation functions developed for multiple structural materials, ATO processes for fibrous structures as well as internal solid structures are carried out. In addition, a heuristic filter method that allows fibrous material to emerge only at the boundaries or rims of an internal solid structure is presented. Finally, the effect of the pressure attenuation on the topological layout for fibrous materials is investigated by solving several illustrative topology optimization examples.