Level-set based topology optimization on acoustic balcony ceiling design of a simplified urban building for noise reduction.

Balconies can provide noise shielding for residents who live in high-rise apartment buildings. The efficiency of noise reduction induced by a balcony largely depends on the shape of the balcony ceiling. This study aims to optimize the shape of the ceiling of a two-dimensional simplified urban building to enhance noise mitigation by using level-set based topology optimization, which is capable of providing a distinct and smooth interface. Noise sources at both single and multi-frequency optimization are considered. In the single-frequency optimization, two peak frequencies in the spectrum of sound pressure level (SPL) at receivers on the fourth floor of an ordinary ceiling are selected. Results show that significant SPL reduction is attained by the optimized ceiling. In addition, broadband noise suppression at frequencies above the target value is also achieved. The underlying mechanism is that the optimized ceiling consisting of several concaves can redirect the incident wave propagating away from the balcony and effectively avoid forming a trapped mode within the area between the floor and the ceiling. Additionally, more effective noise reduction is achieved by the multi-frequency optimization. Thus, the proposed design strategy can be widely used in various applications of noise reduction in the field of building and environment.