谢宾斯基分形结构声散射特性与视觉偏好评价

Evaluation of acoustic scattering characteristics and visual preference of Sierpinski fractal structures

声扩散界面设计应兼顾声学和美学需求。结合参数化设计方法,谢宾斯基分形的模块化结构具有灵活生成个性化界面的潜力。然而,针对分形结构声学特性与视觉效益尚缺乏综合的量化研究。根据谢宾斯基分形的构造规则提出了一种宽频的扩散结构设计方法,分别从声学性能与视觉偏好的角度,研究模块形状、模块高度和随机排布程度对性能的影响。采用边界元素法的数值仿真与实测验证,结合虚拟仿真技术的主观调查,以及多目标综合分析,探究分形设计要素的作用机制和最佳阈值范围。结果表明,与相同体量的传统二次残差扩散体相比,具有不同平面尺寸和高度模块的分形结构改善了扩散性能,特别是在1 kHz以下的中低频范围。此外,发现在室内使用中高复杂度(迭代3次)、低随机排布、谢宾斯基三角截锥分形结构,有助于提高居住者对环境的偏好度。

Diffusive surfaces should be optimally designed for acoustic and aesthetic purposes.Combining with parametric design methods,the modular structure of Sierpinski fractals has the potential to generate individual interfaces flexibly.However,there is a lack of comprehensive quantitative research on the acoustic properties and visual benefits of fractals.In this paper,we propose a broadband design method for diffusion structures based on the construction rules of the Sierpinski fractal.Focusing on the shape,height,and arrangement randomness of modules,the influence on evaluation is investigated from the perspective of both acoustic performance and visual preference.Numerical simulations using the boundary element method(BEM)combined with experimental measurement validation,a subjective investigation and physiological feedback combined with virtual reality(VR)technology,and a multi-objective comprehensive analysis are used to explore the influence mechanism and the optimal threshold range of fractal design parameters.The results suggest that fractal structures with various horizontal sizes and vertical heights of modules improve diffusion performance compared to the conventional quadratic residual diffuser(QRD)of the same volume,especially in the mid-low frequency range below 1 kHz.In addition,the use of mid-high complexity(three iterations)and low randomness truncated Sierpinski triangular pyramid fractals in meeting rooms would help enhance the visual preferences of occupants.