Sound absorbing elements commonly used to make quieter spaces are very desirable for high-frequency noise control. It is more attractive if it is possible to produce sound absorbing structures that perform well for a wide frequency range, especially in low-frequencies. In this regard, Helmholtz resonator array is a well-known structure but the maximum performance of each resonator unit in an array panel can only be achieved at resonance frequency that is dependent on its size. Therefore, a resonator array panel with equal size units has insufficient performance in a wide frequency range. Hence, the consideration of suitable sizes for each resonator in an array panel consisting of unequal size units is a key point to widen the frequency range of sound absorption. On the other hand, it seems that engineering science can be developed by nature inspiration. In addition, Fibonacci sequence is a famous mathematical model which describes the shape/ratio of different phenomena which exist in nature. In this paper, Fibonacci sequence is utilized to investigate Helmholtz resonator arrangement to increase both the amount of sound absorption coefficient and frequency bandwidth of absorption without changing the total volume of resonator array with equal size units. Analytical solutions based on the modified equivalent electrical circuit theory is used to calculate the sound absorption coefficient of the proposed panel with numerical experiments in MAPLE and COMSOL Multiphysics softwares to validate the proposed overall approach. Results show that the Fibonacci sequence is an optimum candidate to design a resonator-based sound absorber in low-frequency noise.

通常用于营造更安静空间的吸音元件非常适合高频噪声控制。如果能够生产出在很宽的频率范围内，尤其是在低频范围内表现良好的吸音结构，那就更有吸引力了。在这方面，亥姆霍兹谐振器阵列是众所周知的结构，但阵列面板中每个谐振器单元的最大性能只能在取决于其尺寸的谐振频率下实现。因此，单元尺寸相同的谐振器阵列面板在较宽的频率范围内性能不足。因此，在由不等尺寸单元组成的阵列面板中，考虑每个谐振器的合适尺寸是拓宽吸声频率范围的关键。另一方面，似乎工程科学是可以通过大自然的灵感来发展的。此外，斐波那契数列是一个著名的数学模型，它描述了自然界中存在的不同现象的形状/比例。在本文中，利用斐波那契数列研究亥姆霍兹谐振器排列，以在不改变具有相同尺寸单位的谐振器阵列的总体积的情况下增加吸声系数和吸收频率带宽的量。基于修正等效电路理论的解析解用于通过 MAPLE 和 COMSOL Multiphysics 软件中的数值实验计算所提议面板的吸声系数，以验证所提议的整体方法。