應用Fano與Helmholtz共振設計空氣可流通之耳塞

Abstract

本研究以等效電路模型的方式設計低頻可透氣式消音結構，此方法無論解析解、等效電路模擬與有限元素模擬結果對應性皆十分準確，此外，相比於傳統以複數條等長螺旋流道結構組成的Fano-like 消音結構具有較為狹窄的消音頻寬限制，在本研究中以不同半徑的方式設計兩組不同長度螺旋流道使其之共振與反共振頻率相互耦合，從而能將原本限制頻寬範圍之共振頻率穿透損失提高至10 dB 以上，大幅增加消音頻寬。所設計之直徑10cm 結構在截止頻率之下在573 Hz 至2026 Hz 內擁有良好的111.8%之10 dB 比例頻寬，相較於傳統Fano 消音結構提升了近兩倍的寬頻消音性能，空氣可流通截面積比例達19.2%；對於入耳式耳塞設計，將結構微型化後之直徑7mm 之結構，在547 Hz 至1872 Hz 間擁有良好的109.6%之10 dB 比例頻寬，空氣可流通截面積比例可高達36.5%，足證明此設計很好地兼顧了消音頻寬與空氣流通表現，並且所設計之二結構尺寸結構厚度都達到次波長，直徑10cm 與7mm 結構厚度依序分別為0.09λ 與0.13λ，在低頻消音結構尺寸上具有很大的優勢，並相比於多數文獻設計結構在相同的結構厚度之下，擁有著極為寬頻的特點並在空氣流通表現方面也維持良好平衡，在此之上更具有能夠因應不同應用下的調變靈活性優勢。

This study designs a low-frequency ventilated silencing structure using an equivalentcircuit model. The accuracy of this method is validated through analytical solutions, equivalent circuit simulations, and finite element simulations. Compared to conventional Fano-like silencing structures, which are composed of multiple identical-length spiral channels and have narrow silencing bandwidth limitations, this study employs spiral channels of varying radii to design two sets of different-length channels. This configuration couples their resonance and anti-resonance frequencies, thereby increasing the transmission loss at the originally bandwidth-limited resonance frequencies to above 10 dB, resulting in an unprecedentedly broad silencing bandwidth. The designed structure with a diameter of 10 cm exhibits an excellent 10 dB fractional bandwidth of 111.8%, ranging from 573 Hz to 2026 Hz, below the cutoff frequency. This represents nearly twice the broadband silencing performance compared to conventional Fano silencing structures. Additionally, the structure features an air ventilation area ratio of 19.2%. For in-ear earplug applications, the miniaturized structure with a diameter of 7 mm demonstrates a 10 dB fractional bandwidth of 109.6%, covering the range of 547 Hz to 1872 Hz, with an air ventilation area ratio of up to 36.5%. This evidence confirms that the design effectively balances silencing bandwidth and air ventilation performance. Moreover, the thickness of both designed structures is subwavelength, with the 10 cm and 7 mm diameter structures having thicknesses of 0.09 and 0.13 wavelengths, respectively. This offers a significant advantage in the dimensions of low-frequency silencing structures. Compared to most literature designs with similar structural thicknesses, this design exhibits an exceptionally wide bandwidth advantage while maintaining good air ventilation performance. Furthermore, it provides the flexibility to adapt to different application requirements.