A generalized model for space-coiling resonators

An ultra-thin absorber with a coiling chamber can realize a total sound absorption in an extremely low frequency. This can be regarded as the extreme case of a resonator with an extended partition. A coiled partition extends into a cavity, paving an elongated path and hence tuning the control band into lower frequency. To theoretically investigate the performance evolution during this process, a theoretical model is proposed in this paper, which is then validated by numerical simulations as well as experiments. In fact, this theory links the space-coiling resonator to the conventional Helmholtz resonator and the quarter-wavelength tube, which are two extreme cases representing no partition and full partition, respectively. It turns out that, by extending the partition, the working wavelength can reach approximately 26 times the side length of the original cavity, revealing the effective capability of low frequency control via a small unit.