Slow-sound propagation in aerogel-inspired hybrid structure with backbone and dangling branch

The slow sound wave effect is generally considered to occur in a narrow resonant frequency region or a complex coiling-up space. By numerical simulation method, this research proposes a simple deep subwavelength (less than 1/570 wavelength) structure inspired by aerogels, containing dead-ends attached to the backbone, which can produce a large non-resonant acoustic delay. The results show that the delay is induced by the exchange of acoustic energy at the dangling branches, and intrinsically influenced by the mass ratio of dead-ends to backbone particles. Interestingly, the delay is accumulated along the propagation, which could further slowdown the sound. Similar to aerogels, the propagation velocity in the hybrid structure shows a scaling law with the proportion of backbone particles, whose minimum (with the thickness less than 1/10 wavelength) is as low as 47.3% of that in the structure without dead-ends. The results indicate that the dangling branches show a definite negative effect on the fast propagation, and the sound speed may decrease accompanied with the density in a porous material with dead-ends. This work could facilitate the understanding of the non-resonant slow sound behaviors of the aerogels, and the proposed structure can be designed as basic material for lighter, thinner, and more broadband acoustic metamaterials.