Multiple broad bandgaps soundproofing for sectoral labyrinthine metamaterials

Abstract

Acoustic metamaterials are notable for their light weight and exceptional ability to control low-frequency sounds, making them ideal for applications requiring both soundproofing and ventilation. In this paper, metamaterials with various labyrinthine structures were designed using the space-coiling strategy, featuring sectoral labyrinthine resonators arranged in a circular pattern around a central circular passage for airflow. The noted metamaterials were categorized into four levels based on the use of different sectoral resonators. In level-1, all resonators were identical, while in levels 2, 3, and 4, two, three, and four different resonators were used, respectively. The sound insulation performance was evaluated through Sound Transmission Loss (STL) test using an impedance tube, as well as numerical simulations. The results indicated that the development of level-1 geometric configurations led to a shift in the STL curves toward higher frequencies and an increase in the width of the first bandgap. The widest observed bandgap was in the frequency range of 937–2078 Hz, covering approximately 55 % of the targeted frequency range (below 2000 Hz). With the introduction of higher-level configurations, multiple bandgaps, along with several peaks, appeared in the STL spectra. These multiple bandgaps result from Fano resonances generated by the various sectoral resonators. Fano resonances are inversely related to the effective length of each sectoral resonator, allowing for tuning to achieve different sound insulation performances. The maximum frequency coverage was approximately 50 % for level-2, around 40 % for level-3, and about 30 % for level-4.