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In this paper, low-frequency band-gaps (BGs) in a phononic crystal (PC) thin plate with periodic spiral resonators are investigated numerically and experimentally. The formation mechanisms of the BGs in the proposed structure are explained based on the modal analysis. We find that the interaction between the local resonances and the traveling wave modes in the plate is responsible for the formation of the BG in low-frequency range. This interaction strength greatly affects the bandwidth of the BG, of which the lower edge depends on the corresponding local resonance frequency. It is shown that the out-of-plane BG can be modulated by changing the geometrical parameters. The proposed PC plate is demonstrated to possess a broad out-of-plane BG in low-frequency range from 42 Hz to 150 Hz, by combining the numerical calculations with experimental measurements. The structure design and its results provide an effective way for phononic crystals to obtain broad BGs in low-frequency range, which has potential applications in the low-frequency vibration and noise reduction.
Zhang et al. (Sun,) studied this question.