Two-channel filter by phononic plate with criss-crossed elliptical holes

Abstract

<p indent=0mm>Phononic crystals (PnCs) are a kind of synthetic composite materials with spatial periodicity. Owing to the unique properties, such as the band gaps (BGs), defect mode, wave localization, and wave beaming, PnCs have been applied in acoustic filters, vibration isolation, noise reduction, and sonar detection, attracting increasing attention in recent years. Among these useful properties, the filter characteristics of PnCs have consistently been a popular research topic. Notably, these existing works primarily focus on the multi-channel output of the same frequency, or the single-channel output of the different frequencies. Studies that investigate a multi-channel output with different frequencies, or specified frequencies, are rare. Most of a filter’s functionality is achieved through structures composed of local resonant PnCs, which usually require a more cumbersome design and more expensive costs. However, compared to local resonant PnCs, Bragg scattering PnCs are more commonly accepted in practical applications because of their simple design and easily available materials. Accordingly, this paper studies the multi-channel output of different frequencies by adopting Bragg scattering PnCs. The finite element methods (FEM) of the band structure and transmission spectrum are performed with COMSOL. The BG in the <italic>ΓX</italic> direction of the band diagram is used as the test target. Periodic plates with criss-crossed elliptical holes can provide wider BGs because of their symmetry breaking. Based on such finding, a two-channel waveguide structure consisting of three representative volume elements (RVE) of different sizes (A, B and C) is constructed, and the two-channel filtering performance is subsequently investigated by the finite element analysis. The research frequency range is set from 0 to <sc>18 kHz.</sc> By comparing three RVE’s energy band structures, we can see that the frequency range of BG of A is almost between those of B and C, with relatively small overlap BG. Such BG characteristic can be utilized for the broadband filtering application. When the elastic wave propagates in the two-channel PnC structure consisting of three different sizes, there is supposed to be three situations. (1) When the frequency range of the input excitation is between 5.15 and <sc>7.55 kHz,</sc> the elastic wave can pass through the up-channel consisting of A and B, but is forbidden to propagate through C due to the BG. (2) When the frequency range of the input excitation is between 7.55 and <sc>15.16 kHz,</sc> the wave is not allowed to propagate neither through up or down-channel because of the BG of A. (3) When the frequency falls into the range between 15.16 and <sc>18 kHz,</sc> then the down-channel formed by A and C is the only choice for the wave to pass through. According to the theoretical model, a two-channel PnC plate of acrylic material (PMMA) is fabricated to conduct the transmission experiments. The experimental data agree well with the numerical results, which indicate that the directional transmission of elastic waves within different frequency ranges in a two-channel structure can be achieved by adjusting the size of the three RVE. This paper could provide a novel approach for the application of PnCs in multi-channel filtering.