Periodic Acoustic Structure Design Based on the Second-Order Butterworth Acoustic Filter

The paper proposes a design method of periodic acoustic structures composed of acoustic filters. Based on acoustic-electric analogy, the second-order Butterworth acoustic filter is first designed, which comprises a main pipe, a Helmholtz resonator, a short tube and an expansion cavity. Second, periodic structures are constructed by taking the acoustic filter as an original unit cell or modifying the acoustic filter to obtain a modified unit cell, and periodically arraying the unit cells along the axial direction of the main pipe. Then, influences of axial and circumferential periodic arrangements of the acoustic structures on the filtering performances are investigated, respectively. Next, multi-period acoustic structure models are established and their transmission losses are simulated and compared. Finally, low-frequency broadband periodic acoustic structures are constructed. The research shows that, the axial period of the acoustic structure composed of the original unit cell has no influence on the resonance frequency of acoustic structure, but contributes to transmission losses and filtering frequency ranges; the increase in the circumferential period can result in a shift in the resonance frequency towards high frequencies and a great increment in the filtering frequency bandwidth; combining unit cells with different resonance frequencies can significantly widen the filtering frequency range; low-frequency broadband performances of the acoustic structure can be implemented by combining unit cells with different resonance frequencies and increasing axial and circumferential periods of the acoustic structures.