Diffraction of Sound Waves by a Periodic Array of Impedance Screens

Air-penetrating and noise-canceling constructions are required for numerous noise control issues. High ventilation performance conflicts with effective sound insulation, and vice versa. For this reason, ventilated noise barriers are currently being intensively researched and developed. One of the most popular solutions is the louvered-type barrier, whose acoustic efficiency depends on its geometric parameters as well as the acoustic properties of the louvers. One of the main challenges is optimizing the acoustic impedance of louver surfaces in order to achieve maximum reflection, absorption, or minimum transmission of sound waves. This paper proposes an analytical solution to the diffraction problem of a plane sound wave incident on a periodic array of similar thin screens with arbitrary impedance surfaces. An infinite system of linear equations is derived, and its numerical solution allows us to find the reflection and transmission coefficients. It has been shown that screens with reactive impedance are necessary to achieve maximum sound reflection. On the other hand, dissipative screens are required for minimal sound transmission. Additionally, the absorption properties of the array have been studied. It has been found that there is an optimal impedance value that provides the maximum absorption coefficient.