Analysis of noise attenuation through soft vibrating barriers: an analytical investigation

Mohammed Alkinidri; Sajjad Hussain; Rab Nawaz; Mohammed Alkinidri; Sajjad Hussain; Rab Nawaz

doi:10.3934/math.2023918

AIMS Mathematics

2023, Volume 8, Issue 8: 18066-18087. doi: 10.3934/math.2023918

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Research article

Analysis of noise attenuation through soft vibrating barriers: an analytical investigation

1.
King Abdulaziz University, College of Science & Arts, Department of Mathematics, Rabigh, Saudi Arabia
2.
School of Qilu Transportation, Shandong University, Jinan 250061, China
3.
Center for Applied Mathematics and Bioinformatics (CAMB), Gulf University for Science and Technology, Hawally 32093, Kuwait

Received: 19 March 2023 Revised: 22 April 2023 Accepted: 27 April 2023 Published: 25 May 2023
MSC : 32W50, 35M12, 35Q35, 76Q05

In this article, the impact of fluid flow and vibration on the acoustics of a subsonic flow is examined. Specifically, it focuses on the noise generated by a convective gust in uniform flow that is scattered by a vibrating plate of limited size. The study analyzes the interaction between acoustics and structures by considering the scattering of sound waves by a soft finite barrier. To achieve this, the Wiener-Hopf technique is utilized for the analytical treatment of the acoustic model. The approach involves performing temporal and spatial Fourier transforms on the governing convective boundary value problem, then formulating the resulting Wiener-Hopf equations. The product decomposition theorem, an extended version of Liouville's theorem, and analytic continuation are employed to solve these equations. Finally, the scattered potential integral equations are computed asymptotically. This study can be significant for understanding the acoustic properties of structures and how they interact with fluid flow in subsonic environments, which could have applications in fields such as aerospace engineering, noise reduction, and structural acoustics.
- noise control,
- vibrating barrier,
- Wiener-Hopf technique,
- asymptotic method
Citation: Mohammed Alkinidri, Sajjad Hussain, Rab Nawaz. Analysis of noise attenuation through soft vibrating barriers: an analytical investigation[J]. AIMS Mathematics, 2023, 8(8): 18066-18087. doi: 10.3934/math.2023918

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Abstract

In this article, the impact of fluid flow and vibration on the acoustics of a subsonic flow is examined. Specifically, it focuses on the noise generated by a convective gust in uniform flow that is scattered by a vibrating plate of limited size. The study analyzes the interaction between acoustics and structures by considering the scattering of sound waves by a soft finite barrier. To achieve this, the Wiener-Hopf technique is utilized for the analytical treatment of the acoustic model. The approach involves performing temporal and spatial Fourier transforms on the governing convective boundary value problem, then formulating the resulting Wiener-Hopf equations. The product decomposition theorem, an extended version of Liouville's theorem, and analytic continuation are employed to solve these equations. Finally, the scattered potential integral equations are computed asymptotically. This study can be significant for understanding the acoustic properties of structures and how they interact with fluid flow in subsonic environments, which could have applications in fields such as aerospace engineering, noise reduction, and structural acoustics.

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