Sound radiation and suppression of an unbaffled long enclosure using Helmholtz resonators

Theoretical, numerical, and experimental investigations are presented to predict and suppress the noise radiated from monopole point sources inside an unbaffled long enclosure including the ground. First, a mathematical model is established to calculate the acoustical fields. The modal superposition method is adopted to express the sound pressure inside the long enclosure, while the radiated noise is described by applying the Wiener-Hopf (W-H) technique. Subsequently, the interior and exterior acoustical fields are coupled using the continuity equations of sound pressure and particle velocity at the opening. After that, the theoretical model is validated through the finite element method. The formation mechanisms of sound peaks, lobes, the shadow, and illuminated zones are explained from the perspective of mode theory. Meanwhile, Helmholtz resonators (HRs) are proposed to control the dominant modal responses at the opening so that the radiated noise near the resonant frequencies is attenuated. Afterwards, the relationship between acoustical modes and radiation patterns is analyzed. The HR locations, optimized to reduce the radiated noise, are obtained. Besides, the influences of different noise sources on the radiated sound field are explored. Finally, a quasi-two-dimensional experiment is carried out to verify the proposed model and examine the feasibility of HRs in suppressing the noise radiated from an unbaffled long enclosure including the ground. This study facilitates the understanding of physics behind the sound radiation phenomenon and provides new insights into noise control strategies.