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• Sound radiation from an unbaffled long enclosure with the ground is modeled analytically. • Preliminary experiment and convergence checks are carried out. • Numerical simulations are conducted to validate the model and examine its effectiveness in dealing with big acoustical domain. • Formation mechanisms of the radiation directivity patterns are investigated. • Potential noise control strategies for long enclosures using acoustic liners are introduced. A theoretical model is presented for the prediction of sound radiated from a semi-infinite unbaffled long enclosure with the ground. This geometrical arrangement forms an idealized representation of traffic tunnels and railway stations where noise propagates inside the long enclosures and radiates to the outside through the openings. Despite the fact that the model described here applies only to idealized situations, it contains essential elements of realistic configurations which are conducive to understanding the physics of the sound radiation phenomenon and significant for the proposal of appropriate noise control strategies. First of all, by expressing the sound field in terms of the superposition of propagating modes inside the long enclosure and adopting the Fourier transform in other regions, the intractable boundary value problem in the natural domain is reduced to a scalar modified Wiener-Hopf (W-H) equation of the second kind in the spectral domain. Then, its solution is obtained using the standard factorization and decomposition procedures, and the radiated sound field is attained through the inverse Fourier transform which involves a contour integral that can be evaluated approximately via the saddle point method. After that, the finite element method (FEM) is adopted to validate the model. Far-field directivity patterns of the radiated sound fields are presented. Finally, the properties of the sound fields both inside and outside three enclosures with different boundary conditions are analyzed, based on which, potential noise reduction methods by using acoustic liners are discussed. [ABSTRACT FROM AUTHOR]

• The noise radiated from an unbaffled long enclosure is predicted and controlled. • Interaction between Helmholtz resonators and the acoustical field is illustrated. • Formation and suppression mechanisms of sound pressure field are investigated. • Quasi-two-dimensional experiments are performed to validate the theoretical model. 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. [ABSTRACT FROM AUTHOR]