Reconstruction of the Acoustic Field Radiated Directly from a Vibrating Structure Located Near a Pressure-Release Boundary

Abstract

Near-field acoustical holography is a powerful tool for reconstructing the three-dimensional acoustic field radiated from a vibrating structure located in free space, but it is not applicable when the source is in a half space bounded by a reflecting boundary. This paper develops a method based on half-space spherical wave function expansion for reconstructing the acoustic field radiated directly from a source located near a pressure-release boundary. First, the series of half-space spherical wave basis functions satisfying the pressure-release boundary condition is formulated. Then the acoustic field in a half space is modeled using an expansion in this basis. The expansion coef?cients are determined by solving an overdetermined linear system of equations, obtained by matching this expansion to the measured half-space acoustic pressures. The pressures radiated directly from the source can finally be reconstructed using the free-space spherical wave function expansion with the obtained expansion coefficients. Numerical simulation examples of a vibrating plate located in water near a pressure-release boundary are demonstrated to validate the proposed method. The effects of various parameters, such as the acoustic frequency, the distance between the source and boundary, and the orientation of the source surface, on the reconstruction accuracy are examined.