Modeling of Focused Acoustic Field of a Concave Multi-annular Phased Array Using Spheroidal Beam Equation

A theoretical model of focused acoustic field for a multi-annular phased array on concave spherical surface is proposed. In this model, the source boundary conditions of the spheroidal beam equation (SBE) for multi-annular phased elements are studied. Acoustic field calculated by the dynamic focusing model of SBE is compared with numerical results of the O'Neil and Khokhlov-Zabolotskaya-Kuznetsov (KZK) model, respectively. Axial dynamic focusing and the harmonic effects are presented. The results demonstrate that the dynamic focusing model of SBE is good valid for a concave multi-annular phased array with a large aperture angle in the linear or nonlinear field. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)