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.