An inverse patch transfer function method based on the Green’s function in free field

The inverse patch transfer function (iPTF) method is one of the nearfield acoustic holography (NAH) methods to identify the normal velocities of the sound sources in non-anechoic environments. The Green’s function with Neumann boundary conditions in the virtual cavity is required to obtain the impedance matrix. An approach to construct the Green’s function satisfying the Neumann boundary conditions is to expand it over the acoustic modes of the interior problems, which involves volume modeling of the cavity and modal analysis with the finite element method. To alleviate the complicated construction of the traditional iPTF, a more natural way is proposed to achieve the impedance matrix with the aid of the Green’s function in the free field and the boundary element method (BEM). It is proved that the impedance matrix is equivalently constructed by the proposed method but only demands one simple universal approach based on BEM. Simulations are designed to reconstruct the local normal velocities of a hollow cylinder which is driven by a concentration force, and a coherent disturbing source is placed besides the cylinder to introduce noise to the reconstruction process. The influence factors, such as the frequencies and signal-to-noise ratios are investigated, and the reconstructed results show that the proposed method could reconstruct the velocities accurately.