A boundary-field integral formulation for nonlinear scattering of acoustic waves by deforming bodies

Sound scattering by deforming bodies is investigated through a novel nonlinear boundary-field integral formulation based on the velocity potential equation. The proposed approach applies an iterative cascade solution strategy to account for nonlinearities due to irrotational flow field generated by moving boundaries. The resulting formulation is solved numerically through a boundary element method combined with the harmonic-balance technique to capture the multi-chromatic scattered signal. The numerical investigation studies the sound scattered by a pulsating sphere impinged by a plane wave. It shows that the proposed iterative solution algorithm is able of providing convergent nonlinear scattered solution in a few iterations. The results demonstrate that fluid nonlinearities associated with the amplitudes of the sphere pulsation and the incident wave significantly affect the directivity pattern of the scattered signal.