A research and modeling of wave processes at the scattering of nonlinear acoustic waves on cylindrical bodies

Abstract

The article is devoted to the study of the scattering of nonlinear acoustic waves on cylindrical bodies. There was made a review of publications on the scattering of acoustic waves by inhomogeneities of the medium in the form of cylindrical bodies and shells. There were noted features of the small parameter method application in nonlinear acoustics. A three-dimensional model of the geometry of the problem in cylindrical coordinates was presented, nonlinear wave processes occurring between the falling plane and scattered cylindrical waves were described. The inhomogeneous wave equation is solved by the method of successive approximations of series expansion in a small parameter. An asymptotic expression for the acoustic pressure of a difference-frequency wave was obtained. A program for calculating scattering diagrams has been developed, and an algorithm for its operation is given. The acoustic pressure scattering diagram of a differential frequency wave on a rigid cylinder and its three-dimensional model are presented. The radius of convergence of the used method of expansion in a small parameter is determined.