Finding, by means of a scattered sound, the geometric parameters of a finite elastic cylinder located near the half-space border

Abstract

The solution of the inverse problem of sound diffraction on a finite circular elastic cylinder is considered. The cylinder T is located near the surface Π of acoustic half-space. The following cylinder parameters are finding according to the scattered sound field: radius, height, distance from the half-space surface, and axis orientation. The solution of the diffraction problem is conducted by expanding the area of the problem to the full space. With that an additional obstacle T′, which is a copy of T, is introduced. The additional obstacle is a mirror reflection of the original one with respect to the surface Π. In addition, a second incident wave, which corresponds to the type of the half-space boundary, is introduced. The solving is based on the linear elastic theory and the model of the small vibrations propagation in ideal fluid. In the external part of the fluid, the solution is sought analytically in the form of expansion in spherical harmonics and Bessel functions. In the ball area, which includes two balls cylinders and an adjacent layer of the fluid, the finite element method (FEM) is used. The cylinder required parameters are detected on the basis of the minimization of the norm of the vector difference () and (pjm). Where () is the vector of measured pressure values in the scattered sound field, and (pjm) is the pressure vector obtained from the theoretical solution of the diffraction problem.