Acoustic eigen oscillations near thin-walled obstacles in an annular cylindrical channel

The articlepresents the analytical and numerical investigations of acoustic eigen oscillations near thin-walled obstacles in a uniform annular cylindrical channel. Acoustical eigen oscillations are described with the help of the Neumann problem for the Laplace operator. Using representation of symmetry groups in the solution space, it is shown that for the large class of thin-walled obstacles in annular channels there always exists a pure point spectrum that is embedded into a continuous spectrum of a self-adjoint extension of the Laplace operator appropriate to the homogeneous Neumann problem. Also we present the results on dependence of eigenfrequencies on the geometrical parameters of thin-walled obstacles in a uniform annular cylindrical channel as well as on the form of eigenfunctions. The influence is also addressed of the geometric characteristics of oscillations on the frequencies, quantity and and form of eigen oscillations.