“Resonance” phenomenon of kinematic excitation by a spherical body in a semi-infinite cylindrical vessel filled with liquid

Abstract

A semi-infinite round cylindrical cavity filled with an ideal compressible fluid is considered. It contains a spherical body located close to its end. The body performs periodic motion with a specified frequency and amplitude. The problem of determining the acoustic field of velocities (pressure) in the fluid is solved depending on the character of excitation and geometrical parameters of the system. The study uses the method of separation of variables, translational addition theorems for spherical wave functions and relationships representing spherical wave functions in terms of cylindrical ones and vice versa. Such an approach satisfies all boundary conditions and yields an exact boundary problem solution. The computations are reduced to an infinite system of algebraic equations, the solution of which with the truncation method is asserted to converge. Determining the pressure and velocity fields has shown that the system being considered has several excitation frequencies, at which the acoustic characteristics exceed the excitation amplitude by several orders. These “resonance” frequencies differ from such frequencies inherent an infinite cylindrical waveguide with a spherical body in both cases. In this case, even when the radius of a spherical radiator is small and abnormal phenomena in an infinite vessel are weak they can manifest themselves substantially in a semi-infinite vessel.