Abnormal Frequencies in a Semi-Infinite Cylindrical Vessel Filled with a Fluid and Dynamically Excited by a Spherical Oscillator

A semi-infinite circular cylindrical cavity filled with a compressible ideal fluid and containing a spherical body near its end is considered. The body surface radiates periodic pressure at given frequency and amplitude. The hydrodynamic characteristics of the system depending on the frequency of excitation and geometrical parameters are determined. The method of separation of variables, the translational addition theorems for spherical wave functions, and the expressions of spherical wave functions in terms of cylindrical ones are applied. This approach allows satisfying all the boundary conditions and finding the exact solution of the boundary-value problem. An infinite system of algebraic equations is solved. Its solution found by the truncation method is stated to converge. The determination of the pressure and velocity fields shows that the system has a number of excitation frequencies at which the acoustic characteristics exceed the amplitude of excitation by several orders of magnitude. These abnormal frequencies differ from the frequencies typical for an infinite cylindrical cavity with a spherical body. Even if the radius of the spherical oscillator is small and the abnormal phenomena in the infinite vessel are weak, they can appear strong in a semi-infinite vessel.