Kinematic Excitation of Fluid in an Infinite Cylindrical Cavity with Two Spherical Bodies

There are two spherical bodies on the axis of an infinite cylindrical cavity filled with an ideal compressible fluid. The surface of one of them is undergoing periodic radial oscillations with a specified frequency and amplitude, while the other body is rigid. This research addresses the determination of the hydrodynamic characteristics of the acoustic medium and the resultant radiation force acting on the rigid body, depending on the oscillator excitation frequency and the geometric parameters of the mechanical system. Employing the methods of separation of variables and translational addition theorems, we have reduced the problem to an infinite system of algebraic equations, which is solved by the truncation method. Numerical experiments have demonstrated that, as in the case of oscillations near the rigid end of a cylindrical cavity, there are certain frequencies at which the hydrodynamic characteristics of the medium and the radiation force acting on the rigid sphere increase manifold. At the principal “conditionally resonant” frequency, the maximum pressure is observed at points external to the distance between the centers on the axis of the cylindrical cavity. The radiation force peaks when the vibrating body is larger than the passive one, and the force is directed to increase the distance between their centers.