Dynamic characteristics of an ideal compressible fluid excited by a spherical segment in a cylindrical cavity

The manuscript presents solving of axisymmetric problem of determining the velocity potential of an ideal compressible fluid in an infinite circular cylindrical cavity with a spherical segment, vibrating according to a given law. The solution of the problem is based on the principle of superposition of potential functions, on the redevelopment of partial solutions of the Helmholtz equation, written in cylindrical (spherical) coordinates, in spherical (cylindrical) wave functions, respectively, which made it possible, also using the theorems of addition of cylindrical functions, to represent the full potential of fluid velocities in both spherical and cylindrical coordinate systems. Satisfying the boundary conditions on the surface of the spherical segment and on the cylindrical surface, the problem is reduced to solving an infinite system of algebraic equations for the coefficients of the expansion of the spherical and cylindrical components of the desired potentials. Numerical experiments allow us to identify the so-called "resonance-like frequencies", at which the hydrodynamic parameters increase significantly. The results of the work can be used in the design of acoustic sensors and arrays based on spherical caps.