“Resonance” phenomenon of kinematic excitation by a spherical body in a semi-infinite cylindrical vessel filled with liquid
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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.
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- 2.Ivanov, Y.A.: Diffraction of Electromagnetic Waves on Two Bodies. Nauka i tekchnika, Minsk (1970). (in Russian)Google Scholar
- 4.Mishchenko, M.I., Travis, I.D., Lacis, A.A.: Multiple Scattering of Light by Particles. Radiative Transfer and Coherent Backscattering. Cambridge University Press, Cambridge (2006)Google Scholar
- 6.Erofeenko, V.T.: Relations between main solutions of Helmholtz and Laplace equations in spherical and cylindrical coordinates. Proc. Natl. Acad. Sci. BSSR 4, 42–46 (1972). [in Russian]Google Scholar
- 16.Kubenko, V.D., Lugovoi, P.Z., Golovko, K.G.: Method of treating of a bottomhole formation zone. The patent of Ukraine for useful model No. 65064 of 25.11.2011 (2011) [in Russian]Google Scholar
- 17.Lurton, X.: An Introduction to Underwater Acoustics: Principles and Applications. Springer, New York, London (2002)Google Scholar
- 20.Marnevskaya, L.: Diffraction of a plane scalar wave by two spheres. Sov. Phys. Acoust. 14, 356–360 (1969)Google Scholar
- 21.Brunning, J.H., Lo, Y.T.: Multiple scattering by spheres. Tech. Rep. Antenna Laboratory, University of Illinois (1969)Google Scholar
- 22.Germogenova, O.A.: The scattering of a plane electromagnetic wave by two spheres. Izvest. Acad. Nauk USSR Ser. Geofizika 4, 403–405 (1963)Google Scholar