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.
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References
Guz, A.N., Kubenko, V.D., Cherevko, M.A.: Diffraction of Elastic Waves. Naukova Dumka, Kyiv (1978). (in Russian)
Ivanov, Y.A.: Diffraction of Electromagnetic Waves on Two Bodies. Nauka i tekchnika, Minsk (1970). (in Russian)
Martin, P.A.: Multiple scattering and scattering cross sections. J. Acoust. Soc. Am. 143(2), 995–1002 (2018). https://doi.org/10.1121/1.5024361
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)
Kubenko, V.D.: Diffraction of steady waves at a set of spherical and cylindrical bodies in an acoustic medium. Int. Appl. Mech. 23, 605–610 (1987)
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]
Friedman, B., Russek, O.: Addition theorems for spherical waves. Quart. Appl. Math. 12, 13–23 (1954)
Olsson, S.: Transmission and reflection of elastic waves by a spherical obstacle in an infinite circular cylindrical rod. Q. J. Mech. Appl. Math. 47, 583–606 (1994). https://doi.org/10.1093/qjmam/47.4.583
Linton, C.M.: Acoustic scattering by a sphere in a circular cylindrical waveguide. Q. J. Mech. Appl. Math. 48, 211–235 (1995). https://doi.org/10.1093/qjmam/48.2.211
Kubenko, V.D., Dzyuba, V.V.: Dynamic interaction of an oscillating sphere and an elastic cylindrical shell filled with a fluid and immersed in an elastic medium. Int. Appl. Mech. 40, 1002–1011 (2004). https://doi.org/10.1007/s10778-005-0004-9
Lee, D.-S.: Scattering of torsional waves by a spherical cavity in a long circular elastic cylinder. Acta Mech. 164, 47–59 (2003). https://doi.org/10.1007/s00707-003-0006-9
Kubenko, V.D., Dzyuba, V.V.: Resonant phenomena in axisymmetric hydroelastic systems from cylindrical shell with inclusion under presence of internal compressible liquid and external elastic medium. J. Fluids Struct. 22(4), 577–594 (2006)
Kubenko, V.D., Dzyuba, V.V.: Diffraction of a plane acoustic wave by a rigid sphere in a cylindrical cavity: an axisymmetric problem. Int. Appl. Mech. 45(4), 424–432 (2009). https://doi.org/10.1007/s10778-009-0195-6
Hasheminejad, S.M., Hosseini, H.: Nonaxisymmetric interaction of a spherical radiator in a fluid-filled permeable borehole. Int. J. Solids Struct. 45, 24–47 (2008). https://doi.org/10.1016/j.ijsolstr.2007.07.008
Zhuk, A.P., Kubenko, V.D., Zhuk, Y.A.: Acoustic radiation force on a spherical particle in a fluid-filled cavity. J. Acoust. Soc. Am. 132(4), 2189–2197 (2012). https://doi.org/10.1121/1.4739440
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]
Lurton, X.: An Introduction to Underwater Acoustics: Principles and Applications. Springer, New York, London (2002)
Gaunaurd, G.C., Huang, H.: Acoustic scattering by a spherical body near a plane boundary. J. Acoust. Soc. Am. 96, 2526–2536 (1994). https://doi.org/10.1121/1.410126
Gaunaurd, G.C., Huang, H., Strifors, H.C.: Acoustic scattering by a pair of spheres. J. Acoust. Soc. Am. 98, 495–507 (1995). https://doi.org/10.1121/1.414447
Marnevskaya, L.: Diffraction of a plane scalar wave by two spheres. Sov. Phys. Acoust. 14, 356–360 (1969)
Brunning, J.H., Lo, Y.T.: Multiple scattering by spheres. Tech. Rep. Antenna Laboratory, University of Illinois (1969)
Germogenova, O.A.: The scattering of a plane electromagnetic wave by two spheres. Izvest. Acad. Nauk USSR Ser. Geofizika 4, 403–405 (1963)
Wood, R.W.: Anomalous diffraction gratings. Phys. Rev. 48, 928–933 (1935)
Morse, PhM, Feshbach, H.: Methods of Theoretical Physics. Pt. I. McGraw-Hill, New York (1953)
Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. National Bureau of Standards, Washington (1964)
Cruzan, O.R.: Translation addition theorem for spherical wave functions. Q. Appl. Math. 20(1), 33–40 (1962)
Makovsky, D.W.: Configurations analysis of radiative scattering for multiple sphere. Proc. R. Soc. Lond. A. 433, 599–614 (1991). https://doi.org/10.1098/rspa.1991.0066
Lentz, W.J.: Generating Bessel functions in Mie scattering calculations using continued fractions. Appl. Opt. 15(3), 668–671 (1976). https://doi.org/10.1364/AO.15.000668
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Kubenko, V.D., Yanchevskyi, I.V. “Resonance” phenomenon of kinematic excitation by a spherical body in a semi-infinite cylindrical vessel filled with liquid. Acta Mech 230, 1009–1025 (2019). https://doi.org/10.1007/s00707-018-2310-4
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DOI: https://doi.org/10.1007/s00707-018-2310-4