A semi-infinite circular cylindrical cavity filled with an ideal compressible fluid and containing a spherical body located near its end is considered. A plain acoustic wave propagates along the axis of the cavity. The hydrodynamic characteristics of the system are determined depending on the frequency of the plane wave and the geometrical parameters. 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 functions are applied. This approach allows satisfying all the boundary conditions and obtaining the exact solution of the boundary problem. The calculations are reduced to solving an infinite system of algebraic equations. Determining the pressure and velocity fields shows that the system has a number of frequencies at which the hydrodynamic characteristics can increase substantially. These abnormal frequencies differ from the frequencies of an infinite cylindrical cavity with a spherical body. Thus, the developed approach can detect anomalous features of the diffraction of a plane wave due to the influence of the end wall.
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References
H. Bateman and A. Erdelyi, Higher Transcendental Functions, Vol. 1, McGraw-Hill, New York (1953).
H. Bateman and A. Erdelyi, Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York (1953).
A. N. Guz and V. T. Golovchan, Diffraction of Elastic Waves in Multiply Connected Bodies [in Russian], Naukova Dumka, Kyiv (1972).
A. N. Guz, V. D. Kubenko, and M. A. Cherevko, Diffraction of Elastic Waves [in Russian], Naukova Dumka, Kyiv (1978).
V. T. Erofeenko, “Relation between the fundamental solutions of the Helmholtz and Laplace equations in cylindrical and spherical coordinates,” Izv. AN BSSR, Ser. Fiz.-Mat. Nauk., No. 4, 42–46 (1972).
E. A. Ivanov, Diffraction of Electromagnetic Waves by Two Bodies [in Russian], Nauka i Tekhnika, Minsk (1968).
V. D. Kubenko, P. S. Lugovyi, and K. G. Golovko, Method of Treatment of the Bottomhole Zone [in Ukrainian], Utility Model Patent Ukraine No. 65064 of November 25, 2011.
P. M. Morse and H. Feshbach, Methods of Theoretical Physics, McGraw–Hill, New York (1953).
S. M. Hasheminejad and E. K. Miri, “Dynamic interaction of an eccentric multipole cylindrical radiator suspended in a fluid-filled borehole within a poroelastic formation,” Acta Mechanica Sinica, 23, 399–408 (2007).
S. M. Hasheminejad and M. Hosseini, “Nonaxisymmetric interaction of a spherical radiator in a fluid-filled permeable borehole,” Int. J. Solids Struct., 45, No. 1, 24–47 (2008).
V. D. Kubenko and I. V. Yanchevskii, “Abnormal frequencies in semi-infinite cylindrical vessel filled with a fluid and dynamically excited by a spherical oscillator,” Int. Appl. Mech., 56, No. 2, 141–155 (2020).
V. D. Kubenko and I. V. Yanchevskyi, “‘Resonance’ phenomenon of kinematic excitation by a spherical body in a semi-infinite cylindrical vessel filled with liquid,” Acta Mechanica, 230, No. 3, 1009–1025 (2019).
P. A. Martin, “Multiple Scattering Interaction of Time-harmonic Waves with N Obstacles,” Encyclopedia of Mathematics and Its Applications, 107, Cambridge: Cambridge University Press (2006).
M. I. Mishchenko, I. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles. Radiative Transfer and Coherent Backscattering, Cambridge University Press, Cambridge (2006).
Y. H. Pao and C. C. Mow, Diffraction of Elastic Waves and Dynamic Stress Concentrations, Crane, Russak & Co., New York (1973).
J. Shi, X. Zhang, R. Chen, and X. Zhang, “Acoustic radiation force of a solid elastic sphere immersed in a cylindrical cavity filled with ideal fluid,” Wave Motion, 80, 37–46 (2018).
J. Shi, S. Li, Y. Deng, X. Zhang, and G. Zhang, “Analysis of acoustic radiation force on a rigid sphere in a fluid-filled cylindrical cavity with an abruptly changed cross-section,” J. Acoust. Soc. America, 147, 516–520 (2020).
R. W. Wood, “Anomalous diffraction gratings,” Phys. Rev., 48, 928–933 (1935).
A. P. Zhuk, V. D. Kubenko, and Y. A. Zhuk, “Acoustic radiation force on a spherical particle in a fluid-filled cavity,” J. Acoust. Soc. America, 132, 2189–2197 (2012).
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This study was sponsored from the National Research Foundation of Ukraine (Project 2020.02/0112 Diffraction Processes and Radiation Forces in Bounded Hydroelastic Systems).
Translated from Prykladna Mekhanika, Vol. 59, No. 2, pp. 3–18, March–April 2023.
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Kubenko, V.D., Yanchevs’kyi, I.V., Zhuk, Y.O. et al. Hydrodynamic Characteristics of a Plane Wave Interacting with a Spherical Body in a Semi-Infinite Cylindrical Cavity Filled with a Compressible Fluid. Int Appl Mech 59, 131–144 (2023). https://doi.org/10.1007/s10778-023-01207-z
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DOI: https://doi.org/10.1007/s10778-023-01207-z