Abnormal Frequencies in a Semi-Infinite Cylindrical Vessel Filled with a Fluid and Dynamically Excited by a Spherical Os
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International Applied Mechanics, Vol. 56, No. 2, March, 2020
ABNORMAL FREQUENCIES IN A SEMI-INFINITE CYLINDRICAL VESSEL FILLED WITH A FLUID AND DYNAMICALLY EXCITED BY A SPHERICAL OSCILLATOR* V. D. Kubenko1 and I. V. Yanchevskii2
A semi-infinite circular cylindrical cavity filled with a compressible ideal fluid and containing a spherical body near its end is considered. The body surface radiates periodic pressure at given frequency and amplitude. The hydrodynamic characteristics of the system depending on the frequency of excitation and geometrical parameters are determined. 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 ones are applied. This approach allows satisfying all the boundary conditions and finding the exact solution of the boundary-value problem. An infinite system of algebraic equations is solved. Its solution found by the truncation method is stated to converge. The determination of the pressure and velocity fields shows that the system has a number of excitation frequencies at which the acoustic characteristics exceed the amplitude of excitation by several orders of magnitude. These abnormal frequencies differ from the frequencies typical for an infinite cylindrical cavity with a spherical body. Even if the radius of the spherical oscillator is small and the abnormal phenomena in the infinite vessel are weak, they can appear strong in a semi-infinite vessel. Keywords: semi-infinite cylindrical vessel, compressible fluid, spherical oscillator, abnormal phenomena Introduction. The interaction of acoustic, elastic, and electromagnetic waves with reflecting bodies in a infinite space has been the subject of numerous studies for more than a century and described in a number of monographs and articles. In most cases, systems of like bodies were considered, such as cylindrical or spherical bodies [5, 7, 18, 27, 29]. The analytic approach to the solution of problems for such systems involves the separation of variables in the general solution of the wave equations in the appropriate coordinate systems and the use of translation summation theorems to express wave functions in the coordinates of each body of the system. Numerical methods and methods of boundary integral equations are used as well. Diffraction problems for bodies bounded by unlike surfaces, such as cylindrical and spherical, have been studied to a much lesser degree. Noteworthy is the approach outlined in [19] where the expressions for cylindrical wave functions in terms of spherical functions [6, 19] and the summation theorems for cylindrical wave functions and, separately, for spherical functions [7, 13] were used to develop a method to study the diffraction of stationary acoustic waves by systems of unlike obstacles by reducing the initial boundary-value problem to an infinite systems of algebraic equations with improper integrals as coefficients.
1
S. P. Timoshenko Institute of Mechanics, National Academy of S
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