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Analytical study of exciting forces acting on a rigid sphere in a fluid with flexible base surface
Author(s) -
Das Lopamudra,
Mohapatra Smrutiranjan
Publication year - 2020
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.202000052
Subject(s) - free surface , multipole expansion , wavenumber , diffraction , mechanics , surface tension , classical mechanics , surface wave , surface (topology) , physics , flexural rigidity , optics , geometry , mathematics , quantum mechanics , thermodynamics
A three‐dimensional problem of wave diffraction by a neutrally buoyant immersed sphere in a fluid having a flexible bottom surface is studied within the framework of linear potential theory. The flexible base surface of the fluid is modelled as a narrow flexible sheet and it follows on the Euler‐Bernoulli bar condition. The impact of the free‐surface tension is ignored. In such circumstances, the time‐harmonic proliferating waves with two distinct wavenumbers propagate in the fluid for any specific frequency. The proliferating waves having higher wavenumber spread along the flexible bottom surface, say, flexural mode and the proliferating waves having smaller wavenumber spread along the free‐surface of the fluid, say, free‐surface mode. By applying the multipole technique, we acquire the analytical solution for the issue of wave diffraction by a rigid sphere immersed in a fluid having flexible bottom surface. This technique reduces the boundary value problem to the solution of an infinite number of algebraic linear non‐homogeneous equations which can easily resolve numerically by any conventional technique. The exciting forces acting on the submerged sphere along the horizontal and vertical directions in the fluid are estimated in the case of both the flexural and free‐surface wave modes. These forces are plotted graphically for several immersion depths of the rigid sphere and the rigidity factors of the flexible base surface of the fluid.