| Summary: | This paper unprecedentedly addresses the effect of vibrations of a cylindrical structure on dynamic pressures in a compressible and incompressible fluid situation. To obtain analytical solutions, the density of the fluid is simplified as a constant, but the rates of the density with respect to time and to space are considered as a dynamic and time-dependent function. In addition, the low velocity of the vibration is taken into account so the lower order terms are negligible. According to the assumption that the vibration at the boundary of the structure behaves as a harmonic function, some interesting and new analytical solutions can be established. Both analytical solutions in the cases of the compressible and incompressible fluid are rigorously verified by the calibrated numerical simulations. New findings reveal that, in the case of the incompressible fluid, dynamic pressure at the surface of the cylindrical shell is proportional to the acceleration of the vibration, which acts like an added mass. In the case of the compressible fluid, the pressure at the surface of the cylindrical structure is proportional to the velocity of the vibration, which acts as a damping. In addition, the proportional ratio is derived as <inline-formula> <math display="inline"> <semantics> <mrow> <mi>ρ</mi> <mi>c</mi> </mrow> </semantics> </math> </inline-formula>.
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