Analytical Modelling of Fluid-Structure Interaction

Abstract

The activities of humans in the marine environment are on a steady rise; this trend follows the exposure of offshore structures and vessels to harsh environmental conditions. On the other hand, there is continuous demand for lighter, faster and more efficient vessels. Technological advancement in composite materials and better design methods invariably leads to more sophisticated computational tools. In these tools, the inherent flexibility of the structure is involved in the calculation of its
loading and response – introducing the aspect of fluid-structure interaction. However, more than fluid-structure interaction, hydroelasticity which is a subset of fluid-structure interaction allows for deformation of the structures due to fluid. Current industry practice neglects these deformations and all structures are designed as rigid bodies. These practices lead to overestimation of the frequency which translates to the mass and how stiff the structure is. Design based on hydroelasticity
allows for knowing the true behaviour of the structure; thus, a coupling of fluid and structure yields a true appreciation of these designs. The objective of this study is to formulate and solve analytically the coupling phenomenon behind fluid-structure interaction. An experiment designed by Lampros Rizos in 2016 which modelled fluid-structure interaction consisted of a set-up with a cylinder immersed in a larger cylindrical tank. The immersed cylinder having a flexible circular membrane (structure) located at its bottom. The cylinders were filled with non-viscous liquid and exhibited free surface. The designed experiment was decoupled and a systematic build up in understanding the dynamics of all components – structure and fluid were solved. Firstly, the dynamics of the structure when dry (In vacuo) was idealized in 2-D and 3-D. Secondly, the system was coupled and solved
in 2-D and 3-D when structure is located at the top and bottom of a single cylinder individually. The use of a series solution: Fourier-Cosine and Fourier-Bessel series solutions were used for 2-D and 3-D cases respectively. Along with these series solutions, the fluid governing equations were employed to solve for the coupled frequencies. Lastly, the entire submerged structure was analysed and solved. The hydroelastic or coupled frequencies and vibration patterns are determined for lower angular and radial modes for which the influences of various parameters are investigated. A trend was observed – that for lower modes, the hydroelastic frequencies are lower than individual membrane natural frequencies at low frequencies. At higher frequencies, the coupling effects are larger making the coupled frequency higher than uncoupled frequencies. There is a strong relationship between the tension of the membrane and the hydroelastic frequencies. An increase in the tension causes an increase in the hydroelastic frequencies. Also, the hydroelastic frequencies increase as the fluid depth increases. More so, the increase in fluid depth tends to converge towards the uncoupled fluid free-surface frequency. The comparison of the analytical solution with experimental and numerical solutions does not match perfectly and thus, further works to improve this study are recommended.