The effect of neighboring bodies on the vortex-excited response of a structure

All major Civil Engineering structures, be they buildings, bridges, or even off shore risers and conductor pipes are continuously acted upon by fluid forces. For slender structures, the fluid structure interaction is a critical factor in the dynamic response. In some instances, this fluid-structure coupling can result in a resonant structural condition yielding severe structural displacements, which in turn may lead to failure of the structure.In modern structural design, tall slender structural components such as cooling towers, chimneys, cylindrical tanks and bridge pylons may exhibit large deflections or unstable oscillations due to wind forces: the presence of a fixed bluff body in the path of a uniform incident fluid flow forces it to separate into two shear layers that become the sites for the build up of vorticity. The vorticity in the shear layers then develops as they separate from the body into the familiar vortex street. This low-pressure wake creates large lift forces on bodies located in it, and for flexible bodies the problem becomes further complicated by the interaction between the dynamics of the body and the flow field, creating an aeroelastic phenomenon.Vortex-excited oscillations of bluff structures are one of the important problems in wind engineering. If one of the natural frequencies of the structural system is close to the vortex shedding frequency, and damping of the system is low, self-excited vibrations can be induced. Also the large amplitude vibrations of the system may influence the surrounding flow pattern. This can lead to non-linear interaction between the flow and the system\u27s motion. And when a body is immersed in the wake of another body this additional buffeting force, due to the vortices shed from the upstream structure, magnifies the amplitude of vibration of the downstream structure with the flow pattern gaining in complexity. The vortex-induced vibration occurs around the wind speed where the periodic vortex-shedding frequency locks-in with one of the natural frequencies of the structure. When this detuning state persists over a considerable period of time, fatigue stresses become predominant which then may lead to structural damage and even failure.The model proposed for the examination of the interference phenomenon is of the coupled wake-oscillator type consisting of the equation of motion coupled with the self-limiting type Van der Pol oscillator equation. The equation of motion contains a magnification term, which is the innovative addition in the current model. This term was established based on the experimental work of Bishop and Hassan where it was observed that for a cylinder subjected to fluid forces, the lift force experienced by the cylinder was proportional to the amplitude of vibration. Since it has been established by various works that the lift response of a structure is inversely proportional to its Scruton number, the lift force acting on a structure can then be taken as proportional to the inverse of the Scruton number. So for two flexible structures consisting of different structural parameters and acting in tandem with a wind flow, the buffeting force experienced by the downstream structure can be extrapolated by using the lift force of the upstream structure, along with the ratio of the Scruton\u27s numbers for the two structures.The model developed is semi-empirical, and therefore relies on experimental results for the determination of introduced constants