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Response of a flexible marine column to base excitation Vernon, Thomas A.


The displacement response of a flexible, surface-piercing cylinder subjected to a unidirectional base motion is considered in this study. Laboratory experiments have been performed with a circular, fixed-base model using sinusoidal and scaled seismic input motion. Sinusoidal tests were designed to investigate the dependence of cylinder tip response on the ratio of base motion frequency to cylinder natural frequency and base displacement amplitude, for a fixed water depth, inertia ratio and damping ratio. Further tests with a base motion corresponding to past earthquake records were then used to determine the cylinder's response to seismic excitation. The sinusoidal test results are compared with predictions derived from analyses of the motion in terms of the first and second undamped mode shapes of a cantilever beam. The Morison equation is used to estimate hydrodynamic loads in this formulation, and three treatments of the drag term in the equation of motion are considered: neglect of drag, drag linearization and retention of the complete nonlinear form. A closed-form solution for the former two approximations is developed, and a numerical approach is adopted for the complete nonlinear formulation. The numerical method is used to predict the response of the column to seismic input. The dependence of cylinder tip displacement on frequency ratio and base motion amplitude follows predictable patterns of dynamic response. Peak amplitudes occur at resonance and increase with base motion amplitudes. However, this relationship is not linear because of the damping contribution of nonlinear drag forces near the free surface. The numerical and linearized drag predictions agree well with the experimental response if a suitable choice of drag coefficient is made. The neglect of drag results in very conservative resonant response predictions for large excitation amplitudes in which the free surface Keulegan-Carpenter number exceeds about 4. Drag forces can generally be neglected, however, in the estimation of response to earthquake motion because displacement amplitudes are small. In extreme cases, small lift forces can result from flow separation about the cylinder near the free surface.

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