The dynamics of a long flexible horizontal circular cylinder in water waves

Abstract

This thesis examines the dynamics of a long flexible horizontal circular cylinder when immersed in water and exposed to waves. The cylinder exhibits a flexural resonance, dependent on its stiffness, which is stimulated by particular combinations of wave frequency and angle. Linearity is assumed and analysis performed in the frequency domain. Experimental work is based on a 16 metre long 125 millimetre diameter model consisting of 40 segments with motorised joints of controllable stiffness. The bending moment and relative angular velocity are measured at each joint. The model is tested in a three-dimensional wave tank in which multiple wavefronts of specified amplitude, frequency, angle and phase can be generated. The model response to single wavefronts is displayed as an array of plots of bending moment against distance along the cylinder axis. The shape and size of the plots vary strongly with wave frequency and angle, and cylinder stiffness. Two theoretical descriptions are explored. One treats the model as a finite continuous beam, combining beam stiffness with hydrodynamic forces in an equation which is solved analytically. The other is a more exact nodal analysis treating each segment as a rigid body, specifying the forces and moments on it, and solving by a matrix operation for all segments. Both approaches require knowledge of the body hydrodynamics as a function of frequency. This is obtained in a set of experiments using short cylinders in a two-dimensional wave tank. Each experiment measures the wave field, the force on the cylinder and its velocity when the cylinder is driven in the water and acted on by waves. A matrix calculation is performed on the data to extract the wave force coefficient and the radiation impedance in a single operation which eliminates the masking effect of wave reflections in the tank. When these hydrodynamic data are used with the nodal beam theory to predict bending moments in single wavefronts there is good agreement with experiment. The model is then tested in multiple-wavefront sea-states representative of the North Atlantic. The results are compared with calculations for each sea-state made by superposing the theoretical responses of the cylinder to the component wavefronts. The agreement is good enough to allow the use of nodal beam theory as a predictive tool