Bending-torsion vibration of a partially submerged cylinder with an arbitrary cross-section

An analytical method is presented to investigate the bending-torsion vibration characteristics of a cylinder with an arbitrary cross-section and partially submerged in water. The compressibility and the free surface waves of the water are considered simultaneously in the analysis. The exact solution of structure–water interaction is obtained mathematically. Firstly, the analytical expression of the velocity potential of the water is derived by using the method of separation of variables. The unknown coefficients in the velocity potential are determined by the longitudinal and circumferential Fourier expansions along the outer surface of the cylinder and are expressed in the form of integral equations including the unknown dynamic bending deflection and torsional angle of the cylinder. Secondly, the force and torque acting on the cylinder per unit length, provided by the water, are obtained by integrating the water dynamic pressure along the circumference of the cylinder. The general solution of bending-torsion vibration of the cylinder under the water dynamic pressure is derived analytically. The integral equations included in the velocity potential of the water can be solved exactly. Finally, the eigenfrequency equation of cylinder–water interaction is obtained by means of the boundary conditions of the cylinder. Some numerical examples for elliptical columns partially submerged in water are provided to show the application of the present method.