Second Order Effect Induced by a Forced Heaving

Abstract

Abstract In this paper, the 2 nd order hydrodynamic force effect of heaving submerged circular cylinder is considered, with the linear potential theory. Boundary value problem (BVP) is expanded up to the 2 nd order by using of the perturbation method and the 2 nd order velocity potential is calculated by means of integral equation technique using the classical Green’s function expressed in cylindrical coordinates. The method of solving BVP is based on eigenfunction expansions. With different cylinder heights and heaving frequencies, graphical results are present-ed. As a result of the study, the cause of oscillatory force pattern is analyzed with the occurrence of negative add-ed mass when a top of the cylinder gets closer to the free surface. Keywords: Second order force, Potential theory, Heaving cylinder, Eigen function expansions, Green function, Negative added mass. 1. Introduction When the wave loads on the structure are calculated, velocity potential is calculated through the linearization of the nonlinear free surface boundary condition with a linear potential theory. However, a sudden increase in the demand of the fossil energy has brought an increase in the demand for the offshore structures with a low natural frequency such as Tension leg platforms (TLP) or Gravity base towers. Accordingly, approximated high order solutions using potential theory has been widely studied. 2