Comparison of linear and nonlinear responses of a compliant tower to random wave forces

A vertical member of a compliant offshore structure is modeled as a beam undergoing both bending and extension. The beam has a point mass and is subjected to a point axial load at the free end. The equations of motion for the axial and transverse displacements are nonlinear and coupled. A linear tension model is derived as a special case of the nonlinear coupled model with negligible axial displacement. The responses are obtained numerically for both models. A quarter of the International Ship and Offshore Structures Congress (ISSC) tension leg platform model is used as a numerical example. The free and forced responses obtained using the nonlinear coupled modeled are compared to those of the linear tension model.