Coupled transverse and axial vibration of a compliant tower: Comparison of linear and nonlinear models

A vertical member osf 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 zero axial displacement. The responses are obtained numerically for the nonlinear coupled model and analytically for the linear transverse model. A quarter of the International Ship and Offshore Structures Congress (ISSC) tension leg platform model is used as a numerical example. The free responses obtained using the nonlinear coupled modeled are compared to those of the linear tension model. Two sets of initial conditions are used. The first initial displacements are set such that the transverse displacement is considerably larger than the axial displacement. The second initial displacements are set such that the transverse and axial displacements are comparable. It is found that the linear tension model can predict the transverse motion, the average normal strain, the kinetic energies and the binding energy very well in both cases. It is concluded that the linear tension model can still be used even when the axial motion is no longer negligible.