One of the useful methods for offshore oil exploration in the deep regions is
the use of tension leg platforms (TLP). The effective mass fluctuating of the structure
which due to its vibration can be noted as one of the important issues about these platforms.
With this description, dynamic analysis of these structures will play a signifi-
cant role in their design. Differential equations of motion of such systems are nonlinear
and providing a useful method for its analysis is very important. Also, the amount of
added mass coefficient has a direct effect on the level of nonlinearity of partial differential
equation of these systems. In this study, Homotopy analysis method has been
used for closed form solution of the governing differential equation. Linear springs
have been used for modeling the stiffness of this system and the effects of torsion,
bending and damping of water have been ignored. In the study of obtained results,
the effect of added mass coefficient has been investigated. The results show that
increasing of this coefficient decreases the bottom amplitude of fluctuations and the
system frequency. The obtained results from this method are in good agreement with
the published results on the valid articles.