Nonlinear Vertical Vibration of Tension Leg Platforms with Homotopy Analysis Method (Advances in Applied Mathematics and Mechanics, 2018)
One of the useful methods for offshore oil exploration in the deep regions isthe use of tension leg platforms (TLP). The effective mass fluctuating of the structurewhich 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 significant role in their design. Differential equations of motion of such systems are nonlinearand providing a useful method for its analysis is very important. Also, the amount ofadded mass coefficient has a direct effect on the level of nonlinearity of partial differentialequation of these systems. In this study, Homotopy analysis method has beenused for closed form solution of the governing differential equation. Linear springshave 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 thatincreasing of this coefficient decreases the bottom amplitude of fluctuations and thesystem frequency. The obtained results from this method are in good agreement withthe published results on the valid articles.