Nonlinear Vertical Vibration of Tension Leg Platforms with Homotopy Analysis Method

Abstract

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 significant 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.

Double‐mode modeling of nonlinear flexural vibration analysis for a symmetric rectangular honeycomb sandwich thin panel by the homotopy analysis method

“…Besides, the HAM provides us a simple way to guarantee the convergence of solution series, the convergence region, and rate of each solution might be determined conveniently by the auxiliary parameter ħ. 21 This method has been successfully applied to solve nonlinear vibration problem 22–24 …”

“…21 This method has been successfully applied to solve nonlinear vibration problem. [22][23][24] In studying the nonlinear vibration analysis of honeycomb sandwich structure, researchers in the past focused mainly on cases in which only one single mode is being strongly excited. However, the fact is that the multimode responses may sometimes possibly lead to instability in certain specific conditions.…”

Nonlinear dynamic characteristics of symmetric rectangular honeycomb sandwich thin panel

“…Besides, the HAM provides us a simple way to guarantee the convergence of solution series, the convergence region, and rate of each solution might be determined conveniently by the auxiliary parameter ħ [21]. This method has been successfully applied to solve nonlinear vibration problem [22–24].…”

Dynamic Analysis of a Tension Leg Platforms (TLPs) Inspired by Parallel Robotic Manipulators

“…Yang et al [9] analyzed random dynamic responses of TLPs under different sea states and different wave approach angles. Reza and Sedighi [10] used the homotopy analysis method to study the dynamic behavior of a tension leg platform. Wang et al [11] investigated the dynamic of a Tension Leg Platform by combining wind and wave loads within the typhoon area.…”