An approximate method for the surge response of the tension leg platform

The solution for the Duffing equation in a nonlinear vibration problem is studied in this paper. Clearly, in the case of the perturb parameter being a larger value, the traditional perturbation method is no longer valid but the Homotopy Perturbation Method (HPM) is applicable usually. HPM is used to solve the weak and strong nonlinear differential equations for finding the perturbed frequency of the response. The obtained frequencies via HPM and the approximate method have good accordance for weak and strong nonlinear differential equations. Additionally, the calculated responses by use of the approximate method are compared with the responses obtained from the Numerical method in the time history of the response and phase plane. The results represent good accordance between them.