تحلیل ارتعاشات اجباری رایزرهای دریایی غیرخطی با روش تحلیلی هموتوپی

In this study, Homotopy analysis method is employed for nonlinear vibrational analysis of marine riser subjected to variable axial loads. Mid-plane stretching effect has been considered in the model. Galerkin's decomposition technique is used to convert the Partial differential equation of the motion to nonlinear ordinary differential equation. Homotopy analysis method (HAM) is applied to find analytical expressions for nonlinear natural frequencies of the riser. Effects of design parameters such as riser’s length and Initial static displacement of upper support on riser frequency are investigated. The analytical expressions are valid for a wide range of vibration amplitudes. Comparing the semi-analytical solutions with numerical results, presented in the literature, indicates proper agreement.