Analysis Of Nonlinear Dynamic Behavior Of An Offshore Compliant Structure

Offshore structures are used in the oil industry as exploratory, production, storage and landing facilities. In recent years, they have also been used in the ocean engineering field, such as basic structures of offshore wind turbines. In general, there are two types of offshore structures: fixed and compliant ones. For deep-sea oil and gas exploitation, compliant structures, such as tension leg platforms (TLPs) and articulated towers, are appropriate. The compliant structures in an ocean environment will show remarkable horizontal motion and geometric nonlinearity. Therefore, it is necessary to take compliant structures as elastic-plastic ones and employ continuum mechanics model to study the dynamic behavior of the compliant structures under typical environmental loads. The results are helpful in building a theoretical foundation for the design of offshore compliant structures.In this paper, the tendon of a tension leg platform, the shaft of an articulated tower or the main body of an offshore wind turbine is modeled as a flexible beam submerged into water partially or fully. The beam is subjected to a point axial load and has a lumped mass without rotary inertia at the top and is supported by a linear-elastic torsinal spring at the base. It is assumed that the beam can undergo axial extension and transversal bending. Under the assumpation of large deflection and accurate rotation angle and by the method of continuum mechanics, the dynamic responses of a beam for nonlinear free and forced vibrtations are investigated theoretically and numerically. In particular, the influence of interaction between the flexible beam in water and the linear or nonlinear waves on the nonlinear dynamic behavior of the beam is examined.First, under hypothesis of beam's large deflection and accurate rotation angle and considering its axial extension and transversal bending, the nonlinear governing equations of motion and boundary conditions of an elastic beam submerged into water partially or fully are derived, then, the nonlinear model based on approximate rotation angle and the linear one are also given. The fluid forces are modeled by a semi-empirical Morison equation, and wave velocities and accelerations of the definite and stochastic wave are presented. Second, finite difference approach in space domain and Runge-Kutta method in time domain are employed to solve the nonlinear governing equations, and the difference scheme is presented. Third, nonlinear free vibrations of the beam in vacuum and in water with and without damping are analyzed. The influences of initial conditions on free vibrations are discussed. The results of the nonlinear beam based on large deflection model, the nonlinear beam with approximate angle and the linear beam are compared. Fourth, forced vibrations of the beam based on Airy linear wave theory and second-order Stokes wave theory are studied. The results based on two wave theories are compared, and the influence of nonlinearity of the second-order Stokes wave on the vibrations is discussed. The dynamic characteristics of the beam with zero initial condition, such as principal resonance and ultraharmonic resonance, are analyzed for two varying wave heights and different excited frequencies. The results from three models are compared too. Finally, forced vibrations under random Airy linear wave theory are investigated. The wave height follows the Pierson-Moskowitz spectrum, and Borgman's method is adopted to obtain the wave height from the Pierson-Moskowitz spectrum. The dynamic responses of two kinds of beam structures from the lab and the typical TLP are analyzed numerically for different significant wave heights. The response characteristics of the beam under zero initial condition and nonzero initial condition are investigated. The forced responses obtained with three models are compared.