Classical and approximate methods in the dynamic response analysis of a truss spar in waves
It is shown that, in the context of a linear theory, all radiation actions of fluid on a floating body can solely be represented by the fluid kinetic and potential energy associated with the wetted surface of the body. In this regard, it is indicated that the linear radiation damping can be expressed by a part of the fluid kinetic energy which has a bilinear form. The linear problem of a floating body motion is then studied in the context of a general linear dynamical system with such form of kinetic energy. From the Lagrange's equations of motion, an equation of motion is derived which generates the linear damping force directly from the bilinear kinetic energy without using any dissipation function. A variant of Hamilton's principle is introduced as the variational generator of this equation of motion. It has been shown that in the context of a linear theory for a floating body with six degrees of freedom each of the 6x6 added mass and damping matrices contains three distinct Cartesian second-order tensors in regard to translational, rotational and interaction between translational and rotational oscillations. As a result of this, a new technique based on the transformation law of second order tensors is introduced for motion analysis of offshore platforms that can be used as an alternative to the common methods of motion analysis in offshore engineering. Consistent with the transformation method, a viscous-radiation-diffraction model is proposed to include viscosity effects in the linear equations of motion derived from a potential radiation-diffraction analysis. This model is developed for both first- and second-order dynamic response analysis of a truss spar platform. The results obtained from this analysis are compared with experi- mental data and the results of more conventional numerical approach. In case of the first-order uncoupled heave, the equation of motion with a nonlinear drag term is solved without any iteration in the frequency domain. For the slowly varying drift motion, the model yields a simple equation of motion which can be solved in the frequency domain easily and with fairly good accuracy. Also in the first-order diffraction problem an approximate theory is proposed for the prediction of surge and pitch loads acting on a truncated vertical cylinder. The results of this theory are compared with the numerical results reported in the literature.