Biplanar Linearization Of Drag Forces With Application To Riser Analysis

ABSTRACT The hydrodynamic drag forces acting on slender marine structures are of a nonlinear character. For application in frequency domain dynamic analyses the corresponding equilibrium equations are usually linearized. Procedures for stochastic linearization when waves, current and response displacements are coplanar are well established. In this Paper a method is proposed for extension to multiplanar excitation and three-dimensional response. A simplified linearization method is also described and discussed. Example cases of marine riser analysis with biplanar excitation are presented comparing results from these methods with time domain dynamic analysis techniques. The comparisons indicate that the proposed method agrees well for the range of wave/current velocity ratios of practical interest. INTRODUCTION The feasibility of frequency domain approaches for dynamic structural analysis is widely recognized. For design of offshore structures it offers a convenient tool for parameter studies involving a large number of analyses. This is due not only to the modest amount of computer time required, but also to the direct way of assessing the influence of natural frequencies on the response. For slender structural members the hydrodynamic load is expressed by a nonlinear equation due to drag effects. Usually this load term is linearized before application in stochastic frequency domain analysis procedures. A number of different criteria for choice of linearization strategy can obviously be formulated. For the one-dimensional case minimization of the mean square error is commonly adopted as such a criterion1, 2. Extension to the multidimensional case does not seem to be straightforward, and frequently the quadratic velocity component expressions are just linearized independently3, 4, 5, 6, 7. Such a procedure does not yield a frame invariant Method due to neglection of component coupling terms. In this paper the minimum mean square error (MMSE) method is described, and a restricted MMSE method with diagonal linearization matrices is proposed. The accuracy as compared to time domain analysis results is studied and comparison with the independent decomposition method is also made. DRAG FORCE AND INVARIANCE PROPERTIES The hydrodynamic force acting on a slender Vertical cylinder element of unit length and Diameter D is assumed to be expressed by a Generalization of the Morison's equation8,9:(Mathematical equation available in full paper) where CA and CD are inertia and drag coefficients which are independent of her, flow direction:w is the water density [x] denotes the modulus of x; A is the cross-section area; Un = [Ux, UY]T is the current velocity vector normal to the element axis with components Ux and Uy in the global x- and y-direction respectively.