This paper describes a study on the application of analytical methods for evaluating the response of Steel Catenary Risers (SCR) subjected to dynamic loading. In the first part of the paper, equations of equilibrium are derived using a linear theory, based on the assumption of small displacements, near the reference catenary configuration. These equations are obtained for in-plane and out-of plane displacements. Simplifications of these equations are then presented and lead to the determination of eigenmodes and eigenfrequencies for both in and outof- plane modes. A comprehensive comparison for high and low frequencies of in and out-of-plane vibrations is then performed. Finally, comparisons are given with numerical results obtained by the Finite Element code DeepLines. The comparisons show good agreement for both directions frequencies and modes, for a wide domain of frequencies.
A, B geometrical quantities referring to the catenary d horizontal extension of the SCR D pipe external diameter ex, ey, ez unit vectors ES axial stiffness G vector of forces H horizontal component of the SCR axial force k catenary parameter m riser line-weight mfi internal fluid line-weight ma external fluid added mass mx, my, mz added mass according to movement direction q mode frequency number s, s' abscissas in the reference and current configurations t, t' tangent vectors in the reference and current configurations T tension u, v, w displacements from the reference configuration x, y, z positions in the reference configuration xTDP, yTDP positions of the Touch Down point x(non-dimensional abscissa ω mode pulsation ρ water density τ, τrw increment of effective and total tension
Risers are a key component for the development of offshore fields, and are subjected to the combined actions of floating support motions, waves and current.