Dynamic responses of rigs subject to drag forces: exact solution with discontinuous property and loading Alexander N. Papusha 1 ,Tore M. Jonassen 2 , Ove T. Gudmestad 3,4,5 1. Murmansk State Technical University, Murmansk, Russia 2. Oslo University College, Oslo, Norway 3. Statoil, Stavanger, Norway 4. NTNU, Trondheim, Norway 5. University of Stavanger, Stavanger, Norway A l e x a n d e r . P a p u s h a @ m s t u . e d u . r u, t o r e j o @ h i o . n o, o t g @ s t a t o i l . c o m Keywords: Offshore structure, drag forces, waves and currents, linearization, exact solution for drag loading on rigs, dynamics and ringing response. Abstract: The authors developed symbolic solutions for responses of a single degree-of-freedom vibrating model depicting offshore structures subject to drag loading due to waves and currents. Currently, considerable interest in the oil extraction industry motivated only numerical (not analytical) solutions from Fourier expansion of loading and time integration of the governing equation. Mathematica has empowered users to construct the exact nonlinear solution that we document here. The advantage is to capture terms, which are numerically intractable, in the case of discontinuities by selective appropriate value of integration constants of the homogenous solution. The authors present several symbolic and numeric solution details.  Introduction The problem of interaction between offshore rigs and currents of flowing streams in water has been widely studied during last 30 years by well-known specialists on offshore technology. The offshore structure in question is a complicated aggregation. As a first approximation, for the purpose of design-analysis the motion of a rig is conceived as that of a simple harmonic oscillator subjected to drag forces generated by wave and current loading. Such responses have been extensively studied, both theoretically and numerically over the last several years. Linearization of the drag forcing term was discussed by Gudmestad and Connor (1983) and the effects of considering different deterministic wave theories and integrating the total loading up to the free surface were discussed by Gudmestad and Poumbouras (1988). An attempt to extend the analysis of the effects of wave kinematics to irregular Avignon, June 2006 8th International Mathematica Symposium