An Investigation of the Non-Linear Transverse Vibrations of Parametrically Excited Vertical Marine Risers and Cables Under Tension

The present paper examines specific aspects of the non-linear dynamics of vertical marine cables and risers. The formulation of the dynamic system accounts for both elastic and bending effects and can satisfactorily describe the dynamic behavior of a riser or a tensioned vertical marine cable. The analysis is restricted in the study of transverse vibrations of the dynamic system under consideration. We first examine the free vibration of the system and consequently the forced transverse vibration due to motions imposed longitudinally. That is, we examine the coupled longitudinal and transverse inducted motions in the 2D reference plane, including damping effects. We first examine the un-damped system and consequently we assess the effects of damping by incorporating the damping terms into the theoretical model. The study is conducted both theoretically and numerically and the resultant theoretical conclusions are evaluated with the corresponding numerical predictions in regards to the dynamic behavior of the system.