Parametric excitation of an immersed, vertical and slender beam using reduced-order models: influence of hydrodynamic coefficients

The paper addresses the effects of hydrodynamic parameters in the post-critical transversal vibration of an immersed, vertical, slender, extensible and flexible cylinder subjected to parametric excitation due to harmonic vertical displacements imposed at the upper extremity. The main objective of this research paper is to numerically investigate the influence of two hydrodynamic parameters, namely added mass and mean drag coefficients on the post-critical transversal oscillation amplitude. A single degree-of-freedom nonlinear reduced-order model is derived from the continuum beam equation of motion and numerically integrated using a Runge–Kutta scheme. Considering different values of added mass and mean drag coefficients, maps of post-critical amplitude are presented as functions of the amplitude and frequency of the parametric excitation. The results obtained are expected to be of importance to offshore engineering, particularly to riser and tether dynamics, since standard analysis approaches usually assume both hydrodynamic coefficients to be constant ab initio , no matter their values might vary significantly according to distinct design conditions.