In this study a new two degrees-of-freedom wake oscillator model is proposed to describe vortex-induced vibrations of elastically supported cylinders capable of moving in cross-flow and in-line directions. Total hydrodynamic force acting on the cylinder is obtained here as a sum of lift and drag forces, which are defined as being proportional to the square of the magnitude of the relative flow velocity around the cylinder. The two van der Pol type oscillators are then used to model fluctuating drag and lift coefficients. As the relative velocity around the cylinder depends both on the fluid flow velocity and the velocity of the cylinder, the equations of motions of the cylinder in cross-flow and in-line directions become coupled through the fluid forces. It is shown that such approximation of the fluid forces allows to obtain the well known low dimensional models in the limit case, and the model proposed by Facchinetti et al.  to describe the cross-flow vibrations is used as an example. Experimental data and Computational Fluid Dynamics (CFD) results are used to calibrate the proposed model and to verify the obtained predictions of complex fluid-structure interactions for different mass ratios. A number of phenomena such as the ”super-upper” branch, exclusive for a two degrees-of-freedom motion at low mass ratios, are observed. Influence of the empirical parameters of the wake oscillators equations and fluid forces coefficients on the response is also discussed.
This work is supported by the National Subsea Research Institute (NSRI) UK.