Characterization of variable hydrodynamic coefficients and maximum responses in two-dimensional vortex-induced vibrations with dual resonances

A phenomenological model and analytical-numerical approach to systematically characterize variable hydrodynamic coefficients and maximum achievable responses in two-dimensional vortex-induced vibrations with dual two-to-one resonances are presented. The model is based on double Duffing and van der Pol oscillators which simulate a flexibly-mounted circular cylinder subjected to uniform flow and oscillating in simultaneous cross-flow/in-line directions. Depending on system quadratic and cubic nonlinearities, amplitudes, oscillation frequencies and phase relationships, analytical closed-form expressions are derived to parametrically evaluate key hydrodynamic coefficients governing the fluid excitation, inertia and added mass force components, as well as maximum dual-resonant responses. The amplification of the mean drag is ascertained. Qualitative validations of numerical predictions with experimental comparisons are discussed. Parametric investigations are performed to highlight the important effects of system nonlinearities, mass, damping and natural frequency ratios.